From 8f7153eb3867048ab90d35cbc075071bced993f0 Mon Sep 17 00:00:00 2001
From: Patrick Simianer <p@simianer.de>
Date: Sat, 22 May 2010 01:13:22 +0200
Subject: almost done

---
 javascripts/Graph.js               |   60 -
 javascripts/Nfa.js                 |   50 +-
 javascripts/Nfa2Dfa.js             |  101 +-
 javascripts/NfaSimulator.js        |   54 +-
 javascripts/NfaState.js            |   12 +-
 javascripts/RegexParser.js         |   76 +-
 javascripts/Stack.js               |   39 +-
 javascripts/globals.js             |    6 +
 javascripts/graph.js               |  213 ++
 javascripts/lib/graffle.js         |  158 -
 javascripts/lib/jquery-ui.js       |  207 ++
 javascripts/lib/jquery.js          |  154 +
 javascripts/lib/raphael.js         |   18 +
 javascripts/main.js                |   28 -
 javascripts/uifunc.js              |   61 +
 presentation/simianer-regexvis.bib |    7 +
 presentation/simianer-regexvis.tex |  170 +
 regexvis.html                      |   73 +-
 resources/RENFADFA.doc             |  Bin 131072 -> 0 bytes
 resources/RegExSource.zip          |  Bin 8691 -> 0 bytes
 resources/fsmnlp.ps                | 6674 ------------------------------------
 resources/graphregexpr.jar         |  Bin 54806 -> 0 bytes
 resources/literature/RENFADFA.doc  |  Bin 0 -> 131072 bytes
 resources/literature/fsmnlp.ps     | 6674 ++++++++++++++++++++++++++++++++++++
 resources/regexprdemo.jar          |  Bin 36642 -> 0 bytes
 resources/sources/RegExSource.zip  |  Bin 0 -> 8691 bytes
 resources/sources/graphregexpr.jar |  Bin 0 -> 54806 bytes
 resources/sources/regexprdemo.jar  |  Bin 0 -> 36642 bytes
 stylesheets/RegexVis.css           |    0
 stylesheets/styles.css             |   42 +
 30 files changed, 7782 insertions(+), 7095 deletions(-)
 delete mode 100644 javascripts/Graph.js
 create mode 100644 javascripts/globals.js
 create mode 100644 javascripts/graph.js
 delete mode 100644 javascripts/lib/graffle.js
 create mode 100755 javascripts/lib/jquery-ui.js
 create mode 100644 javascripts/lib/jquery.js
 delete mode 100644 javascripts/main.js
 create mode 100644 javascripts/uifunc.js
 create mode 100644 presentation/simianer-regexvis.bib
 create mode 100644 presentation/simianer-regexvis.tex
 delete mode 100644 resources/RENFADFA.doc
 delete mode 100644 resources/RegExSource.zip
 delete mode 100644 resources/fsmnlp.ps
 delete mode 100644 resources/graphregexpr.jar
 create mode 100644 resources/literature/RENFADFA.doc
 create mode 100644 resources/literature/fsmnlp.ps
 delete mode 100644 resources/regexprdemo.jar
 create mode 100644 resources/sources/RegExSource.zip
 create mode 100644 resources/sources/graphregexpr.jar
 create mode 100644 resources/sources/regexprdemo.jar
 delete mode 100644 stylesheets/RegexVis.css
 create mode 100644 stylesheets/styles.css

diff --git a/javascripts/Graph.js b/javascripts/Graph.js
deleted file mode 100644
index c2f350d..0000000
--- a/javascripts/Graph.js
+++ /dev/null
@@ -1,60 +0,0 @@
-//alert(ttable)
-
-Object.size = function(obj) {
-    var size = 0, key;
-    for (key in obj) {
-        if (obj.hasOwnProperty(key)) size++;
-    }
-    return size;
-};
-
-
-
-function drawGraph() {
-	document.write('<pre>')
-	for (var state in ttable) {
-		document.write(state+' --><br />')
-		for (var i=0; i < ALPHABET.length; i++) {
-			if(ttable[state][ALPHABET[i]]) {
-				document.write('\t'+ALPHABET[i]+': ')
-				document.write(ttable[state][ALPHABET[i]]+'<br />');	
-			}
-		}
-	}
-	document.write('</pre>');
-	
-	
-	
-	var dragger = function () {
-        this.ox = this.type == "rect" ? this.attr("x") : this.attr("cx");
-        this.oy = this.type == "rect" ? this.attr("y") : this.attr("cy");
-        this.animate({"fill-opacity": .2}, 500);
-    },
-        move = function (dx, dy) {
-            var att = this.type == "rect" ? {x: this.ox + dx, y: this.oy + dy} : {cx: this.ox + dx, cy: this.oy + dy};
-            this.attr(att);
-            for (var i = connections.length; i--;) {
-                r.connection(connections[i]);
-            }
-            r.safari();
-        },
-        up = function () {
-            this.animate({"fill-opacity": 0}, 500);
-        },
-        r = Raphael("holder", 640, 480),
-        connections = [],
-        shapes = [  r.ellipse(190, 100, 30, 20),
-                    r.rect(290, 80, 60, 40, 10),
-                    r.rect(290, 180, 60, 40, 2),
-                    r.ellipse(450, 100, 20, 20)
-                ];
-    for (var i = 0, ii = shapes.length; i < ii; i++) {
-        var color = Raphael.getColor();
-        shapes[i].attr({fill: color, stroke: color, "fill-opacity": 0, "stroke-width": 2, cursor: "move"});
-        shapes[i].drag(move, dragger, up);
-    }
-    connections.push(r.connection(shapes[0], shapes[1], "#000"));
-    connections.push(r.connection(shapes[1], shapes[2], "#000", "#ccc"));
-    connections.push(r.connection(shapes[1], shapes[3], "#000", "#ccc"));
-}
-
diff --git a/javascripts/Nfa.js b/javascripts/Nfa.js
index 12ffe23..2edc4b7 100644
--- a/javascripts/Nfa.js
+++ b/javascripts/Nfa.js
@@ -3,28 +3,31 @@
  *
  */
 function Nfa(symbol) {
-	this.startState     = null;
-	this.acceptingState = null;
+	this.startState = null;
+	this.finalState = null;
 	
     if (symbol) {
         this.setStartState(new NfaState(symbol));
-        this.setAcceptingState(new NfaState(false));
-        this.getStartState().setFollowUp(0, this.getAcceptingState());
-    }
-}
-
-Nfa.prototype.getStartState     = function() { return this.startState }
-Nfa.prototype.setStartState     = function(s) { this.startState = s }
-Nfa.prototype.getAcceptingState = function() { return this.acceptingState }
-Nfa.prototype.setAcceptingState = function(s) { this.acceptingState = s }
-
+        this.setFinalState(new NfaState(false));
+        this.getStartState().setFollowUp(0, this.getFinalState());
+    };
+};
+
+// 
+Nfa.prototype.getStartState = function()  { return this.startState; };
+Nfa.prototype.setStartState = function(s) { this.startState = s; };
+Nfa.prototype.getFinalState = function()  { return this.finalState; };
+Nfa.prototype.setFinalState = function(s) { this.finalState = s; };
+
+// 
 Nfa.prototype.concat = function(nfa) {
-    this.getAcceptingState().setFollowUp(0, nfa.getStartState());
-    this.setAcceptingState(nfa.getAcceptingState());
+    this.getFinalState().setFollowUp(0, nfa.getStartState());
+    this.setFinalState(nfa.getFinalState());
     
 	return this;
-}
+};
 
+// 
 Nfa.prototype.union = function(nfa) {
     var s = new NfaState();
     var t = new NfaState();
@@ -32,15 +35,16 @@ Nfa.prototype.union = function(nfa) {
     s.setFollowUp(0, this.getStartState());
     s.setFollowUp(1, nfa.getStartState());
     
-    this.getAcceptingState().setFollowUp(0, t);
-    nfa.getAcceptingState().setFollowUp(0, t);
+    this.getFinalState().setFollowUp(0, t);
+    nfa.getFinalState().setFollowUp(0, t);
     
     this.setStartState(s);
-    this.setAcceptingState(t);
+    this.setFinalState(t);
 
 	return this;
-}
+};
 
+// 
 Nfa.prototype.kleene = function() {
     var s = new NfaState();
     var t = new NfaState();
@@ -48,11 +52,11 @@ Nfa.prototype.kleene = function() {
     s.setFollowUp(0, this.getStartState());
     s.setFollowUp(1, t);
 
-    this.getAcceptingState().setFollowUp(0, this.getStartState());
-    this.getAcceptingState().setFollowUp(1, t);
+    this.getFinalState().setFollowUp(0, this.getStartState());
+    this.getFinalState().setFollowUp(1, t);
 
     this.setStartState(s);
-    this.setAcceptingState(t);
+    this.setFinalState(t);
 
     return this;
-}
+};
diff --git a/javascripts/Nfa2Dfa.js b/javascripts/Nfa2Dfa.js
index cbdd766..0e889f8 100644
--- a/javascripts/Nfa2Dfa.js
+++ b/javascripts/Nfa2Dfa.js
@@ -2,31 +2,37 @@
  * Nfa2Dfa
  *
  */
+
+// 
 function StateCmp(a, b) {
 	if (a.id == b.id) {
 		return true
-	}
+	};
 	return false
-}
+};
 
+// 
 function NfaStackCmp(x, y) {
 	var ret = true;
 	if (x.length != y.length) { return false }
 	for (var i=0; i < x.length; i++) {
 		ret = ret && StateCmp(x.get(i), y.get(i));
-	}
+	};
 	return ret;
-}
+};
 
+// 
 function Nfa2Dfa(nfa) {
-	this.startState     = nfa.getStartState();
-    this.acceptingState = nfa.getAcceptingState();
+	this.startState = nfa.getStartState();
+    this.finalState = nfa.getFinalState();
 }
 
-Nfa2Dfa.prototype.getStartState = function() { return this.startState }
-Nfa2Dfa.prototype.getAcceptingState = function() { return this.acceptingState }
+// 
+Nfa2Dfa.prototype.getStartState = function() { return this.startState; };
+Nfa2Dfa.prototype.getFinalState = function() { return this.finalState; };
 
-ttable = new Object();
+// 
+var ttable = new Object();
 Nfa2Dfa.prototype.do = function() {
 	var dfaStates = new Stack();
 	var q = new Stack();
@@ -34,12 +40,8 @@ Nfa2Dfa.prototype.do = function() {
 	var p = this.epsclosure(q)
 	var q = p.copy();
 	dfaStates.push(p);
-	document.write('S '+p.str()+'<br />');
-	
-	var done = new Array();
-	
-	//var ttable = new Object();
-	
+	//document.write('S '+p.str()+'<br />');
+	var done = new Array();	
 	var ds = null;
 	var j = 0;
 	while (!dfaStates.isEmpty()) {
@@ -56,39 +58,37 @@ Nfa2Dfa.prototype.do = function() {
 				if(NfaStackCmp(done[w], x)) {
 					adone = true;
 					break;
-				}
-			}
+				};
+			};
 			
 			var q = ds.str().replace(/ /g, '_');
 			var qq = x.str().replace(/ /g, '_');
 			
 			if (!ttable[q]) {
 				ttable[q] = new Object();
-				if(q.split('_').indexOf(''+this.getAcceptingState().id) >= 0) {
+				if(q.split('_').indexOf(''+this.getFinalState().id) >= 0) {
 					ttable[q].isFinal = true;
 				} else {
 					ttable[q].isFinal = false;
-				}	
-			}
-			
-			
+				};
+			};
 			
 			ttable[q][a] = qq;
 			
 			if (x.length > 0 && !adone) {
 				for (var h=0; h < j; h++) {
-					document.write("\t");
-				}
-				
-				document.write(a+' '+x.str()+'<br />');
+					//document.write("\t");
+				};
+				//document.write(a+' '+x.str()+'<br />');
 				dfaStates.push(x);
-			}
-	    }
+			};
+	    };
 		done.push(ds);
 		j++;
-	}
-}
+	};
+};
 
+// 
 Nfa2Dfa.prototype.epsclosure = function(q) {
     var s = null;
     var t = null;
@@ -104,17 +104,16 @@ Nfa2Dfa.prototype.epsclosure = function(q) {
                 t = s.getFollowUp(i);
                 if (t!=null) {
  					q.push(t);
-                }
-            }
-        }
-    }
+                };
+            };
+        };
+    };
 	return p;
-}
-
+};
 
+// 
 Nfa2Dfa.prototype.move = function(str, p) {
 	var s = null;
-	
 	var q = new Stack();
 
     while(!p.isEmpty()) {
@@ -123,29 +122,7 @@ Nfa2Dfa.prototype.move = function(str, p) {
         if (s.symbol == str) {
             s.getFollowUp(0).mark(true);
             q.push(s.getFollowUp(0));
-        }
-    }
+        };
+    };
 	return q;
-}
-
-
-/*
- * DfaStates
- *
- */
-function DfaState(nfaStates) {
-	this.nfaStates = nfaStates;
-	this.marked = false;
-}
-
-DfaState.prototype.compare = function(b) {
-	
-}
-
-DfaState.prototype.str = function() {
-	res = '';
-	for (var i=0; i < this.nfaStates.length; i++) {
-		res += this.nfaStates[i].id + ' '
-	}
-	return res
-}
\ No newline at end of file
+};
diff --git a/javascripts/NfaSimulator.js b/javascripts/NfaSimulator.js
index b7a4473..0c29914 100644
--- a/javascripts/NfaSimulator.js
+++ b/javascripts/NfaSimulator.js
@@ -3,38 +3,37 @@
  *
  */
 function NfaSimulator(nfa) {
-	this.startState     = nfa.getStartState();
-    this.acceptingState = nfa.getAcceptingState();
-}
+	this.startState = nfa.getStartState();
+    this.finalState = nfa.getFinalState();
+};
 
-NfaSimulator.prototype.getStartState = function() { return this.startState }
-NfaSimulator.prototype.getAcceptingState = function() { return this.acceptingState }
+NfaSimulator.prototype.getStartState = function() { return this.startState; };
+NfaSimulator.prototype.getFinalState = function() { return this.finalState; };
 
+// 
 NfaSimulator.prototype.simulate = function(word) {
-	var a = '';
-	var accepted = false;
+	var a, accepted = false;
     this.p = new Stack();
     this.q = new Stack();
     this.getStartState().mark(true);
     this.q.push(this.getStartState());
-    word += REDELIMITER;
-    for (var i = 0; i < word.length; i++) {	
+    word += REDELIMITER;  
+	for (var i = 0; i < word.length; i++) {	
         accepted = this.epsclosure();
 		a = word.substring(i, i+1);
 		this.move(a);
-    }
+    };
     return accepted;
-}
+};
 
+// 
 NfaSimulator.prototype.epsclosure = function() {
-    var s = null;
-    var t = null;
-	var accepted = false;
+    var s, t, accepted = false;
 
     while(!this.q.isEmpty()) {
         s = this.q.pop();
         this.p.push(s);
-        accepted = accepted || s == this.getAcceptingState();
+        accepted = accepted || s == this.getFinalState();
 
         if(s.symbol == EPSILON) {
             for (var i = 0; i < 2; i++) {
@@ -43,23 +42,24 @@ NfaSimulator.prototype.epsclosure = function() {
                     if(!t.marked) {
                         t.mark(true);
                         this.q.push(t);
-                    }
-                }
-            }
-        }
-    }
+                    };
+                };
+            };
+        };
+    };
     return accepted;
-}
+};
 
-NfaSimulator.prototype.move = function(str) {
-    var s = null;
+// 
+NfaSimulator.prototype.move = function(symbol) {
+    var s;
 
     while(!this.p.isEmpty()) {
         s = this.p.pop();
         s.mark(false);
-        if (s.symbol == str) {
+        if (s.symbol == symbol) {
             s.getFollowUp(0).mark(true);
             this.q.push(s.getFollowUp(0));
-        }
-    }
-}
+        };
+    };
+};
diff --git a/javascripts/NfaState.js b/javascripts/NfaState.js
index 6e7a413..2de256d 100644
--- a/javascripts/NfaState.js
+++ b/javascripts/NfaState.js
@@ -7,15 +7,15 @@ function NfaState(symbol) {
         this.symbol = EPSILON;
     } else {
 		this.symbol = symbol;
-	}
+	};
     this.followUps = [];
     this.marked    = false;
 	this.id		   = NEXTSTATE++;
-}
+};
 
-NfaState.prototype.mark = function(bool) { this.marked = bool }
-NfaState.prototype.getFollowUp = function(index) { return this.followUps[index] }
+NfaState.prototype.mark = function(bool) { this.marked = bool; };
+NfaState.prototype.getFollowUp = function(index) { return this.followUps[index]; };
 NfaState.prototype.setFollowUp = function(index, state) {
-    if (!((index == 0) || (index==1)) ) return;
+    if (! ((index == 0) || (index==1)) ) return;
     this.followUps[index] = state;
-}
+};
diff --git a/javascripts/RegexParser.js b/javascripts/RegexParser.js
index 1f04c50..3abe426 100644
--- a/javascripts/RegexParser.js
+++ b/javascripts/RegexParser.js
@@ -2,109 +2,123 @@
  * RegexParser
  *
  */
-function RegexParser() {}
+function RegexParser() {};
 
-RegexParser.prototype.getRegex = function() { return this.regex }
-RegexParser.prototype.getErrorMessage = function() { return this.errorMessage }
-RegexParser.prototype.getErrorPosition = function() { return this.errorPosition }
+RegexParser.prototype.getRegex = function() { return this.regex; };
+RegexParser.prototype.getErrorMessage = function() { return this.errorMessage; };
+RegexParser.prototype.getErrorPosition = function() { return this.errorPosition; };
 
+// 
 RegexParser.prototype.lookahead = function() {
     if (this.str.length > 0) {
         return this.str.substring(0, 1);
-    }
+    };
     return '';
-}
+};
 
+// 
 RegexParser.prototype.consume = function(symbol) {
     this.str = this.str.substring(1);
-}
+};
 
+// 
 RegexParser.prototype.trymatch = function(symbol) {
     if (this.str.substring(0, symbol.length) == symbol) {
         this.consume(symbol);
         return true;
-    }
+    };
     return false;
-}
+};
 
+// 
 RegexParser.prototype.match = function(symbol) {
     if (!this.trymatch(symbol)) {
-        throw("Expected symbol '"+symbol+"'.");
-    }
-}
+        throw("RegexParser.match(): Expected symbol '"+symbol+"'.");
+    };
+};
 
+// 
 RegexParser.prototype.isIn = function(symbol, set) {
 	if (symbol.length > 0) {
 		return set.indexOf(symbol) >= 0;
-	}
+	};
 	return false;
-}
+};
 
+// 
 RegexParser.prototype.isLetter = function(symbol) {
     return this.isIn(symbol, ALPHABET);
-}
+};
 
+// 
 RegexParser.prototype.literal = function() {
     var symbol = this.lookahead();
     if(this.isLetter(symbol)) {
         this.consume(symbol);
         return new Nfa(symbol);
-    }
-    throw("Expected a letter or '"+EMPTYSYMBOL+"'."); 
-}
+    };
+    throw("RegexParser.literal(): Expected a letter or '"+EMPTYSYMBOL+"'."); 
+};
 
+// 
 RegexParser.prototype.atom = function() {
     if(this.trymatch('(')) {
         var nfa = this.expr();
         this.match(')');
         return nfa;
-    }
+    };
     return this.literal();
-}
+};
 
+// 
 RegexParser.prototype.factor = function() {
     return this.star(this.atom());
-}
+};
 
+// 
 RegexParser.prototype.star = function(nfa) {
     if (this.trymatch('*')) {
         return this.star(nfa.kleene());
-    }
+    };
     return nfa;
-}
+};
 
+// 
 RegexParser.prototype.term = function() {
     var nfa = this.factor();
     var symbol = this.lookahead();
     if (this.isLetter(symbol) || (symbol == '(')) {
         return nfa.concat(this.term());
-    }
+    };
     return nfa;
-}
+};
 
+// 
 RegexParser.prototype.expr = function() {
 	var nfa = this.term();
     if (this.trymatch('|')) {
         return nfa.union(this.expr());
-    }
+    };
     return nfa;
-}
+};
 
+// 
+var nfa;
 RegexParser.prototype.parse = function(regex) {
     this.str = regex;
     this.errorMessage  = 'Ok'
     this.errorPosition = -1;
-    var nfa = null;
+    var nfa;
 
     try {
         nfa = this.expr();
         if(this.str.length > 0) {
-            throw('Supernumerous symbols.');
-        }
+            throw('RegexParser.parse(): Supernumerous symbols.');
+        };
     } catch(e) {
         this.errorMessage = e;
 		this.errorPosition = regex.length - this.str.length;        
         nfa = null;
-    }
+    };
     return nfa;
 }
diff --git a/javascripts/Stack.js b/javascripts/Stack.js
index 808dea9..c4e2db9 100644
--- a/javascripts/Stack.js
+++ b/javascripts/Stack.js
@@ -3,46 +3,53 @@
  *
  */
 function Stack() {
-	this.a = new Array();
+	this.a 		= new Array();
 	this.length = 0;
-}
+};
 
+// 
 Stack.prototype.push = function(obj) {
 	this.a.push(obj);
 	this.length++;
-}
+};
 
+// 
 Stack.prototype.pop = function() {
 	if (this.isEmpty()) {
-		throw('Pop from empty stack.');
-	}
+		throw('Stack.pop(): Pop from empty stack.');
+	};
 	this.length--;
 	return this.a.pop();
-}
+};
 
+// 
 Stack.prototype.isEmpty = function() {
 	if (this.length == 0) {
 		return true;
-	}
+	};
 	return false;
-}
+};
 
+// 
 Stack.prototype.get = function(index) {
 	return this.a[index];
-}
+};
 
+// 
 Stack.prototype.copy = function() {
 	var c = ((new Array()).concat(this.a));
 	var ret = new Stack();
 	ret.a = c;
 	ret.length = this.length;
 	return ret;
-}
+};
 
-Stack.prototype.str = function() {
-	ret = '';
+// 
+Stack.prototype.str = function(separator) {
+	if (!separator) { separator=' ' };
+	var a = new Array();
 	for (var i=0; i < this.length; i++) {
-		ret += this.a[i].id + ' ';
-	}
-	return ret;
-}
+		a.push(this.a[i].id);
+	};
+	return a.join(separator);
+};
diff --git a/javascripts/globals.js b/javascripts/globals.js
new file mode 100644
index 0000000..88d5b2a
--- /dev/null
+++ b/javascripts/globals.js
@@ -0,0 +1,6 @@
+// globals
+var EPSILON     = '~';
+var NEXTSTATE   = 0;
+var EMPTYSYMBOL = '%';
+var ALPHABET    = 'abc'+EMPTYSYMBOL;
+var REDELIMITER = '$';
diff --git a/javascripts/graph.js b/javascripts/graph.js
new file mode 100644
index 0000000..9e1c6b5
--- /dev/null
+++ b/javascripts/graph.js
@@ -0,0 +1,213 @@
+// spurce: http://raphaeljs.com/graffle.html
+Raphael.fn.connection = function (obj1, obj2, line, bg, strokeColor) {	
+    if (obj1.line && obj1.from && obj1.to) {
+        line = obj1;
+        obj1 = line.from;
+        obj2 = line.to;
+    };
+    var bb1 = obj1.getBBox(),
+        bb2 = obj2.getBBox(),
+        p = [{x: bb1.x + bb1.width / 2, y: bb1.y - 1},
+        {x: bb1.x + bb1.width / 2, y: bb1.y + bb1.height + 1},
+        {x: bb1.x - 1, y: bb1.y + bb1.height / 2},
+        {x: bb1.x + bb1.width + 1, y: bb1.y + bb1.height / 2},
+        {x: bb2.x + bb2.width / 2, y: bb2.y - 1},
+        {x: bb2.x + bb2.width / 2, y: bb2.y + bb2.height + 1},
+        {x: bb2.x - 1, y: bb2.y + bb2.height / 2},
+        {x: bb2.x + bb2.width + 1, y: bb2.y + bb2.height / 2}],
+        d = {}, dis = [];
+    for (var i = 0; i < 4; i++) {
+        for (var j = 4; j < 8; j++) {
+            var dx = Math.abs(p[i].x - p[j].x),
+                dy = Math.abs(p[i].y - p[j].y);
+            if ((i == j - 4) || (((i != 3 && j != 6) || p[i].x < p[j].x) && ((i != 2 && j != 7) || p[i].x > p[j].x) && ((i != 0 && j != 5) || p[i].y > p[j].y) && ((i != 1 && j != 4) || p[i].y < p[j].y))) {
+                dis.push(dx + dy);
+                d[dis[dis.length - 1]] = [i, j];
+            };
+        };
+    };
+    if (dis.length == 0) {
+        var res = [0, 4];
+    } else {
+        res = d[Math.min.apply(Math, dis)];
+    };
+    var x1 = p[res[0]].x,
+        y1 = p[res[0]].y,
+        x4 = p[res[1]].x,
+        y4 = p[res[1]].y;
+    dx = Math.max(Math.abs(x1 - x4) / 2, 10);
+    dy = Math.max(Math.abs(y1 - y4) / 2, 10);
+    var x2 = [x1, x1, x1 - dx, x1 + dx][res[0]].toFixed(3),
+        y2 = [y1 - dy, y1 + dy, y1, y1][res[0]].toFixed(3),
+        x3 = [0, 0, 0, 0, x4, x4, x4 - dx, x4 + dx][res[1]].toFixed(3),
+        y3 = [0, 0, 0, 0, y1 + dy, y1 - dy, y4, y4][res[1]].toFixed(3);
+    var path = ["M", x1.toFixed(3), y1.toFixed(3),
+				"C", x2, y2, x3, y3, x4.toFixed(3), y4.toFixed(3)].join(",");
+	
+	if (line && line.line) {
+        line.bg && line.bg.attr({path: path});
+        line.line.attr({path: path});
+    } else {
+        var color = typeof line == "string" ? line : strokeColor;
+        return {
+            bg: bg && bg.split && this.path(path
+				).attr({stroke: bg.split("|")[0],
+						fill: "none", "stroke-width": bg.split("|")[1] || 3}),
+            line: this.path(path).attr({stroke: color, fill: "none"}),
+            from: obj1,
+			to: obj2
+        };
+    };
+};
+// source: http://stackoverflow.com/questions/2627436/svg-animation-along-path-with-raphael
+Raphael.fn.circlePath = function(x , y, r) {      
+	return "M"+x+","+(y-r)+"A"+r+","+r+",0,1,1,"+(x-0.1)+","+(y-r)+" z";
+};
+// nodes
+Raphael.fn.aNode = function(x, y, r, isFinal, hasSelfConn,
+			strokeWidth, strokeColor,labelText, labelFontSize) {
+	var res = this.set();
+	// two circle element for dragging and binding connections
+	var connector = this.circle(x, y, r).attr({stroke:0}).attr({fill: 'none'});
+	res.push(connector);
+	var dragger = this.circle(x, y, r).attr({stroke:0}).attr({fill: 'none'});
+	res.push(dragger);
+	// outer circle
+	var co = this.path(this.circlePath(x, y, r)).attr({stroke:'none'});
+	res.push(co);
+	if (isFinal) {
+		// inner circle
+		var ci = this.path(this.circlePath(x, y, r/1.2)).attr({
+					stroke:'#fff', 'stroke-width':strokeWidth});
+	};
+	// self connection
+	if (hasSelfConn) {
+		var p1 = co.getPointAtLength(co.getTotalLength()-r/3); 
+		var p2 = co.getPointAtLength(r/3);
+		var selfConn = this.path('M'+p1.x+','+p1.y+
+			' C'+(p1.x-r)+','+(p1.y-2.5*r)+' '+
+			(p2.x+r)+','+(p1.y-2.5*r)+' '+p2.x+','+p2.y);
+		res.push(selfConn.attr({'stroke-width': strokeWidth,
+								stroke: strokeColor}));
+		// another path for animation (connected to the center of co)
+		var selfConnAnimPath = this.path('M'+x+','+y+selfConn.attrs.path[1]+'z'
+			).attr({stroke:0})
+		res.push(selfConnAnimPath);
+		// arrow head
+		var ahSize 	= r/8;
+		var ahRef 	= selfConn.getPointAtLength(selfConn.getTotalLength()-1)
+		var ahAngle = Math.atan2(ahRef.x-p2.x,p2.x-ahRef.y);
+	    ahAngle 	= (ahAngle / (2 * Math.PI)) * 360;
+	    var ah = this.path("M" + ahRef.x + " " + ahRef.y +
+			" L" + (ahRef.x - ahSize) + " " + (ahRef.y - ahSize) +
+			" L" + (ahRef.x - ahSize) + " " + (ahRef.y + ahSize) +
+			" L" + ahRef.x + " " + ahRef.y
+			).attr({stroke:strokeColor, fill:strokeColor}
+				).rotate((112+ahAngle), ahRef.x, ahRef.y);
+		res.push(ah);
+		// label on self connection
+		var label = this.text(
+			selfConn.getPointAtLength(
+				selfConn.getTotalLength()/2).x,
+			selfConn.getPointAtLength(
+				selfConn.getTotalLength()/2).y-labelFontSize/1.25,
+			labelText
+			).attr({font: this.getFont("Helvetica"), 'font-size': labelFontSize});
+		res.push(label);
+	};
+	if (isFinal) {
+		res.push(ci);
+	};
+	return res;
+};
+
+
+function graph() {
+	var nodeRadius 	 = 30;
+	var nodeRadiusHi = nodeRadius + 10;
+	var nodeOpacity   = 1;
+	var nodeOpacityHi = .5;
+	var labelFontSize = 16;
+	var strokeWidth = 2;
+	var strokeColor = '#ccc';
+	
+	r = Raphael("holder", 1024, 640);
+	
+	// dragging, see: http://raphaeljs.com/touches.html
+	var start = function () {
+		this.animate({r: nodeRadiusHi, opacity: nodeOpacityHi}, 500, ">");
+	},
+		move = function (dx, dy) {
+			this.moveTo(dx, dy);
+			for (var i = nodeById[this.id].length - 1; i >= 0; i--){
+				nodeById[this.id][i].translate(dx, dy);
+			};
+			for (var i = connections.length; i--;) {
+            	r.connection(connections[i]);
+        	};
+        	r.safari();
+		},
+		up = function () {
+			this.animate({r:nodeRadius, opacity:nodeOpacity}, 500, ">");
+		};
+	// nodes
+	var nodes 		= [];
+	var nodeById	= [];
+	var i = 0, n, color, isFinal, selfConn = false, selfConnSymbol;
+	var nx 	     = 10;
+	var nxOffset = 100;
+	var ny 		 = 120;
+	var nyOffset = 120;
+	for (var state in ttable) {
+		color = Raphael.getColor();
+		if (ttable[state].isFinal) {
+			isFinal = true;
+		} else {
+			isFinal = false;
+		};	
+		for (symbol in ttable[state]) {
+			if (symbol == 'isFinal') { continue; };
+			if (ttable[state][symbol] == state) {	
+				selfConn = true;
+				selfConnSymbol = symbol;
+				break;
+			} else {
+				selfConn = false;
+			};
+		};		
+		if (i % 2 == 0) {
+			ny = nyOffset;
+		} else {
+			ny = ny + nyOffset;
+		};
+		n = r.aNode(nx+nxOffset, ny, nodeRadius, isFinal, selfConn,
+					strokeWidth, strokeColor, symbol, labelFontSize);
+		n[1].attr({fill:color, opacity:nodeOpacity, cursor:'move'});
+		n[1].drag(move, start, up);
+		nodes.push(n);
+		nodeById[n[1].id] = nodes[i];
+		nx = nx + nxOffset;
+		i++;
+	};
+	// connections
+	var connections = [];
+	var k = l = 0;
+	for (var state in ttable) {
+		for (var i = 0; i < ALPHABET.length; i++) {
+			l = 0;
+			if(ttable[state][ALPHABET[i]]) {
+				for (var statex in ttable) {
+					if (ttable[state][ALPHABET[i]] == statex) {
+						if (state == statex) {
+							continue;
+						} else {
+							connections.push(r.connection(nodes[k][0], nodes[l][0], strokeWidth, strokeColor));								
+						};
+					};
+					l++;
+				};
+			};
+		};
+		k++;
+	};
+};
diff --git a/javascripts/lib/graffle.js b/javascripts/lib/graffle.js
deleted file mode 100644
index de1456e..0000000
--- a/javascripts/lib/graffle.js
+++ /dev/null
@@ -1,158 +0,0 @@
-Raphael.fn.connection = function (obj1, obj2, line, bg) {
-    if (obj1.line && obj1.from && obj1.to) {
-        line = obj1;
-        obj1 = line.from;
-        obj2 = line.to;
-    }
-    var bb1 = obj1.getBBox(),
-        bb2 = obj2.getBBox(),
-        p = [{x: bb1.x + bb1.width / 2, y: bb1.y - 1},
-        {x: bb1.x + bb1.width / 2, y: bb1.y + bb1.height + 1},
-        {x: bb1.x - 1, y: bb1.y + bb1.height / 2},
-        {x: bb1.x + bb1.width + 1, y: bb1.y + bb1.height / 2},
-        {x: bb2.x + bb2.width / 2, y: bb2.y - 1},
-        {x: bb2.x + bb2.width / 2, y: bb2.y + bb2.height + 1},
-        {x: bb2.x - 1, y: bb2.y + bb2.height / 2},
-        {x: bb2.x + bb2.width + 1, y: bb2.y + bb2.height / 2}],
-        d = {}, dis = [];
-    for (var i = 0; i < 4; i++) {
-        for (var j = 4; j < 8; j++) {
-            var dx = Math.abs(p[i].x - p[j].x),
-                dy = Math.abs(p[i].y - p[j].y);
-            if ((i == j - 4) || (((i != 3 && j != 6) || p[i].x < p[j].x) && ((i != 2 && j != 7) || p[i].x > p[j].x) && ((i != 0 && j != 5) || p[i].y > p[j].y) && ((i != 1 && j != 4) || p[i].y < p[j].y))) {
-                dis.push(dx + dy);
-                d[dis[dis.length - 1]] = [i, j];
-            }
-        }
-    }
-    if (dis.length == 0) {
-        var res = [0, 4];
-    } else {
-        res = d[Math.min.apply(Math, dis)];
-    }
-    var x1 = p[res[0]].x,
-        y1 = p[res[0]].y,
-        x4 = p[res[1]].x,
-        y4 = p[res[1]].y;
-    dx = Math.max(Math.abs(x1 - x4) / 2, 10);
-    dy = Math.max(Math.abs(y1 - y4) / 2, 10);
-    var x2 = [x1, x1, x1 - dx, x1 + dx][res[0]].toFixed(3),
-        y2 = [y1 - dy, y1 + dy, y1, y1][res[0]].toFixed(3),
-        x3 = [0, 0, 0, 0, x4, x4, x4 - dx, x4 + dx][res[1]].toFixed(3),
-        y3 = [0, 0, 0, 0, y1 + dy, y1 - dy, y4, y4][res[1]].toFixed(3);
-    var path = ["M", x1.toFixed(3), y1.toFixed(3), "C", x2, y2, x3, y3, x4.toFixed(3), y4.toFixed(3)].join(",");
-	//path = Raphael.fn.arrow();
-	
-	if (line && line.line) {
-        line.bg && line.bg.attr({path: path});
-        line.line.attr({path: path});
-    } else {
-        var color = typeof line == "string" ? line : "#000";
-        return {
-            bg: bg && bg.split && this.path(path).attr({stroke: bg.split("|")[0], fill: "none", "stroke-width": bg.split("|")[1] || 3}),
-            line: this.path(path).attr({stroke: color, fill: "none"}),
-            from: obj1,
-            to: obj2
-        };
-    }
-};
-
-Raphael.fn.arrow = function (x1, y1, x2, y2, size) {
-    var angle = Math.atan2(x1-x2,y2-y1);
-    angle = (angle / (2 * Math.PI)) * 360;
-    var arrowPath = this.path("M" + x2 + " " + y2 + " L" + (x2 - size) + " " + (y2 - size) + " L" + (x2 - size) + " " + (y2 + size) + " L" + x2 + " " + y2 ).attr("fill","black").rotate((90+angle),x2,y2);
-    return [linePath,arrowPath];
-};
-
-var el;
-window.onload = function () {
-	//document.write('<pre>')
-	for (var state in ttable) {
-		//document.write(state+' --><br />')
-		for (var i=0; i < ALPHABET.length; i++) {
-			if(ttable[state][ALPHABET[i]]) {
-				//document.write('\t'+ALPHABET[i]+': ')
-				//document.write(ttable[state][ALPHABET[i]]+'<br />');	
-			}
-		}
-	}
-	//document.write('</pre>');
-	
-	
-    var dragger = function () {
-        this.ox = this.type == "rect" ? this.attr("x") : this.attr("cx");
-        this.oy = this.type == "rect" ? this.attr("y") : this.attr("cy");
-        this.animate({"fill-opacity": .2}, 500);
-    },
-        move = function (dx, dy) {
-            var att = this.type == "rect" ? {x: this.ox + dx, y: this.oy + dy} : {cx: this.ox + dx, cy: this.oy + dy};
-            this.attr(att);
-            for (var i = connections.length; i--;) {
-                r.connection(connections[i]);
-            }
-            r.safari();
-        },
-        up = function () {
-            this.animate({"fill-opacity": 0}, 500);
-        },
-        r = Raphael("holder", 640, 480),
-        connections = [],
-		shapes = [];
-		var q = 10;
-		for (var state in ttable) {
-			shapes.push(
-				r.ellipse(190+q, 100, 20, 20)
-			);
-			q+=60;
-		}
-		
-		
-        /*shapes = [  r.ellipse(190, 100, 30, 20),
-                    r.rect(290, 80, 60, 40, 10),
-                    r.rect(290, 180, 60, 40, 2),
-                    r.ellipse(450, 100, 20, 20)
-                ];*/
-    for (var i = 0, ii = shapes.length; i < ii; i++) {
-        var color = Raphael.getColor();
-        shapes[i].attr({fill: color, stroke: color, "fill-opacity": 0, "stroke-width": 2, cursor: "move"});
-        shapes[i].drag(move, dragger, up);
-    }
-    
-	var xx = new Array();
-	var oo = 0;
-	for (var state in ttable) {
-		if (ttable[state].isFinal) {
-			xx[oo] = true;
-		} else {
-			xx[oo] = false;
-		};
-		oo++;
-	}
-
-	for (var i = 0, ii = shapes.length; i < ii; i++) {
-		if (xx[i]) {
-			shapes[i].attr({"stroke-width": 4});
-		};
-	}
-    //connections.push(r.connection(shapes[0], shapes[1], "#000"));
-    //connections.push(r.connection(shapes[1], shapes[2], "#000"));
-    //connections.push(r.connection(shapes[1], shapes[3], "#000"));
-
-	var ii = jj = 0;
-	for (var state in ttable) {
-		for (var i=0; i < ALPHABET.length; i++) {
-			jj =0;
-			if(ttable[state][ALPHABET[i]]) {
-				for (var s2 in ttable) {
-					if (ttable[state][ALPHABET[i]] == s2) {
-						connections.push(r.connection(shapes[ii], shapes[jj], '#000'));	
-					};
-					jj++;
-				};
-		
-			}
-		}
-		ii++;
-	}
-
-};
diff --git a/javascripts/lib/jquery-ui.js b/javascripts/lib/jquery-ui.js
new file mode 100755
index 0000000..c959703
--- /dev/null
+++ b/javascripts/lib/jquery-ui.js
@@ -0,0 +1,207 @@
+/*
+ * jQuery UI Effects 1.8.1
+ *
+ * Copyright (c) 2010 AUTHORS.txt (http://jqueryui.com/about)
+ * Dual licensed under the MIT (MIT-LICENSE.txt)
+ * and GPL (GPL-LICENSE.txt) licenses.
+ *
+ * http://docs.jquery.com/UI/Effects/
+ */
+jQuery.effects||function(f){function k(c){var a;if(c&&c.constructor==Array&&c.length==3)return c;if(a=/rgb\(\s*([0-9]{1,3})\s*,\s*([0-9]{1,3})\s*,\s*([0-9]{1,3})\s*\)/.exec(c))return[parseInt(a[1],10),parseInt(a[2],10),parseInt(a[3],10)];if(a=/rgb\(\s*([0-9]+(?:\.[0-9]+)?)\%\s*,\s*([0-9]+(?:\.[0-9]+)?)\%\s*,\s*([0-9]+(?:\.[0-9]+)?)\%\s*\)/.exec(c))return[parseFloat(a[1])*2.55,parseFloat(a[2])*2.55,parseFloat(a[3])*2.55];if(a=/#([a-fA-F0-9]{2})([a-fA-F0-9]{2})([a-fA-F0-9]{2})/.exec(c))return[parseInt(a[1],
+16),parseInt(a[2],16),parseInt(a[3],16)];if(a=/#([a-fA-F0-9])([a-fA-F0-9])([a-fA-F0-9])/.exec(c))return[parseInt(a[1]+a[1],16),parseInt(a[2]+a[2],16),parseInt(a[3]+a[3],16)];if(/rgba\(0, 0, 0, 0\)/.exec(c))return l.transparent;return l[f.trim(c).toLowerCase()]}function q(c,a){var b;do{b=f.curCSS(c,a);if(b!=""&&b!="transparent"||f.nodeName(c,"body"))break;a="backgroundColor"}while(c=c.parentNode);return k(b)}function m(){var c=document.defaultView?document.defaultView.getComputedStyle(this,null):this.currentStyle,
+a={},b,d;if(c&&c.length&&c[0]&&c[c[0]])for(var e=c.length;e--;){b=c[e];if(typeof c[b]=="string"){d=b.replace(/\-(\w)/g,function(g,h){return h.toUpperCase()});a[d]=c[b]}}else for(b in c)if(typeof c[b]==="string")a[b]=c[b];return a}function n(c){var a,b;for(a in c){b=c[a];if(b==null||f.isFunction(b)||a in r||/scrollbar/.test(a)||!/color/i.test(a)&&isNaN(parseFloat(b)))delete c[a]}return c}function s(c,a){var b={_:0},d;for(d in a)if(c[d]!=a[d])b[d]=a[d];return b}function j(c,a,b,d){if(typeof c=="object"){d=
+a;b=null;a=c;c=a.effect}if(f.isFunction(a)){d=a;b=null;a={}}if(f.isFunction(b)){d=b;b=null}if(typeof a=="number"||f.fx.speeds[a]){d=b;b=a;a={}}a=a||{};b=b||a.duration;b=f.fx.off?0:typeof b=="number"?b:f.fx.speeds[b]||f.fx.speeds._default;d=d||a.complete;return[c,a,b,d]}f.effects={};f.each(["backgroundColor","borderBottomColor","borderLeftColor","borderRightColor","borderTopColor","color","outlineColor"],function(c,a){f.fx.step[a]=function(b){if(!b.colorInit){b.start=q(b.elem,a);b.end=k(b.end);b.colorInit=
+true}b.elem.style[a]="rgb("+Math.max(Math.min(parseInt(b.pos*(b.end[0]-b.start[0])+b.start[0],10),255),0)+","+Math.max(Math.min(parseInt(b.pos*(b.end[1]-b.start[1])+b.start[1],10),255),0)+","+Math.max(Math.min(parseInt(b.pos*(b.end[2]-b.start[2])+b.start[2],10),255),0)+")"}});var l={aqua:[0,255,255],azure:[240,255,255],beige:[245,245,220],black:[0,0,0],blue:[0,0,255],brown:[165,42,42],cyan:[0,255,255],darkblue:[0,0,139],darkcyan:[0,139,139],darkgrey:[169,169,169],darkgreen:[0,100,0],darkkhaki:[189,
+183,107],darkmagenta:[139,0,139],darkolivegreen:[85,107,47],darkorange:[255,140,0],darkorchid:[153,50,204],darkred:[139,0,0],darksalmon:[233,150,122],darkviolet:[148,0,211],fuchsia:[255,0,255],gold:[255,215,0],green:[0,128,0],indigo:[75,0,130],khaki:[240,230,140],lightblue:[173,216,230],lightcyan:[224,255,255],lightgreen:[144,238,144],lightgrey:[211,211,211],lightpink:[255,182,193],lightyellow:[255,255,224],lime:[0,255,0],magenta:[255,0,255],maroon:[128,0,0],navy:[0,0,128],olive:[128,128,0],orange:[255,
+165,0],pink:[255,192,203],purple:[128,0,128],violet:[128,0,128],red:[255,0,0],silver:[192,192,192],white:[255,255,255],yellow:[255,255,0],transparent:[255,255,255]},o=["add","remove","toggle"],r={border:1,borderBottom:1,borderColor:1,borderLeft:1,borderRight:1,borderTop:1,borderWidth:1,margin:1,padding:1};f.effects.animateClass=function(c,a,b,d){if(f.isFunction(b)){d=b;b=null}return this.each(function(){var e=f(this),g=e.attr("style")||" ",h=n(m.call(this)),p,t=e.attr("className");f.each(o,function(u,
+i){c[i]&&e[i+"Class"](c[i])});p=n(m.call(this));e.attr("className",t);e.animate(s(h,p),a,b,function(){f.each(o,function(u,i){c[i]&&e[i+"Class"](c[i])});if(typeof e.attr("style")=="object"){e.attr("style").cssText="";e.attr("style").cssText=g}else e.attr("style",g);d&&d.apply(this,arguments)})})};f.fn.extend({_addClass:f.fn.addClass,addClass:function(c,a,b,d){return a?f.effects.animateClass.apply(this,[{add:c},a,b,d]):this._addClass(c)},_removeClass:f.fn.removeClass,removeClass:function(c,a,b,d){return a?
+f.effects.animateClass.apply(this,[{remove:c},a,b,d]):this._removeClass(c)},_toggleClass:f.fn.toggleClass,toggleClass:function(c,a,b,d,e){return typeof a=="boolean"||a===undefined?b?f.effects.animateClass.apply(this,[a?{add:c}:{remove:c},b,d,e]):this._toggleClass(c,a):f.effects.animateClass.apply(this,[{toggle:c},a,b,d])},switchClass:function(c,a,b,d,e){return f.effects.animateClass.apply(this,[{add:a,remove:c},b,d,e])}});f.extend(f.effects,{version:"1.8.1",save:function(c,a){for(var b=0;b<a.length;b++)a[b]!==
+null&&c.data("ec.storage."+a[b],c[0].style[a[b]])},restore:function(c,a){for(var b=0;b<a.length;b++)a[b]!==null&&c.css(a[b],c.data("ec.storage."+a[b]))},setMode:function(c,a){if(a=="toggle")a=c.is(":hidden")?"show":"hide";return a},getBaseline:function(c,a){var b;switch(c[0]){case "top":b=0;break;case "middle":b=0.5;break;case "bottom":b=1;break;default:b=c[0]/a.height}switch(c[1]){case "left":c=0;break;case "center":c=0.5;break;case "right":c=1;break;default:c=c[1]/a.width}return{x:c,y:b}},createWrapper:function(c){if(c.parent().is(".ui-effects-wrapper"))return c.parent();
+var a={width:c.outerWidth(true),height:c.outerHeight(true),"float":c.css("float")},b=f("<div></div>").addClass("ui-effects-wrapper").css({fontSize:"100%",background:"transparent",border:"none",margin:0,padding:0});c.wrap(b);b=c.parent();if(c.css("position")=="static"){b.css({position:"relative"});c.css({position:"relative"})}else{f.extend(a,{position:c.css("position"),zIndex:c.css("z-index")});f.each(["top","left","bottom","right"],function(d,e){a[e]=c.css(e);if(isNaN(parseInt(a[e],10)))a[e]="auto"});
+c.css({position:"relative",top:0,left:0})}return b.css(a).show()},removeWrapper:function(c){if(c.parent().is(".ui-effects-wrapper"))return c.parent().replaceWith(c);return c},setTransition:function(c,a,b,d){d=d||{};f.each(a,function(e,g){unit=c.cssUnit(g);if(unit[0]>0)d[g]=unit[0]*b+unit[1]});return d}});f.fn.extend({effect:function(c){var a=j.apply(this,arguments);a={options:a[1],duration:a[2],callback:a[3]};var b=f.effects[c];return b&&!f.fx.off?b.call(this,a):this},_show:f.fn.show,show:function(c){if(!c||
+typeof c=="number"||f.fx.speeds[c])return this._show.apply(this,arguments);else{var a=j.apply(this,arguments);a[1].mode="show";return this.effect.apply(this,a)}},_hide:f.fn.hide,hide:function(c){if(!c||typeof c=="number"||f.fx.speeds[c])return this._hide.apply(this,arguments);else{var a=j.apply(this,arguments);a[1].mode="hide";return this.effect.apply(this,a)}},__toggle:f.fn.toggle,toggle:function(c){if(!c||typeof c=="number"||f.fx.speeds[c]||typeof c=="boolean"||f.isFunction(c))return this.__toggle.apply(this,
+arguments);else{var a=j.apply(this,arguments);a[1].mode="toggle";return this.effect.apply(this,a)}},cssUnit:function(c){var a=this.css(c),b=[];f.each(["em","px","%","pt"],function(d,e){if(a.indexOf(e)>0)b=[parseFloat(a),e]});return b}});f.easing.jswing=f.easing.swing;f.extend(f.easing,{def:"easeOutQuad",swing:function(c,a,b,d,e){return f.easing[f.easing.def](c,a,b,d,e)},easeInQuad:function(c,a,b,d,e){return d*(a/=e)*a+b},easeOutQuad:function(c,a,b,d,e){return-d*(a/=e)*(a-2)+b},easeInOutQuad:function(c,
+a,b,d,e){if((a/=e/2)<1)return d/2*a*a+b;return-d/2*(--a*(a-2)-1)+b},easeInCubic:function(c,a,b,d,e){return d*(a/=e)*a*a+b},easeOutCubic:function(c,a,b,d,e){return d*((a=a/e-1)*a*a+1)+b},easeInOutCubic:function(c,a,b,d,e){if((a/=e/2)<1)return d/2*a*a*a+b;return d/2*((a-=2)*a*a+2)+b},easeInQuart:function(c,a,b,d,e){return d*(a/=e)*a*a*a+b},easeOutQuart:function(c,a,b,d,e){return-d*((a=a/e-1)*a*a*a-1)+b},easeInOutQuart:function(c,a,b,d,e){if((a/=e/2)<1)return d/2*a*a*a*a+b;return-d/2*((a-=2)*a*a*a-2)+
+b},easeInQuint:function(c,a,b,d,e){return d*(a/=e)*a*a*a*a+b},easeOutQuint:function(c,a,b,d,e){return d*((a=a/e-1)*a*a*a*a+1)+b},easeInOutQuint:function(c,a,b,d,e){if((a/=e/2)<1)return d/2*a*a*a*a*a+b;return d/2*((a-=2)*a*a*a*a+2)+b},easeInSine:function(c,a,b,d,e){return-d*Math.cos(a/e*(Math.PI/2))+d+b},easeOutSine:function(c,a,b,d,e){return d*Math.sin(a/e*(Math.PI/2))+b},easeInOutSine:function(c,a,b,d,e){return-d/2*(Math.cos(Math.PI*a/e)-1)+b},easeInExpo:function(c,a,b,d,e){return a==0?b:d*Math.pow(2,
+10*(a/e-1))+b},easeOutExpo:function(c,a,b,d,e){return a==e?b+d:d*(-Math.pow(2,-10*a/e)+1)+b},easeInOutExpo:function(c,a,b,d,e){if(a==0)return b;if(a==e)return b+d;if((a/=e/2)<1)return d/2*Math.pow(2,10*(a-1))+b;return d/2*(-Math.pow(2,-10*--a)+2)+b},easeInCirc:function(c,a,b,d,e){return-d*(Math.sqrt(1-(a/=e)*a)-1)+b},easeOutCirc:function(c,a,b,d,e){return d*Math.sqrt(1-(a=a/e-1)*a)+b},easeInOutCirc:function(c,a,b,d,e){if((a/=e/2)<1)return-d/2*(Math.sqrt(1-a*a)-1)+b;return d/2*(Math.sqrt(1-(a-=2)*
+a)+1)+b},easeInElastic:function(c,a,b,d,e){c=1.70158;var g=0,h=d;if(a==0)return b;if((a/=e)==1)return b+d;g||(g=e*0.3);if(h<Math.abs(d)){h=d;c=g/4}else c=g/(2*Math.PI)*Math.asin(d/h);return-(h*Math.pow(2,10*(a-=1))*Math.sin((a*e-c)*2*Math.PI/g))+b},easeOutElastic:function(c,a,b,d,e){c=1.70158;var g=0,h=d;if(a==0)return b;if((a/=e)==1)return b+d;g||(g=e*0.3);if(h<Math.abs(d)){h=d;c=g/4}else c=g/(2*Math.PI)*Math.asin(d/h);return h*Math.pow(2,-10*a)*Math.sin((a*e-c)*2*Math.PI/g)+d+b},easeInOutElastic:function(c,
+a,b,d,e){c=1.70158;var g=0,h=d;if(a==0)return b;if((a/=e/2)==2)return b+d;g||(g=e*0.3*1.5);if(h<Math.abs(d)){h=d;c=g/4}else c=g/(2*Math.PI)*Math.asin(d/h);if(a<1)return-0.5*h*Math.pow(2,10*(a-=1))*Math.sin((a*e-c)*2*Math.PI/g)+b;return h*Math.pow(2,-10*(a-=1))*Math.sin((a*e-c)*2*Math.PI/g)*0.5+d+b},easeInBack:function(c,a,b,d,e,g){if(g==undefined)g=1.70158;return d*(a/=e)*a*((g+1)*a-g)+b},easeOutBack:function(c,a,b,d,e,g){if(g==undefined)g=1.70158;return d*((a=a/e-1)*a*((g+1)*a+g)+1)+b},easeInOutBack:function(c,
+a,b,d,e,g){if(g==undefined)g=1.70158;if((a/=e/2)<1)return d/2*a*a*(((g*=1.525)+1)*a-g)+b;return d/2*((a-=2)*a*(((g*=1.525)+1)*a+g)+2)+b},easeInBounce:function(c,a,b,d,e){return d-f.easing.easeOutBounce(c,e-a,0,d,e)+b},easeOutBounce:function(c,a,b,d,e){return(a/=e)<1/2.75?d*7.5625*a*a+b:a<2/2.75?d*(7.5625*(a-=1.5/2.75)*a+0.75)+b:a<2.5/2.75?d*(7.5625*(a-=2.25/2.75)*a+0.9375)+b:d*(7.5625*(a-=2.625/2.75)*a+0.984375)+b},easeInOutBounce:function(c,a,b,d,e){if(a<e/2)return f.easing.easeInBounce(c,a*2,0,
+d,e)*0.5+b;return f.easing.easeOutBounce(c,a*2-e,0,d,e)*0.5+d*0.5+b}})}(jQuery);
+;/*
+ * jQuery UI Effects Blind 1.8.1
+ *
+ * Copyright (c) 2010 AUTHORS.txt (http://jqueryui.com/about)
+ * Dual licensed under the MIT (MIT-LICENSE.txt)
+ * and GPL (GPL-LICENSE.txt) licenses.
+ *
+ * http://docs.jquery.com/UI/Effects/Blind
+ *
+ * Depends:
+ *	jquery.effects.core.js
+ */
+(function(b){b.effects.blind=function(c){return this.queue(function(){var a=b(this),g=["position","top","left"],f=b.effects.setMode(a,c.options.mode||"hide"),d=c.options.direction||"vertical";b.effects.save(a,g);a.show();var e=b.effects.createWrapper(a).css({overflow:"hidden"}),h=d=="vertical"?"height":"width";d=d=="vertical"?e.height():e.width();f=="show"&&e.css(h,0);var i={};i[h]=f=="show"?d:0;e.animate(i,c.duration,c.options.easing,function(){f=="hide"&&a.hide();b.effects.restore(a,g);b.effects.removeWrapper(a);
+c.callback&&c.callback.apply(a[0],arguments);a.dequeue()})})}})(jQuery);
+;/*
+ * jQuery UI Effects Bounce 1.8.1
+ *
+ * Copyright (c) 2010 AUTHORS.txt (http://jqueryui.com/about)
+ * Dual licensed under the MIT (MIT-LICENSE.txt)
+ * and GPL (GPL-LICENSE.txt) licenses.
+ *
+ * http://docs.jquery.com/UI/Effects/Bounce
+ *
+ * Depends:
+ *	jquery.effects.core.js
+ */
+(function(e){e.effects.bounce=function(b){return this.queue(function(){var a=e(this),l=["position","top","left"],h=e.effects.setMode(a,b.options.mode||"effect"),d=b.options.direction||"up",c=b.options.distance||20,m=b.options.times||5,i=b.duration||250;/show|hide/.test(h)&&l.push("opacity");e.effects.save(a,l);a.show();e.effects.createWrapper(a);var f=d=="up"||d=="down"?"top":"left";d=d=="up"||d=="left"?"pos":"neg";c=b.options.distance||(f=="top"?a.outerHeight({margin:true})/3:a.outerWidth({margin:true})/
+3);if(h=="show")a.css("opacity",0).css(f,d=="pos"?-c:c);if(h=="hide")c/=m*2;h!="hide"&&m--;if(h=="show"){var g={opacity:1};g[f]=(d=="pos"?"+=":"-=")+c;a.animate(g,i/2,b.options.easing);c/=2;m--}for(g=0;g<m;g++){var j={},k={};j[f]=(d=="pos"?"-=":"+=")+c;k[f]=(d=="pos"?"+=":"-=")+c;a.animate(j,i/2,b.options.easing).animate(k,i/2,b.options.easing);c=h=="hide"?c*2:c/2}if(h=="hide"){g={opacity:0};g[f]=(d=="pos"?"-=":"+=")+c;a.animate(g,i/2,b.options.easing,function(){a.hide();e.effects.restore(a,l);e.effects.removeWrapper(a);
+b.callback&&b.callback.apply(this,arguments)})}else{j={};k={};j[f]=(d=="pos"?"-=":"+=")+c;k[f]=(d=="pos"?"+=":"-=")+c;a.animate(j,i/2,b.options.easing).animate(k,i/2,b.options.easing,function(){e.effects.restore(a,l);e.effects.removeWrapper(a);b.callback&&b.callback.apply(this,arguments)})}a.queue("fx",function(){a.dequeue()});a.dequeue()})}})(jQuery);
+;/*
+ * jQuery UI Effects Clip 1.8.1
+ *
+ * Copyright (c) 2010 AUTHORS.txt (http://jqueryui.com/about)
+ * Dual licensed under the MIT (MIT-LICENSE.txt)
+ * and GPL (GPL-LICENSE.txt) licenses.
+ *
+ * http://docs.jquery.com/UI/Effects/Clip
+ *
+ * Depends:
+ *	jquery.effects.core.js
+ */
+(function(b){b.effects.clip=function(e){return this.queue(function(){var a=b(this),i=["position","top","left","height","width"],f=b.effects.setMode(a,e.options.mode||"hide"),c=e.options.direction||"vertical";b.effects.save(a,i);a.show();var d=b.effects.createWrapper(a).css({overflow:"hidden"});d=a[0].tagName=="IMG"?d:a;var g={size:c=="vertical"?"height":"width",position:c=="vertical"?"top":"left"};c=c=="vertical"?d.height():d.width();if(f=="show"){d.css(g.size,0);d.css(g.position,c/2)}var h={};h[g.size]=
+f=="show"?c:0;h[g.position]=f=="show"?0:c/2;d.animate(h,{queue:false,duration:e.duration,easing:e.options.easing,complete:function(){f=="hide"&&a.hide();b.effects.restore(a,i);b.effects.removeWrapper(a);e.callback&&e.callback.apply(a[0],arguments);a.dequeue()}})})}})(jQuery);
+;/*
+ * jQuery UI Effects Drop 1.8.1
+ *
+ * Copyright (c) 2010 AUTHORS.txt (http://jqueryui.com/about)
+ * Dual licensed under the MIT (MIT-LICENSE.txt)
+ * and GPL (GPL-LICENSE.txt) licenses.
+ *
+ * http://docs.jquery.com/UI/Effects/Drop
+ *
+ * Depends:
+ *	jquery.effects.core.js
+ */
+(function(c){c.effects.drop=function(d){return this.queue(function(){var a=c(this),h=["position","top","left","opacity"],e=c.effects.setMode(a,d.options.mode||"hide"),b=d.options.direction||"left";c.effects.save(a,h);a.show();c.effects.createWrapper(a);var f=b=="up"||b=="down"?"top":"left";b=b=="up"||b=="left"?"pos":"neg";var g=d.options.distance||(f=="top"?a.outerHeight({margin:true})/2:a.outerWidth({margin:true})/2);if(e=="show")a.css("opacity",0).css(f,b=="pos"?-g:g);var i={opacity:e=="show"?1:
+0};i[f]=(e=="show"?b=="pos"?"+=":"-=":b=="pos"?"-=":"+=")+g;a.animate(i,{queue:false,duration:d.duration,easing:d.options.easing,complete:function(){e=="hide"&&a.hide();c.effects.restore(a,h);c.effects.removeWrapper(a);d.callback&&d.callback.apply(this,arguments);a.dequeue()}})})}})(jQuery);
+;/*
+ * jQuery UI Effects Explode 1.8.1
+ *
+ * Copyright (c) 2010 AUTHORS.txt (http://jqueryui.com/about)
+ * Dual licensed under the MIT (MIT-LICENSE.txt)
+ * and GPL (GPL-LICENSE.txt) licenses.
+ *
+ * http://docs.jquery.com/UI/Effects/Explode
+ *
+ * Depends:
+ *	jquery.effects.core.js
+ */
+(function(j){j.effects.explode=function(a){return this.queue(function(){var c=a.options.pieces?Math.round(Math.sqrt(a.options.pieces)):3,d=a.options.pieces?Math.round(Math.sqrt(a.options.pieces)):3;a.options.mode=a.options.mode=="toggle"?j(this).is(":visible")?"hide":"show":a.options.mode;var b=j(this).show().css("visibility","hidden"),g=b.offset();g.top-=parseInt(b.css("marginTop"),10)||0;g.left-=parseInt(b.css("marginLeft"),10)||0;for(var h=b.outerWidth(true),i=b.outerHeight(true),e=0;e<c;e++)for(var f=
+0;f<d;f++)b.clone().appendTo("body").wrap("<div></div>").css({position:"absolute",visibility:"visible",left:-f*(h/d),top:-e*(i/c)}).parent().addClass("ui-effects-explode").css({position:"absolute",overflow:"hidden",width:h/d,height:i/c,left:g.left+f*(h/d)+(a.options.mode=="show"?(f-Math.floor(d/2))*(h/d):0),top:g.top+e*(i/c)+(a.options.mode=="show"?(e-Math.floor(c/2))*(i/c):0),opacity:a.options.mode=="show"?0:1}).animate({left:g.left+f*(h/d)+(a.options.mode=="show"?0:(f-Math.floor(d/2))*(h/d)),top:g.top+
+e*(i/c)+(a.options.mode=="show"?0:(e-Math.floor(c/2))*(i/c)),opacity:a.options.mode=="show"?1:0},a.duration||500);setTimeout(function(){a.options.mode=="show"?b.css({visibility:"visible"}):b.css({visibility:"visible"}).hide();a.callback&&a.callback.apply(b[0]);b.dequeue();j("div.ui-effects-explode").remove()},a.duration||500)})}})(jQuery);
+;/*
+ * jQuery UI Effects Fold 1.8.1
+ *
+ * Copyright (c) 2010 AUTHORS.txt (http://jqueryui.com/about)
+ * Dual licensed under the MIT (MIT-LICENSE.txt)
+ * and GPL (GPL-LICENSE.txt) licenses.
+ *
+ * http://docs.jquery.com/UI/Effects/Fold
+ *
+ * Depends:
+ *	jquery.effects.core.js
+ */
+(function(c){c.effects.fold=function(a){return this.queue(function(){var b=c(this),j=["position","top","left"],d=c.effects.setMode(b,a.options.mode||"hide"),g=a.options.size||15,h=!!a.options.horizFirst,k=a.duration?a.duration/2:c.fx.speeds._default/2;c.effects.save(b,j);b.show();var e=c.effects.createWrapper(b).css({overflow:"hidden"}),f=d=="show"!=h,l=f?["width","height"]:["height","width"];f=f?[e.width(),e.height()]:[e.height(),e.width()];var i=/([0-9]+)%/.exec(g);if(i)g=parseInt(i[1],10)/100*
+f[d=="hide"?0:1];if(d=="show")e.css(h?{height:0,width:g}:{height:g,width:0});h={};i={};h[l[0]]=d=="show"?f[0]:g;i[l[1]]=d=="show"?f[1]:0;e.animate(h,k,a.options.easing).animate(i,k,a.options.easing,function(){d=="hide"&&b.hide();c.effects.restore(b,j);c.effects.removeWrapper(b);a.callback&&a.callback.apply(b[0],arguments);b.dequeue()})})}})(jQuery);
+;/*
+ * jQuery UI Effects Highlight 1.8.1
+ *
+ * Copyright (c) 2010 AUTHORS.txt (http://jqueryui.com/about)
+ * Dual licensed under the MIT (MIT-LICENSE.txt)
+ * and GPL (GPL-LICENSE.txt) licenses.
+ *
+ * http://docs.jquery.com/UI/Effects/Highlight
+ *
+ * Depends:
+ *	jquery.effects.core.js
+ */
+(function(b){b.effects.highlight=function(c){return this.queue(function(){var a=b(this),e=["backgroundImage","backgroundColor","opacity"],d=b.effects.setMode(a,c.options.mode||"show"),f={backgroundColor:a.css("backgroundColor")};if(d=="hide")f.opacity=0;b.effects.save(a,e);a.show().css({backgroundImage:"none",backgroundColor:c.options.color||"#ffff99"}).animate(f,{queue:false,duration:c.duration,easing:c.options.easing,complete:function(){d=="hide"&&a.hide();b.effects.restore(a,e);d=="show"&&!b.support.opacity&&
+this.style.removeAttribute("filter");c.callback&&c.callback.apply(this,arguments);a.dequeue()}})})}})(jQuery);
+;/*
+ * jQuery UI Effects Pulsate 1.8.1
+ *
+ * Copyright (c) 2010 AUTHORS.txt (http://jqueryui.com/about)
+ * Dual licensed under the MIT (MIT-LICENSE.txt)
+ * and GPL (GPL-LICENSE.txt) licenses.
+ *
+ * http://docs.jquery.com/UI/Effects/Pulsate
+ *
+ * Depends:
+ *	jquery.effects.core.js
+ */
+(function(d){d.effects.pulsate=function(a){return this.queue(function(){var b=d(this),c=d.effects.setMode(b,a.options.mode||"show");times=(a.options.times||5)*2-1;duration=a.duration?a.duration/2:d.fx.speeds._default/2;isVisible=b.is(":visible");animateTo=0;if(!isVisible){b.css("opacity",0).show();animateTo=1}if(c=="hide"&&isVisible||c=="show"&&!isVisible)times--;for(c=0;c<times;c++){b.animate({opacity:animateTo},duration,a.options.easing);animateTo=(animateTo+1)%2}b.animate({opacity:animateTo},duration,
+a.options.easing,function(){animateTo==0&&b.hide();a.callback&&a.callback.apply(this,arguments)});b.queue("fx",function(){b.dequeue()}).dequeue()})}})(jQuery);
+;/*
+ * jQuery UI Effects Scale 1.8.1
+ *
+ * Copyright (c) 2010 AUTHORS.txt (http://jqueryui.com/about)
+ * Dual licensed under the MIT (MIT-LICENSE.txt)
+ * and GPL (GPL-LICENSE.txt) licenses.
+ *
+ * http://docs.jquery.com/UI/Effects/Scale
+ *
+ * Depends:
+ *	jquery.effects.core.js
+ */
+(function(c){c.effects.puff=function(b){return this.queue(function(){var a=c(this),e=c.effects.setMode(a,b.options.mode||"hide"),g=parseInt(b.options.percent,10)||150,h=g/100,i={height:a.height(),width:a.width()};c.extend(b.options,{fade:true,mode:e,percent:e=="hide"?g:100,from:e=="hide"?i:{height:i.height*h,width:i.width*h}});a.effect("scale",b.options,b.duration,b.callback);a.dequeue()})};c.effects.scale=function(b){return this.queue(function(){var a=c(this),e=c.extend(true,{},b.options),g=c.effects.setMode(a,
+b.options.mode||"effect"),h=parseInt(b.options.percent,10)||(parseInt(b.options.percent,10)==0?0:g=="hide"?0:100),i=b.options.direction||"both",f=b.options.origin;if(g!="effect"){e.origin=f||["middle","center"];e.restore=true}f={height:a.height(),width:a.width()};a.from=b.options.from||(g=="show"?{height:0,width:0}:f);h={y:i!="horizontal"?h/100:1,x:i!="vertical"?h/100:1};a.to={height:f.height*h.y,width:f.width*h.x};if(b.options.fade){if(g=="show"){a.from.opacity=0;a.to.opacity=1}if(g=="hide"){a.from.opacity=
+1;a.to.opacity=0}}e.from=a.from;e.to=a.to;e.mode=g;a.effect("size",e,b.duration,b.callback);a.dequeue()})};c.effects.size=function(b){return this.queue(function(){var a=c(this),e=["position","top","left","width","height","overflow","opacity"],g=["position","top","left","overflow","opacity"],h=["width","height","overflow"],i=["fontSize"],f=["borderTopWidth","borderBottomWidth","paddingTop","paddingBottom"],k=["borderLeftWidth","borderRightWidth","paddingLeft","paddingRight"],p=c.effects.setMode(a,
+b.options.mode||"effect"),n=b.options.restore||false,m=b.options.scale||"both",l=b.options.origin,j={height:a.height(),width:a.width()};a.from=b.options.from||j;a.to=b.options.to||j;if(l){l=c.effects.getBaseline(l,j);a.from.top=(j.height-a.from.height)*l.y;a.from.left=(j.width-a.from.width)*l.x;a.to.top=(j.height-a.to.height)*l.y;a.to.left=(j.width-a.to.width)*l.x}var d={from:{y:a.from.height/j.height,x:a.from.width/j.width},to:{y:a.to.height/j.height,x:a.to.width/j.width}};if(m=="box"||m=="both"){if(d.from.y!=
+d.to.y){e=e.concat(f);a.from=c.effects.setTransition(a,f,d.from.y,a.from);a.to=c.effects.setTransition(a,f,d.to.y,a.to)}if(d.from.x!=d.to.x){e=e.concat(k);a.from=c.effects.setTransition(a,k,d.from.x,a.from);a.to=c.effects.setTransition(a,k,d.to.x,a.to)}}if(m=="content"||m=="both")if(d.from.y!=d.to.y){e=e.concat(i);a.from=c.effects.setTransition(a,i,d.from.y,a.from);a.to=c.effects.setTransition(a,i,d.to.y,a.to)}c.effects.save(a,n?e:g);a.show();c.effects.createWrapper(a);a.css("overflow","hidden").css(a.from);
+if(m=="content"||m=="both"){f=f.concat(["marginTop","marginBottom"]).concat(i);k=k.concat(["marginLeft","marginRight"]);h=e.concat(f).concat(k);a.find("*[width]").each(function(){child=c(this);n&&c.effects.save(child,h);var o={height:child.height(),width:child.width()};child.from={height:o.height*d.from.y,width:o.width*d.from.x};child.to={height:o.height*d.to.y,width:o.width*d.to.x};if(d.from.y!=d.to.y){child.from=c.effects.setTransition(child,f,d.from.y,child.from);child.to=c.effects.setTransition(child,
+f,d.to.y,child.to)}if(d.from.x!=d.to.x){child.from=c.effects.setTransition(child,k,d.from.x,child.from);child.to=c.effects.setTransition(child,k,d.to.x,child.to)}child.css(child.from);child.animate(child.to,b.duration,b.options.easing,function(){n&&c.effects.restore(child,h)})})}a.animate(a.to,{queue:false,duration:b.duration,easing:b.options.easing,complete:function(){a.to.opacity===0&&a.css("opacity",a.from.opacity);p=="hide"&&a.hide();c.effects.restore(a,n?e:g);c.effects.removeWrapper(a);b.callback&&
+b.callback.apply(this,arguments);a.dequeue()}})})}})(jQuery);
+;/*
+ * jQuery UI Effects Shake 1.8.1
+ *
+ * Copyright (c) 2010 AUTHORS.txt (http://jqueryui.com/about)
+ * Dual licensed under the MIT (MIT-LICENSE.txt)
+ * and GPL (GPL-LICENSE.txt) licenses.
+ *
+ * http://docs.jquery.com/UI/Effects/Shake
+ *
+ * Depends:
+ *	jquery.effects.core.js
+ */
+(function(d){d.effects.shake=function(a){return this.queue(function(){var b=d(this),j=["position","top","left"];d.effects.setMode(b,a.options.mode||"effect");var c=a.options.direction||"left",e=a.options.distance||20,l=a.options.times||3,f=a.duration||a.options.duration||140;d.effects.save(b,j);b.show();d.effects.createWrapper(b);var g=c=="up"||c=="down"?"top":"left",h=c=="up"||c=="left"?"pos":"neg";c={};var i={},k={};c[g]=(h=="pos"?"-=":"+=")+e;i[g]=(h=="pos"?"+=":"-=")+e*2;k[g]=(h=="pos"?"-=":"+=")+
+e*2;b.animate(c,f,a.options.easing);for(e=1;e<l;e++)b.animate(i,f,a.options.easing).animate(k,f,a.options.easing);b.animate(i,f,a.options.easing).animate(c,f/2,a.options.easing,function(){d.effects.restore(b,j);d.effects.removeWrapper(b);a.callback&&a.callback.apply(this,arguments)});b.queue("fx",function(){b.dequeue()});b.dequeue()})}})(jQuery);
+;/*
+ * jQuery UI Effects Slide 1.8.1
+ *
+ * Copyright (c) 2010 AUTHORS.txt (http://jqueryui.com/about)
+ * Dual licensed under the MIT (MIT-LICENSE.txt)
+ * and GPL (GPL-LICENSE.txt) licenses.
+ *
+ * http://docs.jquery.com/UI/Effects/Slide
+ *
+ * Depends:
+ *	jquery.effects.core.js
+ */
+(function(c){c.effects.slide=function(d){return this.queue(function(){var a=c(this),h=["position","top","left"],e=c.effects.setMode(a,d.options.mode||"show"),b=d.options.direction||"left";c.effects.save(a,h);a.show();c.effects.createWrapper(a).css({overflow:"hidden"});var f=b=="up"||b=="down"?"top":"left";b=b=="up"||b=="left"?"pos":"neg";var g=d.options.distance||(f=="top"?a.outerHeight({margin:true}):a.outerWidth({margin:true}));if(e=="show")a.css(f,b=="pos"?-g:g);var i={};i[f]=(e=="show"?b=="pos"?
+"+=":"-=":b=="pos"?"-=":"+=")+g;a.animate(i,{queue:false,duration:d.duration,easing:d.options.easing,complete:function(){e=="hide"&&a.hide();c.effects.restore(a,h);c.effects.removeWrapper(a);d.callback&&d.callback.apply(this,arguments);a.dequeue()}})})}})(jQuery);
+;/*
+ * jQuery UI Effects Transfer 1.8.1
+ *
+ * Copyright (c) 2010 AUTHORS.txt (http://jqueryui.com/about)
+ * Dual licensed under the MIT (MIT-LICENSE.txt)
+ * and GPL (GPL-LICENSE.txt) licenses.
+ *
+ * http://docs.jquery.com/UI/Effects/Transfer
+ *
+ * Depends:
+ *	jquery.effects.core.js
+ */
+(function(e){e.effects.transfer=function(a){return this.queue(function(){var b=e(this),c=e(a.options.to),d=c.offset();c={top:d.top,left:d.left,height:c.innerHeight(),width:c.innerWidth()};d=b.offset();var f=e('<div class="ui-effects-transfer"></div>').appendTo(document.body).addClass(a.options.className).css({top:d.top,left:d.left,height:b.innerHeight(),width:b.innerWidth(),position:"absolute"}).animate(c,a.duration,a.options.easing,function(){f.remove();a.callback&&a.callback.apply(b[0],arguments);
+b.dequeue()})})}})(jQuery);
+;
\ No newline at end of file
diff --git a/javascripts/lib/jquery.js b/javascripts/lib/jquery.js
new file mode 100644
index 0000000..7c24308
--- /dev/null
+++ b/javascripts/lib/jquery.js
@@ -0,0 +1,154 @@
+/*!
+ * jQuery JavaScript Library v1.4.2
+ * http://jquery.com/
+ *
+ * Copyright 2010, John Resig
+ * Dual licensed under the MIT or GPL Version 2 licenses.
+ * http://jquery.org/license
+ *
+ * Includes Sizzle.js
+ * http://sizzlejs.com/
+ * Copyright 2010, The Dojo Foundation
+ * Released under the MIT, BSD, and GPL Licenses.
+ *
+ * Date: Sat Feb 13 22:33:48 2010 -0500
+ */
+(function(A,w){function ma(){if(!c.isReady){try{s.documentElement.doScroll("left")}catch(a){setTimeout(ma,1);return}c.ready()}}function Qa(a,b){b.src?c.ajax({url:b.src,async:false,dataType:"script"}):c.globalEval(b.text||b.textContent||b.innerHTML||"");b.parentNode&&b.parentNode.removeChild(b)}function X(a,b,d,f,e,j){var i=a.length;if(typeof b==="object"){for(var o in b)X(a,o,b[o],f,e,d);return a}if(d!==w){f=!j&&f&&c.isFunction(d);for(o=0;o<i;o++)e(a[o],b,f?d.call(a[o],o,e(a[o],b)):d,j);return a}return i?
+e(a[0],b):w}function J(){return(new Date).getTime()}function Y(){return false}function Z(){return true}function na(a,b,d){d[0].type=a;return c.event.handle.apply(b,d)}function oa(a){var b,d=[],f=[],e=arguments,j,i,o,k,n,r;i=c.data(this,"events");if(!(a.liveFired===this||!i||!i.live||a.button&&a.type==="click")){a.liveFired=this;var u=i.live.slice(0);for(k=0;k<u.length;k++){i=u[k];i.origType.replace(O,"")===a.type?f.push(i.selector):u.splice(k--,1)}j=c(a.target).closest(f,a.currentTarget);n=0;for(r=
+j.length;n<r;n++)for(k=0;k<u.length;k++){i=u[k];if(j[n].selector===i.selector){o=j[n].elem;f=null;if(i.preType==="mouseenter"||i.preType==="mouseleave")f=c(a.relatedTarget).closest(i.selector)[0];if(!f||f!==o)d.push({elem:o,handleObj:i})}}n=0;for(r=d.length;n<r;n++){j=d[n];a.currentTarget=j.elem;a.data=j.handleObj.data;a.handleObj=j.handleObj;if(j.handleObj.origHandler.apply(j.elem,e)===false){b=false;break}}return b}}function pa(a,b){return"live."+(a&&a!=="*"?a+".":"")+b.replace(/\./g,"`").replace(/ /g,
+"&")}function qa(a){return!a||!a.parentNode||a.parentNode.nodeType===11}function ra(a,b){var d=0;b.each(function(){if(this.nodeName===(a[d]&&a[d].nodeName)){var f=c.data(a[d++]),e=c.data(this,f);if(f=f&&f.events){delete e.handle;e.events={};for(var j in f)for(var i in f[j])c.event.add(this,j,f[j][i],f[j][i].data)}}})}function sa(a,b,d){var f,e,j;b=b&&b[0]?b[0].ownerDocument||b[0]:s;if(a.length===1&&typeof a[0]==="string"&&a[0].length<512&&b===s&&!ta.test(a[0])&&(c.support.checkClone||!ua.test(a[0]))){e=
+true;if(j=c.fragments[a[0]])if(j!==1)f=j}if(!f){f=b.createDocumentFragment();c.clean(a,b,f,d)}if(e)c.fragments[a[0]]=j?f:1;return{fragment:f,cacheable:e}}function K(a,b){var d={};c.each(va.concat.apply([],va.slice(0,b)),function(){d[this]=a});return d}function wa(a){return"scrollTo"in a&&a.document?a:a.nodeType===9?a.defaultView||a.parentWindow:false}var c=function(a,b){return new c.fn.init(a,b)},Ra=A.jQuery,Sa=A.$,s=A.document,T,Ta=/^[^<]*(<[\w\W]+>)[^>]*$|^#([\w-]+)$/,Ua=/^.[^:#\[\.,]*$/,Va=/\S/,
+Wa=/^(\s|\u00A0)+|(\s|\u00A0)+$/g,Xa=/^<(\w+)\s*\/?>(?:<\/\1>)?$/,P=navigator.userAgent,xa=false,Q=[],L,$=Object.prototype.toString,aa=Object.prototype.hasOwnProperty,ba=Array.prototype.push,R=Array.prototype.slice,ya=Array.prototype.indexOf;c.fn=c.prototype={init:function(a,b){var d,f;if(!a)return this;if(a.nodeType){this.context=this[0]=a;this.length=1;return this}if(a==="body"&&!b){this.context=s;this[0]=s.body;this.selector="body";this.length=1;return this}if(typeof a==="string")if((d=Ta.exec(a))&&
+(d[1]||!b))if(d[1]){f=b?b.ownerDocument||b:s;if(a=Xa.exec(a))if(c.isPlainObject(b)){a=[s.createElement(a[1])];c.fn.attr.call(a,b,true)}else a=[f.createElement(a[1])];else{a=sa([d[1]],[f]);a=(a.cacheable?a.fragment.cloneNode(true):a.fragment).childNodes}return c.merge(this,a)}else{if(b=s.getElementById(d[2])){if(b.id!==d[2])return T.find(a);this.length=1;this[0]=b}this.context=s;this.selector=a;return this}else if(!b&&/^\w+$/.test(a)){this.selector=a;this.context=s;a=s.getElementsByTagName(a);return c.merge(this,
+a)}else return!b||b.jquery?(b||T).find(a):c(b).find(a);else if(c.isFunction(a))return T.ready(a);if(a.selector!==w){this.selector=a.selector;this.context=a.context}return c.makeArray(a,this)},selector:"",jquery:"1.4.2",length:0,size:function(){return this.length},toArray:function(){return R.call(this,0)},get:function(a){return a==null?this.toArray():a<0?this.slice(a)[0]:this[a]},pushStack:function(a,b,d){var f=c();c.isArray(a)?ba.apply(f,a):c.merge(f,a);f.prevObject=this;f.context=this.context;if(b===
+"find")f.selector=this.selector+(this.selector?" ":"")+d;else if(b)f.selector=this.selector+"."+b+"("+d+")";return f},each:function(a,b){return c.each(this,a,b)},ready:function(a){c.bindReady();if(c.isReady)a.call(s,c);else Q&&Q.push(a);return this},eq:function(a){return a===-1?this.slice(a):this.slice(a,+a+1)},first:function(){return this.eq(0)},last:function(){return this.eq(-1)},slice:function(){return this.pushStack(R.apply(this,arguments),"slice",R.call(arguments).join(","))},map:function(a){return this.pushStack(c.map(this,
+function(b,d){return a.call(b,d,b)}))},end:function(){return this.prevObject||c(null)},push:ba,sort:[].sort,splice:[].splice};c.fn.init.prototype=c.fn;c.extend=c.fn.extend=function(){var a=arguments[0]||{},b=1,d=arguments.length,f=false,e,j,i,o;if(typeof a==="boolean"){f=a;a=arguments[1]||{};b=2}if(typeof a!=="object"&&!c.isFunction(a))a={};if(d===b){a=this;--b}for(;b<d;b++)if((e=arguments[b])!=null)for(j in e){i=a[j];o=e[j];if(a!==o)if(f&&o&&(c.isPlainObject(o)||c.isArray(o))){i=i&&(c.isPlainObject(i)||
+c.isArray(i))?i:c.isArray(o)?[]:{};a[j]=c.extend(f,i,o)}else if(o!==w)a[j]=o}return a};c.extend({noConflict:function(a){A.$=Sa;if(a)A.jQuery=Ra;return c},isReady:false,ready:function(){if(!c.isReady){if(!s.body)return setTimeout(c.ready,13);c.isReady=true;if(Q){for(var a,b=0;a=Q[b++];)a.call(s,c);Q=null}c.fn.triggerHandler&&c(s).triggerHandler("ready")}},bindReady:function(){if(!xa){xa=true;if(s.readyState==="complete")return c.ready();if(s.addEventListener){s.addEventListener("DOMContentLoaded",
+L,false);A.addEventListener("load",c.ready,false)}else if(s.attachEvent){s.attachEvent("onreadystatechange",L);A.attachEvent("onload",c.ready);var a=false;try{a=A.frameElement==null}catch(b){}s.documentElement.doScroll&&a&&ma()}}},isFunction:function(a){return $.call(a)==="[object Function]"},isArray:function(a){return $.call(a)==="[object Array]"},isPlainObject:function(a){if(!a||$.call(a)!=="[object Object]"||a.nodeType||a.setInterval)return false;if(a.constructor&&!aa.call(a,"constructor")&&!aa.call(a.constructor.prototype,
+"isPrototypeOf"))return false;var b;for(b in a);return b===w||aa.call(a,b)},isEmptyObject:function(a){for(var b in a)return false;return true},error:function(a){throw a;},parseJSON:function(a){if(typeof a!=="string"||!a)return null;a=c.trim(a);if(/^[\],:{}\s]*$/.test(a.replace(/\\(?:["\\\/bfnrt]|u[0-9a-fA-F]{4})/g,"@").replace(/"[^"\\\n\r]*"|true|false|null|-?\d+(?:\.\d*)?(?:[eE][+\-]?\d+)?/g,"]").replace(/(?:^|:|,)(?:\s*\[)+/g,"")))return A.JSON&&A.JSON.parse?A.JSON.parse(a):(new Function("return "+
+a))();else c.error("Invalid JSON: "+a)},noop:function(){},globalEval:function(a){if(a&&Va.test(a)){var b=s.getElementsByTagName("head")[0]||s.documentElement,d=s.createElement("script");d.type="text/javascript";if(c.support.scriptEval)d.appendChild(s.createTextNode(a));else d.text=a;b.insertBefore(d,b.firstChild);b.removeChild(d)}},nodeName:function(a,b){return a.nodeName&&a.nodeName.toUpperCase()===b.toUpperCase()},each:function(a,b,d){var f,e=0,j=a.length,i=j===w||c.isFunction(a);if(d)if(i)for(f in a){if(b.apply(a[f],
+d)===false)break}else for(;e<j;){if(b.apply(a[e++],d)===false)break}else if(i)for(f in a){if(b.call(a[f],f,a[f])===false)break}else for(d=a[0];e<j&&b.call(d,e,d)!==false;d=a[++e]);return a},trim:function(a){return(a||"").replace(Wa,"")},makeArray:function(a,b){b=b||[];if(a!=null)a.length==null||typeof a==="string"||c.isFunction(a)||typeof a!=="function"&&a.setInterval?ba.call(b,a):c.merge(b,a);return b},inArray:function(a,b){if(b.indexOf)return b.indexOf(a);for(var d=0,f=b.length;d<f;d++)if(b[d]===
+a)return d;return-1},merge:function(a,b){var d=a.length,f=0;if(typeof b.length==="number")for(var e=b.length;f<e;f++)a[d++]=b[f];else for(;b[f]!==w;)a[d++]=b[f++];a.length=d;return a},grep:function(a,b,d){for(var f=[],e=0,j=a.length;e<j;e++)!d!==!b(a[e],e)&&f.push(a[e]);return f},map:function(a,b,d){for(var f=[],e,j=0,i=a.length;j<i;j++){e=b(a[j],j,d);if(e!=null)f[f.length]=e}return f.concat.apply([],f)},guid:1,proxy:function(a,b,d){if(arguments.length===2)if(typeof b==="string"){d=a;a=d[b];b=w}else if(b&&
+!c.isFunction(b)){d=b;b=w}if(!b&&a)b=function(){return a.apply(d||this,arguments)};if(a)b.guid=a.guid=a.guid||b.guid||c.guid++;return b},uaMatch:function(a){a=a.toLowerCase();a=/(webkit)[ \/]([\w.]+)/.exec(a)||/(opera)(?:.*version)?[ \/]([\w.]+)/.exec(a)||/(msie) ([\w.]+)/.exec(a)||!/compatible/.test(a)&&/(mozilla)(?:.*? rv:([\w.]+))?/.exec(a)||[];return{browser:a[1]||"",version:a[2]||"0"}},browser:{}});P=c.uaMatch(P);if(P.browser){c.browser[P.browser]=true;c.browser.version=P.version}if(c.browser.webkit)c.browser.safari=
+true;if(ya)c.inArray=function(a,b){return ya.call(b,a)};T=c(s);if(s.addEventListener)L=function(){s.removeEventListener("DOMContentLoaded",L,false);c.ready()};else if(s.attachEvent)L=function(){if(s.readyState==="complete"){s.detachEvent("onreadystatechange",L);c.ready()}};(function(){c.support={};var a=s.documentElement,b=s.createElement("script"),d=s.createElement("div"),f="script"+J();d.style.display="none";d.innerHTML="   <link/><table></table><a href='/a' style='color:red;float:left;opacity:.55;'>a</a><input type='checkbox'/>";
+var e=d.getElementsByTagName("*"),j=d.getElementsByTagName("a")[0];if(!(!e||!e.length||!j)){c.support={leadingWhitespace:d.firstChild.nodeType===3,tbody:!d.getElementsByTagName("tbody").length,htmlSerialize:!!d.getElementsByTagName("link").length,style:/red/.test(j.getAttribute("style")),hrefNormalized:j.getAttribute("href")==="/a",opacity:/^0.55$/.test(j.style.opacity),cssFloat:!!j.style.cssFloat,checkOn:d.getElementsByTagName("input")[0].value==="on",optSelected:s.createElement("select").appendChild(s.createElement("option")).selected,
+parentNode:d.removeChild(d.appendChild(s.createElement("div"))).parentNode===null,deleteExpando:true,checkClone:false,scriptEval:false,noCloneEvent:true,boxModel:null};b.type="text/javascript";try{b.appendChild(s.createTextNode("window."+f+"=1;"))}catch(i){}a.insertBefore(b,a.firstChild);if(A[f]){c.support.scriptEval=true;delete A[f]}try{delete b.test}catch(o){c.support.deleteExpando=false}a.removeChild(b);if(d.attachEvent&&d.fireEvent){d.attachEvent("onclick",function k(){c.support.noCloneEvent=
+false;d.detachEvent("onclick",k)});d.cloneNode(true).fireEvent("onclick")}d=s.createElement("div");d.innerHTML="<input type='radio' name='radiotest' checked='checked'/>";a=s.createDocumentFragment();a.appendChild(d.firstChild);c.support.checkClone=a.cloneNode(true).cloneNode(true).lastChild.checked;c(function(){var k=s.createElement("div");k.style.width=k.style.paddingLeft="1px";s.body.appendChild(k);c.boxModel=c.support.boxModel=k.offsetWidth===2;s.body.removeChild(k).style.display="none"});a=function(k){var n=
+s.createElement("div");k="on"+k;var r=k in n;if(!r){n.setAttribute(k,"return;");r=typeof n[k]==="function"}return r};c.support.submitBubbles=a("submit");c.support.changeBubbles=a("change");a=b=d=e=j=null}})();c.props={"for":"htmlFor","class":"className",readonly:"readOnly",maxlength:"maxLength",cellspacing:"cellSpacing",rowspan:"rowSpan",colspan:"colSpan",tabindex:"tabIndex",usemap:"useMap",frameborder:"frameBorder"};var G="jQuery"+J(),Ya=0,za={};c.extend({cache:{},expando:G,noData:{embed:true,object:true,
+applet:true},data:function(a,b,d){if(!(a.nodeName&&c.noData[a.nodeName.toLowerCase()])){a=a==A?za:a;var f=a[G],e=c.cache;if(!f&&typeof b==="string"&&d===w)return null;f||(f=++Ya);if(typeof b==="object"){a[G]=f;e[f]=c.extend(true,{},b)}else if(!e[f]){a[G]=f;e[f]={}}a=e[f];if(d!==w)a[b]=d;return typeof b==="string"?a[b]:a}},removeData:function(a,b){if(!(a.nodeName&&c.noData[a.nodeName.toLowerCase()])){a=a==A?za:a;var d=a[G],f=c.cache,e=f[d];if(b){if(e){delete e[b];c.isEmptyObject(e)&&c.removeData(a)}}else{if(c.support.deleteExpando)delete a[c.expando];
+else a.removeAttribute&&a.removeAttribute(c.expando);delete f[d]}}}});c.fn.extend({data:function(a,b){if(typeof a==="undefined"&&this.length)return c.data(this[0]);else if(typeof a==="object")return this.each(function(){c.data(this,a)});var d=a.split(".");d[1]=d[1]?"."+d[1]:"";if(b===w){var f=this.triggerHandler("getData"+d[1]+"!",[d[0]]);if(f===w&&this.length)f=c.data(this[0],a);return f===w&&d[1]?this.data(d[0]):f}else return this.trigger("setData"+d[1]+"!",[d[0],b]).each(function(){c.data(this,
+a,b)})},removeData:function(a){return this.each(function(){c.removeData(this,a)})}});c.extend({queue:function(a,b,d){if(a){b=(b||"fx")+"queue";var f=c.data(a,b);if(!d)return f||[];if(!f||c.isArray(d))f=c.data(a,b,c.makeArray(d));else f.push(d);return f}},dequeue:function(a,b){b=b||"fx";var d=c.queue(a,b),f=d.shift();if(f==="inprogress")f=d.shift();if(f){b==="fx"&&d.unshift("inprogress");f.call(a,function(){c.dequeue(a,b)})}}});c.fn.extend({queue:function(a,b){if(typeof a!=="string"){b=a;a="fx"}if(b===
+w)return c.queue(this[0],a);return this.each(function(){var d=c.queue(this,a,b);a==="fx"&&d[0]!=="inprogress"&&c.dequeue(this,a)})},dequeue:function(a){return this.each(function(){c.dequeue(this,a)})},delay:function(a,b){a=c.fx?c.fx.speeds[a]||a:a;b=b||"fx";return this.queue(b,function(){var d=this;setTimeout(function(){c.dequeue(d,b)},a)})},clearQueue:function(a){return this.queue(a||"fx",[])}});var Aa=/[\n\t]/g,ca=/\s+/,Za=/\r/g,$a=/href|src|style/,ab=/(button|input)/i,bb=/(button|input|object|select|textarea)/i,
+cb=/^(a|area)$/i,Ba=/radio|checkbox/;c.fn.extend({attr:function(a,b){return X(this,a,b,true,c.attr)},removeAttr:function(a){return this.each(function(){c.attr(this,a,"");this.nodeType===1&&this.removeAttribute(a)})},addClass:function(a){if(c.isFunction(a))return this.each(function(n){var r=c(this);r.addClass(a.call(this,n,r.attr("class")))});if(a&&typeof a==="string")for(var b=(a||"").split(ca),d=0,f=this.length;d<f;d++){var e=this[d];if(e.nodeType===1)if(e.className){for(var j=" "+e.className+" ",
+i=e.className,o=0,k=b.length;o<k;o++)if(j.indexOf(" "+b[o]+" ")<0)i+=" "+b[o];e.className=c.trim(i)}else e.className=a}return this},removeClass:function(a){if(c.isFunction(a))return this.each(function(k){var n=c(this);n.removeClass(a.call(this,k,n.attr("class")))});if(a&&typeof a==="string"||a===w)for(var b=(a||"").split(ca),d=0,f=this.length;d<f;d++){var e=this[d];if(e.nodeType===1&&e.className)if(a){for(var j=(" "+e.className+" ").replace(Aa," "),i=0,o=b.length;i<o;i++)j=j.replace(" "+b[i]+" ",
+" ");e.className=c.trim(j)}else e.className=""}return this},toggleClass:function(a,b){var d=typeof a,f=typeof b==="boolean";if(c.isFunction(a))return this.each(function(e){var j=c(this);j.toggleClass(a.call(this,e,j.attr("class"),b),b)});return this.each(function(){if(d==="string")for(var e,j=0,i=c(this),o=b,k=a.split(ca);e=k[j++];){o=f?o:!i.hasClass(e);i[o?"addClass":"removeClass"](e)}else if(d==="undefined"||d==="boolean"){this.className&&c.data(this,"__className__",this.className);this.className=
+this.className||a===false?"":c.data(this,"__className__")||""}})},hasClass:function(a){a=" "+a+" ";for(var b=0,d=this.length;b<d;b++)if((" "+this[b].className+" ").replace(Aa," ").indexOf(a)>-1)return true;return false},val:function(a){if(a===w){var b=this[0];if(b){if(c.nodeName(b,"option"))return(b.attributes.value||{}).specified?b.value:b.text;if(c.nodeName(b,"select")){var d=b.selectedIndex,f=[],e=b.options;b=b.type==="select-one";if(d<0)return null;var j=b?d:0;for(d=b?d+1:e.length;j<d;j++){var i=
+e[j];if(i.selected){a=c(i).val();if(b)return a;f.push(a)}}return f}if(Ba.test(b.type)&&!c.support.checkOn)return b.getAttribute("value")===null?"on":b.value;return(b.value||"").replace(Za,"")}return w}var o=c.isFunction(a);return this.each(function(k){var n=c(this),r=a;if(this.nodeType===1){if(o)r=a.call(this,k,n.val());if(typeof r==="number")r+="";if(c.isArray(r)&&Ba.test(this.type))this.checked=c.inArray(n.val(),r)>=0;else if(c.nodeName(this,"select")){var u=c.makeArray(r);c("option",this).each(function(){this.selected=
+c.inArray(c(this).val(),u)>=0});if(!u.length)this.selectedIndex=-1}else this.value=r}})}});c.extend({attrFn:{val:true,css:true,html:true,text:true,data:true,width:true,height:true,offset:true},attr:function(a,b,d,f){if(!a||a.nodeType===3||a.nodeType===8)return w;if(f&&b in c.attrFn)return c(a)[b](d);f=a.nodeType!==1||!c.isXMLDoc(a);var e=d!==w;b=f&&c.props[b]||b;if(a.nodeType===1){var j=$a.test(b);if(b in a&&f&&!j){if(e){b==="type"&&ab.test(a.nodeName)&&a.parentNode&&c.error("type property can't be changed");
+a[b]=d}if(c.nodeName(a,"form")&&a.getAttributeNode(b))return a.getAttributeNode(b).nodeValue;if(b==="tabIndex")return(b=a.getAttributeNode("tabIndex"))&&b.specified?b.value:bb.test(a.nodeName)||cb.test(a.nodeName)&&a.href?0:w;return a[b]}if(!c.support.style&&f&&b==="style"){if(e)a.style.cssText=""+d;return a.style.cssText}e&&a.setAttribute(b,""+d);a=!c.support.hrefNormalized&&f&&j?a.getAttribute(b,2):a.getAttribute(b);return a===null?w:a}return c.style(a,b,d)}});var O=/\.(.*)$/,db=function(a){return a.replace(/[^\w\s\.\|`]/g,
+function(b){return"\\"+b})};c.event={add:function(a,b,d,f){if(!(a.nodeType===3||a.nodeType===8)){if(a.setInterval&&a!==A&&!a.frameElement)a=A;var e,j;if(d.handler){e=d;d=e.handler}if(!d.guid)d.guid=c.guid++;if(j=c.data(a)){var i=j.events=j.events||{},o=j.handle;if(!o)j.handle=o=function(){return typeof c!=="undefined"&&!c.event.triggered?c.event.handle.apply(o.elem,arguments):w};o.elem=a;b=b.split(" ");for(var k,n=0,r;k=b[n++];){j=e?c.extend({},e):{handler:d,data:f};if(k.indexOf(".")>-1){r=k.split(".");
+k=r.shift();j.namespace=r.slice(0).sort().join(".")}else{r=[];j.namespace=""}j.type=k;j.guid=d.guid;var u=i[k],z=c.event.special[k]||{};if(!u){u=i[k]=[];if(!z.setup||z.setup.call(a,f,r,o)===false)if(a.addEventListener)a.addEventListener(k,o,false);else a.attachEvent&&a.attachEvent("on"+k,o)}if(z.add){z.add.call(a,j);if(!j.handler.guid)j.handler.guid=d.guid}u.push(j);c.event.global[k]=true}a=null}}},global:{},remove:function(a,b,d,f){if(!(a.nodeType===3||a.nodeType===8)){var e,j=0,i,o,k,n,r,u,z=c.data(a),
+C=z&&z.events;if(z&&C){if(b&&b.type){d=b.handler;b=b.type}if(!b||typeof b==="string"&&b.charAt(0)==="."){b=b||"";for(e in C)c.event.remove(a,e+b)}else{for(b=b.split(" ");e=b[j++];){n=e;i=e.indexOf(".")<0;o=[];if(!i){o=e.split(".");e=o.shift();k=new RegExp("(^|\\.)"+c.map(o.slice(0).sort(),db).join("\\.(?:.*\\.)?")+"(\\.|$)")}if(r=C[e])if(d){n=c.event.special[e]||{};for(B=f||0;B<r.length;B++){u=r[B];if(d.guid===u.guid){if(i||k.test(u.namespace)){f==null&&r.splice(B--,1);n.remove&&n.remove.call(a,u)}if(f!=
+null)break}}if(r.length===0||f!=null&&r.length===1){if(!n.teardown||n.teardown.call(a,o)===false)Ca(a,e,z.handle);delete C[e]}}else for(var B=0;B<r.length;B++){u=r[B];if(i||k.test(u.namespace)){c.event.remove(a,n,u.handler,B);r.splice(B--,1)}}}if(c.isEmptyObject(C)){if(b=z.handle)b.elem=null;delete z.events;delete z.handle;c.isEmptyObject(z)&&c.removeData(a)}}}}},trigger:function(a,b,d,f){var e=a.type||a;if(!f){a=typeof a==="object"?a[G]?a:c.extend(c.Event(e),a):c.Event(e);if(e.indexOf("!")>=0){a.type=
+e=e.slice(0,-1);a.exclusive=true}if(!d){a.stopPropagation();c.event.global[e]&&c.each(c.cache,function(){this.events&&this.events[e]&&c.event.trigger(a,b,this.handle.elem)})}if(!d||d.nodeType===3||d.nodeType===8)return w;a.result=w;a.target=d;b=c.makeArray(b);b.unshift(a)}a.currentTarget=d;(f=c.data(d,"handle"))&&f.apply(d,b);f=d.parentNode||d.ownerDocument;try{if(!(d&&d.nodeName&&c.noData[d.nodeName.toLowerCase()]))if(d["on"+e]&&d["on"+e].apply(d,b)===false)a.result=false}catch(j){}if(!a.isPropagationStopped()&&
+f)c.event.trigger(a,b,f,true);else if(!a.isDefaultPrevented()){f=a.target;var i,o=c.nodeName(f,"a")&&e==="click",k=c.event.special[e]||{};if((!k._default||k._default.call(d,a)===false)&&!o&&!(f&&f.nodeName&&c.noData[f.nodeName.toLowerCase()])){try{if(f[e]){if(i=f["on"+e])f["on"+e]=null;c.event.triggered=true;f[e]()}}catch(n){}if(i)f["on"+e]=i;c.event.triggered=false}}},handle:function(a){var b,d,f,e;a=arguments[0]=c.event.fix(a||A.event);a.currentTarget=this;b=a.type.indexOf(".")<0&&!a.exclusive;
+if(!b){d=a.type.split(".");a.type=d.shift();f=new RegExp("(^|\\.)"+d.slice(0).sort().join("\\.(?:.*\\.)?")+"(\\.|$)")}e=c.data(this,"events");d=e[a.type];if(e&&d){d=d.slice(0);e=0;for(var j=d.length;e<j;e++){var i=d[e];if(b||f.test(i.namespace)){a.handler=i.handler;a.data=i.data;a.handleObj=i;i=i.handler.apply(this,arguments);if(i!==w){a.result=i;if(i===false){a.preventDefault();a.stopPropagation()}}if(a.isImmediatePropagationStopped())break}}}return a.result},props:"altKey attrChange attrName bubbles button cancelable charCode clientX clientY ctrlKey currentTarget data detail eventPhase fromElement handler keyCode layerX layerY metaKey newValue offsetX offsetY originalTarget pageX pageY prevValue relatedNode relatedTarget screenX screenY shiftKey srcElement target toElement view wheelDelta which".split(" "),
+fix:function(a){if(a[G])return a;var b=a;a=c.Event(b);for(var d=this.props.length,f;d;){f=this.props[--d];a[f]=b[f]}if(!a.target)a.target=a.srcElement||s;if(a.target.nodeType===3)a.target=a.target.parentNode;if(!a.relatedTarget&&a.fromElement)a.relatedTarget=a.fromElement===a.target?a.toElement:a.fromElement;if(a.pageX==null&&a.clientX!=null){b=s.documentElement;d=s.body;a.pageX=a.clientX+(b&&b.scrollLeft||d&&d.scrollLeft||0)-(b&&b.clientLeft||d&&d.clientLeft||0);a.pageY=a.clientY+(b&&b.scrollTop||
+d&&d.scrollTop||0)-(b&&b.clientTop||d&&d.clientTop||0)}if(!a.which&&(a.charCode||a.charCode===0?a.charCode:a.keyCode))a.which=a.charCode||a.keyCode;if(!a.metaKey&&a.ctrlKey)a.metaKey=a.ctrlKey;if(!a.which&&a.button!==w)a.which=a.button&1?1:a.button&2?3:a.button&4?2:0;return a},guid:1E8,proxy:c.proxy,special:{ready:{setup:c.bindReady,teardown:c.noop},live:{add:function(a){c.event.add(this,a.origType,c.extend({},a,{handler:oa}))},remove:function(a){var b=true,d=a.origType.replace(O,"");c.each(c.data(this,
+"events").live||[],function(){if(d===this.origType.replace(O,""))return b=false});b&&c.event.remove(this,a.origType,oa)}},beforeunload:{setup:function(a,b,d){if(this.setInterval)this.onbeforeunload=d;return false},teardown:function(a,b){if(this.onbeforeunload===b)this.onbeforeunload=null}}}};var Ca=s.removeEventListener?function(a,b,d){a.removeEventListener(b,d,false)}:function(a,b,d){a.detachEvent("on"+b,d)};c.Event=function(a){if(!this.preventDefault)return new c.Event(a);if(a&&a.type){this.originalEvent=
+a;this.type=a.type}else this.type=a;this.timeStamp=J();this[G]=true};c.Event.prototype={preventDefault:function(){this.isDefaultPrevented=Z;var a=this.originalEvent;if(a){a.preventDefault&&a.preventDefault();a.returnValue=false}},stopPropagation:function(){this.isPropagationStopped=Z;var a=this.originalEvent;if(a){a.stopPropagation&&a.stopPropagation();a.cancelBubble=true}},stopImmediatePropagation:function(){this.isImmediatePropagationStopped=Z;this.stopPropagation()},isDefaultPrevented:Y,isPropagationStopped:Y,
+isImmediatePropagationStopped:Y};var Da=function(a){var b=a.relatedTarget;try{for(;b&&b!==this;)b=b.parentNode;if(b!==this){a.type=a.data;c.event.handle.apply(this,arguments)}}catch(d){}},Ea=function(a){a.type=a.data;c.event.handle.apply(this,arguments)};c.each({mouseenter:"mouseover",mouseleave:"mouseout"},function(a,b){c.event.special[a]={setup:function(d){c.event.add(this,b,d&&d.selector?Ea:Da,a)},teardown:function(d){c.event.remove(this,b,d&&d.selector?Ea:Da)}}});if(!c.support.submitBubbles)c.event.special.submit=
+{setup:function(){if(this.nodeName.toLowerCase()!=="form"){c.event.add(this,"click.specialSubmit",function(a){var b=a.target,d=b.type;if((d==="submit"||d==="image")&&c(b).closest("form").length)return na("submit",this,arguments)});c.event.add(this,"keypress.specialSubmit",function(a){var b=a.target,d=b.type;if((d==="text"||d==="password")&&c(b).closest("form").length&&a.keyCode===13)return na("submit",this,arguments)})}else return false},teardown:function(){c.event.remove(this,".specialSubmit")}};
+if(!c.support.changeBubbles){var da=/textarea|input|select/i,ea,Fa=function(a){var b=a.type,d=a.value;if(b==="radio"||b==="checkbox")d=a.checked;else if(b==="select-multiple")d=a.selectedIndex>-1?c.map(a.options,function(f){return f.selected}).join("-"):"";else if(a.nodeName.toLowerCase()==="select")d=a.selectedIndex;return d},fa=function(a,b){var d=a.target,f,e;if(!(!da.test(d.nodeName)||d.readOnly)){f=c.data(d,"_change_data");e=Fa(d);if(a.type!=="focusout"||d.type!=="radio")c.data(d,"_change_data",
+e);if(!(f===w||e===f))if(f!=null||e){a.type="change";return c.event.trigger(a,b,d)}}};c.event.special.change={filters:{focusout:fa,click:function(a){var b=a.target,d=b.type;if(d==="radio"||d==="checkbox"||b.nodeName.toLowerCase()==="select")return fa.call(this,a)},keydown:function(a){var b=a.target,d=b.type;if(a.keyCode===13&&b.nodeName.toLowerCase()!=="textarea"||a.keyCode===32&&(d==="checkbox"||d==="radio")||d==="select-multiple")return fa.call(this,a)},beforeactivate:function(a){a=a.target;c.data(a,
+"_change_data",Fa(a))}},setup:function(){if(this.type==="file")return false;for(var a in ea)c.event.add(this,a+".specialChange",ea[a]);return da.test(this.nodeName)},teardown:function(){c.event.remove(this,".specialChange");return da.test(this.nodeName)}};ea=c.event.special.change.filters}s.addEventListener&&c.each({focus:"focusin",blur:"focusout"},function(a,b){function d(f){f=c.event.fix(f);f.type=b;return c.event.handle.call(this,f)}c.event.special[b]={setup:function(){this.addEventListener(a,
+d,true)},teardown:function(){this.removeEventListener(a,d,true)}}});c.each(["bind","one"],function(a,b){c.fn[b]=function(d,f,e){if(typeof d==="object"){for(var j in d)this[b](j,f,d[j],e);return this}if(c.isFunction(f)){e=f;f=w}var i=b==="one"?c.proxy(e,function(k){c(this).unbind(k,i);return e.apply(this,arguments)}):e;if(d==="unload"&&b!=="one")this.one(d,f,e);else{j=0;for(var o=this.length;j<o;j++)c.event.add(this[j],d,i,f)}return this}});c.fn.extend({unbind:function(a,b){if(typeof a==="object"&&
+!a.preventDefault)for(var d in a)this.unbind(d,a[d]);else{d=0;for(var f=this.length;d<f;d++)c.event.remove(this[d],a,b)}return this},delegate:function(a,b,d,f){return this.live(b,d,f,a)},undelegate:function(a,b,d){return arguments.length===0?this.unbind("live"):this.die(b,null,d,a)},trigger:function(a,b){return this.each(function(){c.event.trigger(a,b,this)})},triggerHandler:function(a,b){if(this[0]){a=c.Event(a);a.preventDefault();a.stopPropagation();c.event.trigger(a,b,this[0]);return a.result}},
+toggle:function(a){for(var b=arguments,d=1;d<b.length;)c.proxy(a,b[d++]);return this.click(c.proxy(a,function(f){var e=(c.data(this,"lastToggle"+a.guid)||0)%d;c.data(this,"lastToggle"+a.guid,e+1);f.preventDefault();return b[e].apply(this,arguments)||false}))},hover:function(a,b){return this.mouseenter(a).mouseleave(b||a)}});var Ga={focus:"focusin",blur:"focusout",mouseenter:"mouseover",mouseleave:"mouseout"};c.each(["live","die"],function(a,b){c.fn[b]=function(d,f,e,j){var i,o=0,k,n,r=j||this.selector,
+u=j?this:c(this.context);if(c.isFunction(f)){e=f;f=w}for(d=(d||"").split(" ");(i=d[o++])!=null;){j=O.exec(i);k="";if(j){k=j[0];i=i.replace(O,"")}if(i==="hover")d.push("mouseenter"+k,"mouseleave"+k);else{n=i;if(i==="focus"||i==="blur"){d.push(Ga[i]+k);i+=k}else i=(Ga[i]||i)+k;b==="live"?u.each(function(){c.event.add(this,pa(i,r),{data:f,selector:r,handler:e,origType:i,origHandler:e,preType:n})}):u.unbind(pa(i,r),e)}}return this}});c.each("blur focus focusin focusout load resize scroll unload click dblclick mousedown mouseup mousemove mouseover mouseout mouseenter mouseleave change select submit keydown keypress keyup error".split(" "),
+function(a,b){c.fn[b]=function(d){return d?this.bind(b,d):this.trigger(b)};if(c.attrFn)c.attrFn[b]=true});A.attachEvent&&!A.addEventListener&&A.attachEvent("onunload",function(){for(var a in c.cache)if(c.cache[a].handle)try{c.event.remove(c.cache[a].handle.elem)}catch(b){}});(function(){function a(g){for(var h="",l,m=0;g[m];m++){l=g[m];if(l.nodeType===3||l.nodeType===4)h+=l.nodeValue;else if(l.nodeType!==8)h+=a(l.childNodes)}return h}function b(g,h,l,m,q,p){q=0;for(var v=m.length;q<v;q++){var t=m[q];
+if(t){t=t[g];for(var y=false;t;){if(t.sizcache===l){y=m[t.sizset];break}if(t.nodeType===1&&!p){t.sizcache=l;t.sizset=q}if(t.nodeName.toLowerCase()===h){y=t;break}t=t[g]}m[q]=y}}}function d(g,h,l,m,q,p){q=0;for(var v=m.length;q<v;q++){var t=m[q];if(t){t=t[g];for(var y=false;t;){if(t.sizcache===l){y=m[t.sizset];break}if(t.nodeType===1){if(!p){t.sizcache=l;t.sizset=q}if(typeof h!=="string"){if(t===h){y=true;break}}else if(k.filter(h,[t]).length>0){y=t;break}}t=t[g]}m[q]=y}}}var f=/((?:\((?:\([^()]+\)|[^()]+)+\)|\[(?:\[[^[\]]*\]|['"][^'"]*['"]|[^[\]'"]+)+\]|\\.|[^ >+~,(\[\\]+)+|[>+~])(\s*,\s*)?((?:.|\r|\n)*)/g,
+e=0,j=Object.prototype.toString,i=false,o=true;[0,0].sort(function(){o=false;return 0});var k=function(g,h,l,m){l=l||[];var q=h=h||s;if(h.nodeType!==1&&h.nodeType!==9)return[];if(!g||typeof g!=="string")return l;for(var p=[],v,t,y,S,H=true,M=x(h),I=g;(f.exec(""),v=f.exec(I))!==null;){I=v[3];p.push(v[1]);if(v[2]){S=v[3];break}}if(p.length>1&&r.exec(g))if(p.length===2&&n.relative[p[0]])t=ga(p[0]+p[1],h);else for(t=n.relative[p[0]]?[h]:k(p.shift(),h);p.length;){g=p.shift();if(n.relative[g])g+=p.shift();
+t=ga(g,t)}else{if(!m&&p.length>1&&h.nodeType===9&&!M&&n.match.ID.test(p[0])&&!n.match.ID.test(p[p.length-1])){v=k.find(p.shift(),h,M);h=v.expr?k.filter(v.expr,v.set)[0]:v.set[0]}if(h){v=m?{expr:p.pop(),set:z(m)}:k.find(p.pop(),p.length===1&&(p[0]==="~"||p[0]==="+")&&h.parentNode?h.parentNode:h,M);t=v.expr?k.filter(v.expr,v.set):v.set;if(p.length>0)y=z(t);else H=false;for(;p.length;){var D=p.pop();v=D;if(n.relative[D])v=p.pop();else D="";if(v==null)v=h;n.relative[D](y,v,M)}}else y=[]}y||(y=t);y||k.error(D||
+g);if(j.call(y)==="[object Array]")if(H)if(h&&h.nodeType===1)for(g=0;y[g]!=null;g++){if(y[g]&&(y[g]===true||y[g].nodeType===1&&E(h,y[g])))l.push(t[g])}else for(g=0;y[g]!=null;g++)y[g]&&y[g].nodeType===1&&l.push(t[g]);else l.push.apply(l,y);else z(y,l);if(S){k(S,q,l,m);k.uniqueSort(l)}return l};k.uniqueSort=function(g){if(B){i=o;g.sort(B);if(i)for(var h=1;h<g.length;h++)g[h]===g[h-1]&&g.splice(h--,1)}return g};k.matches=function(g,h){return k(g,null,null,h)};k.find=function(g,h,l){var m,q;if(!g)return[];
+for(var p=0,v=n.order.length;p<v;p++){var t=n.order[p];if(q=n.leftMatch[t].exec(g)){var y=q[1];q.splice(1,1);if(y.substr(y.length-1)!=="\\"){q[1]=(q[1]||"").replace(/\\/g,"");m=n.find[t](q,h,l);if(m!=null){g=g.replace(n.match[t],"");break}}}}m||(m=h.getElementsByTagName("*"));return{set:m,expr:g}};k.filter=function(g,h,l,m){for(var q=g,p=[],v=h,t,y,S=h&&h[0]&&x(h[0]);g&&h.length;){for(var H in n.filter)if((t=n.leftMatch[H].exec(g))!=null&&t[2]){var M=n.filter[H],I,D;D=t[1];y=false;t.splice(1,1);if(D.substr(D.length-
+1)!=="\\"){if(v===p)p=[];if(n.preFilter[H])if(t=n.preFilter[H](t,v,l,p,m,S)){if(t===true)continue}else y=I=true;if(t)for(var U=0;(D=v[U])!=null;U++)if(D){I=M(D,t,U,v);var Ha=m^!!I;if(l&&I!=null)if(Ha)y=true;else v[U]=false;else if(Ha){p.push(D);y=true}}if(I!==w){l||(v=p);g=g.replace(n.match[H],"");if(!y)return[];break}}}if(g===q)if(y==null)k.error(g);else break;q=g}return v};k.error=function(g){throw"Syntax error, unrecognized expression: "+g;};var n=k.selectors={order:["ID","NAME","TAG"],match:{ID:/#((?:[\w\u00c0-\uFFFF-]|\\.)+)/,
+CLASS:/\.((?:[\w\u00c0-\uFFFF-]|\\.)+)/,NAME:/\[name=['"]*((?:[\w\u00c0-\uFFFF-]|\\.)+)['"]*\]/,ATTR:/\[\s*((?:[\w\u00c0-\uFFFF-]|\\.)+)\s*(?:(\S?=)\s*(['"]*)(.*?)\3|)\s*\]/,TAG:/^((?:[\w\u00c0-\uFFFF\*-]|\\.)+)/,CHILD:/:(only|nth|last|first)-child(?:\((even|odd|[\dn+-]*)\))?/,POS:/:(nth|eq|gt|lt|first|last|even|odd)(?:\((\d*)\))?(?=[^-]|$)/,PSEUDO:/:((?:[\w\u00c0-\uFFFF-]|\\.)+)(?:\((['"]?)((?:\([^\)]+\)|[^\(\)]*)+)\2\))?/},leftMatch:{},attrMap:{"class":"className","for":"htmlFor"},attrHandle:{href:function(g){return g.getAttribute("href")}},
+relative:{"+":function(g,h){var l=typeof h==="string",m=l&&!/\W/.test(h);l=l&&!m;if(m)h=h.toLowerCase();m=0;for(var q=g.length,p;m<q;m++)if(p=g[m]){for(;(p=p.previousSibling)&&p.nodeType!==1;);g[m]=l||p&&p.nodeName.toLowerCase()===h?p||false:p===h}l&&k.filter(h,g,true)},">":function(g,h){var l=typeof h==="string";if(l&&!/\W/.test(h)){h=h.toLowerCase();for(var m=0,q=g.length;m<q;m++){var p=g[m];if(p){l=p.parentNode;g[m]=l.nodeName.toLowerCase()===h?l:false}}}else{m=0;for(q=g.length;m<q;m++)if(p=g[m])g[m]=
+l?p.parentNode:p.parentNode===h;l&&k.filter(h,g,true)}},"":function(g,h,l){var m=e++,q=d;if(typeof h==="string"&&!/\W/.test(h)){var p=h=h.toLowerCase();q=b}q("parentNode",h,m,g,p,l)},"~":function(g,h,l){var m=e++,q=d;if(typeof h==="string"&&!/\W/.test(h)){var p=h=h.toLowerCase();q=b}q("previousSibling",h,m,g,p,l)}},find:{ID:function(g,h,l){if(typeof h.getElementById!=="undefined"&&!l)return(g=h.getElementById(g[1]))?[g]:[]},NAME:function(g,h){if(typeof h.getElementsByName!=="undefined"){var l=[];
+h=h.getElementsByName(g[1]);for(var m=0,q=h.length;m<q;m++)h[m].getAttribute("name")===g[1]&&l.push(h[m]);return l.length===0?null:l}},TAG:function(g,h){return h.getElementsByTagName(g[1])}},preFilter:{CLASS:function(g,h,l,m,q,p){g=" "+g[1].replace(/\\/g,"")+" ";if(p)return g;p=0;for(var v;(v=h[p])!=null;p++)if(v)if(q^(v.className&&(" "+v.className+" ").replace(/[\t\n]/g," ").indexOf(g)>=0))l||m.push(v);else if(l)h[p]=false;return false},ID:function(g){return g[1].replace(/\\/g,"")},TAG:function(g){return g[1].toLowerCase()},
+CHILD:function(g){if(g[1]==="nth"){var h=/(-?)(\d*)n((?:\+|-)?\d*)/.exec(g[2]==="even"&&"2n"||g[2]==="odd"&&"2n+1"||!/\D/.test(g[2])&&"0n+"+g[2]||g[2]);g[2]=h[1]+(h[2]||1)-0;g[3]=h[3]-0}g[0]=e++;return g},ATTR:function(g,h,l,m,q,p){h=g[1].replace(/\\/g,"");if(!p&&n.attrMap[h])g[1]=n.attrMap[h];if(g[2]==="~=")g[4]=" "+g[4]+" ";return g},PSEUDO:function(g,h,l,m,q){if(g[1]==="not")if((f.exec(g[3])||"").length>1||/^\w/.test(g[3]))g[3]=k(g[3],null,null,h);else{g=k.filter(g[3],h,l,true^q);l||m.push.apply(m,
+g);return false}else if(n.match.POS.test(g[0])||n.match.CHILD.test(g[0]))return true;return g},POS:function(g){g.unshift(true);return g}},filters:{enabled:function(g){return g.disabled===false&&g.type!=="hidden"},disabled:function(g){return g.disabled===true},checked:function(g){return g.checked===true},selected:function(g){return g.selected===true},parent:function(g){return!!g.firstChild},empty:function(g){return!g.firstChild},has:function(g,h,l){return!!k(l[3],g).length},header:function(g){return/h\d/i.test(g.nodeName)},
+text:function(g){return"text"===g.type},radio:function(g){return"radio"===g.type},checkbox:function(g){return"checkbox"===g.type},file:function(g){return"file"===g.type},password:function(g){return"password"===g.type},submit:function(g){return"submit"===g.type},image:function(g){return"image"===g.type},reset:function(g){return"reset"===g.type},button:function(g){return"button"===g.type||g.nodeName.toLowerCase()==="button"},input:function(g){return/input|select|textarea|button/i.test(g.nodeName)}},
+setFilters:{first:function(g,h){return h===0},last:function(g,h,l,m){return h===m.length-1},even:function(g,h){return h%2===0},odd:function(g,h){return h%2===1},lt:function(g,h,l){return h<l[3]-0},gt:function(g,h,l){return h>l[3]-0},nth:function(g,h,l){return l[3]-0===h},eq:function(g,h,l){return l[3]-0===h}},filter:{PSEUDO:function(g,h,l,m){var q=h[1],p=n.filters[q];if(p)return p(g,l,h,m);else if(q==="contains")return(g.textContent||g.innerText||a([g])||"").indexOf(h[3])>=0;else if(q==="not"){h=
+h[3];l=0;for(m=h.length;l<m;l++)if(h[l]===g)return false;return true}else k.error("Syntax error, unrecognized expression: "+q)},CHILD:function(g,h){var l=h[1],m=g;switch(l){case "only":case "first":for(;m=m.previousSibling;)if(m.nodeType===1)return false;if(l==="first")return true;m=g;case "last":for(;m=m.nextSibling;)if(m.nodeType===1)return false;return true;case "nth":l=h[2];var q=h[3];if(l===1&&q===0)return true;h=h[0];var p=g.parentNode;if(p&&(p.sizcache!==h||!g.nodeIndex)){var v=0;for(m=p.firstChild;m;m=
+m.nextSibling)if(m.nodeType===1)m.nodeIndex=++v;p.sizcache=h}g=g.nodeIndex-q;return l===0?g===0:g%l===0&&g/l>=0}},ID:function(g,h){return g.nodeType===1&&g.getAttribute("id")===h},TAG:function(g,h){return h==="*"&&g.nodeType===1||g.nodeName.toLowerCase()===h},CLASS:function(g,h){return(" "+(g.className||g.getAttribute("class"))+" ").indexOf(h)>-1},ATTR:function(g,h){var l=h[1];g=n.attrHandle[l]?n.attrHandle[l](g):g[l]!=null?g[l]:g.getAttribute(l);l=g+"";var m=h[2];h=h[4];return g==null?m==="!=":m===
+"="?l===h:m==="*="?l.indexOf(h)>=0:m==="~="?(" "+l+" ").indexOf(h)>=0:!h?l&&g!==false:m==="!="?l!==h:m==="^="?l.indexOf(h)===0:m==="$="?l.substr(l.length-h.length)===h:m==="|="?l===h||l.substr(0,h.length+1)===h+"-":false},POS:function(g,h,l,m){var q=n.setFilters[h[2]];if(q)return q(g,l,h,m)}}},r=n.match.POS;for(var u in n.match){n.match[u]=new RegExp(n.match[u].source+/(?![^\[]*\])(?![^\(]*\))/.source);n.leftMatch[u]=new RegExp(/(^(?:.|\r|\n)*?)/.source+n.match[u].source.replace(/\\(\d+)/g,function(g,
+h){return"\\"+(h-0+1)}))}var z=function(g,h){g=Array.prototype.slice.call(g,0);if(h){h.push.apply(h,g);return h}return g};try{Array.prototype.slice.call(s.documentElement.childNodes,0)}catch(C){z=function(g,h){h=h||[];if(j.call(g)==="[object Array]")Array.prototype.push.apply(h,g);else if(typeof g.length==="number")for(var l=0,m=g.length;l<m;l++)h.push(g[l]);else for(l=0;g[l];l++)h.push(g[l]);return h}}var B;if(s.documentElement.compareDocumentPosition)B=function(g,h){if(!g.compareDocumentPosition||
+!h.compareDocumentPosition){if(g==h)i=true;return g.compareDocumentPosition?-1:1}g=g.compareDocumentPosition(h)&4?-1:g===h?0:1;if(g===0)i=true;return g};else if("sourceIndex"in s.documentElement)B=function(g,h){if(!g.sourceIndex||!h.sourceIndex){if(g==h)i=true;return g.sourceIndex?-1:1}g=g.sourceIndex-h.sourceIndex;if(g===0)i=true;return g};else if(s.createRange)B=function(g,h){if(!g.ownerDocument||!h.ownerDocument){if(g==h)i=true;return g.ownerDocument?-1:1}var l=g.ownerDocument.createRange(),m=
+h.ownerDocument.createRange();l.setStart(g,0);l.setEnd(g,0);m.setStart(h,0);m.setEnd(h,0);g=l.compareBoundaryPoints(Range.START_TO_END,m);if(g===0)i=true;return g};(function(){var g=s.createElement("div"),h="script"+(new Date).getTime();g.innerHTML="<a name='"+h+"'/>";var l=s.documentElement;l.insertBefore(g,l.firstChild);if(s.getElementById(h)){n.find.ID=function(m,q,p){if(typeof q.getElementById!=="undefined"&&!p)return(q=q.getElementById(m[1]))?q.id===m[1]||typeof q.getAttributeNode!=="undefined"&&
+q.getAttributeNode("id").nodeValue===m[1]?[q]:w:[]};n.filter.ID=function(m,q){var p=typeof m.getAttributeNode!=="undefined"&&m.getAttributeNode("id");return m.nodeType===1&&p&&p.nodeValue===q}}l.removeChild(g);l=g=null})();(function(){var g=s.createElement("div");g.appendChild(s.createComment(""));if(g.getElementsByTagName("*").length>0)n.find.TAG=function(h,l){l=l.getElementsByTagName(h[1]);if(h[1]==="*"){h=[];for(var m=0;l[m];m++)l[m].nodeType===1&&h.push(l[m]);l=h}return l};g.innerHTML="<a href='#'></a>";
+if(g.firstChild&&typeof g.firstChild.getAttribute!=="undefined"&&g.firstChild.getAttribute("href")!=="#")n.attrHandle.href=function(h){return h.getAttribute("href",2)};g=null})();s.querySelectorAll&&function(){var g=k,h=s.createElement("div");h.innerHTML="<p class='TEST'></p>";if(!(h.querySelectorAll&&h.querySelectorAll(".TEST").length===0)){k=function(m,q,p,v){q=q||s;if(!v&&q.nodeType===9&&!x(q))try{return z(q.querySelectorAll(m),p)}catch(t){}return g(m,q,p,v)};for(var l in g)k[l]=g[l];h=null}}();
+(function(){var g=s.createElement("div");g.innerHTML="<div class='test e'></div><div class='test'></div>";if(!(!g.getElementsByClassName||g.getElementsByClassName("e").length===0)){g.lastChild.className="e";if(g.getElementsByClassName("e").length!==1){n.order.splice(1,0,"CLASS");n.find.CLASS=function(h,l,m){if(typeof l.getElementsByClassName!=="undefined"&&!m)return l.getElementsByClassName(h[1])};g=null}}})();var E=s.compareDocumentPosition?function(g,h){return!!(g.compareDocumentPosition(h)&16)}:
+function(g,h){return g!==h&&(g.contains?g.contains(h):true)},x=function(g){return(g=(g?g.ownerDocument||g:0).documentElement)?g.nodeName!=="HTML":false},ga=function(g,h){var l=[],m="",q;for(h=h.nodeType?[h]:h;q=n.match.PSEUDO.exec(g);){m+=q[0];g=g.replace(n.match.PSEUDO,"")}g=n.relative[g]?g+"*":g;q=0;for(var p=h.length;q<p;q++)k(g,h[q],l);return k.filter(m,l)};c.find=k;c.expr=k.selectors;c.expr[":"]=c.expr.filters;c.unique=k.uniqueSort;c.text=a;c.isXMLDoc=x;c.contains=E})();var eb=/Until$/,fb=/^(?:parents|prevUntil|prevAll)/,
+gb=/,/;R=Array.prototype.slice;var Ia=function(a,b,d){if(c.isFunction(b))return c.grep(a,function(e,j){return!!b.call(e,j,e)===d});else if(b.nodeType)return c.grep(a,function(e){return e===b===d});else if(typeof b==="string"){var f=c.grep(a,function(e){return e.nodeType===1});if(Ua.test(b))return c.filter(b,f,!d);else b=c.filter(b,f)}return c.grep(a,function(e){return c.inArray(e,b)>=0===d})};c.fn.extend({find:function(a){for(var b=this.pushStack("","find",a),d=0,f=0,e=this.length;f<e;f++){d=b.length;
+c.find(a,this[f],b);if(f>0)for(var j=d;j<b.length;j++)for(var i=0;i<d;i++)if(b[i]===b[j]){b.splice(j--,1);break}}return b},has:function(a){var b=c(a);return this.filter(function(){for(var d=0,f=b.length;d<f;d++)if(c.contains(this,b[d]))return true})},not:function(a){return this.pushStack(Ia(this,a,false),"not",a)},filter:function(a){return this.pushStack(Ia(this,a,true),"filter",a)},is:function(a){return!!a&&c.filter(a,this).length>0},closest:function(a,b){if(c.isArray(a)){var d=[],f=this[0],e,j=
+{},i;if(f&&a.length){e=0;for(var o=a.length;e<o;e++){i=a[e];j[i]||(j[i]=c.expr.match.POS.test(i)?c(i,b||this.context):i)}for(;f&&f.ownerDocument&&f!==b;){for(i in j){e=j[i];if(e.jquery?e.index(f)>-1:c(f).is(e)){d.push({selector:i,elem:f});delete j[i]}}f=f.parentNode}}return d}var k=c.expr.match.POS.test(a)?c(a,b||this.context):null;return this.map(function(n,r){for(;r&&r.ownerDocument&&r!==b;){if(k?k.index(r)>-1:c(r).is(a))return r;r=r.parentNode}return null})},index:function(a){if(!a||typeof a===
+"string")return c.inArray(this[0],a?c(a):this.parent().children());return c.inArray(a.jquery?a[0]:a,this)},add:function(a,b){a=typeof a==="string"?c(a,b||this.context):c.makeArray(a);b=c.merge(this.get(),a);return this.pushStack(qa(a[0])||qa(b[0])?b:c.unique(b))},andSelf:function(){return this.add(this.prevObject)}});c.each({parent:function(a){return(a=a.parentNode)&&a.nodeType!==11?a:null},parents:function(a){return c.dir(a,"parentNode")},parentsUntil:function(a,b,d){return c.dir(a,"parentNode",
+d)},next:function(a){return c.nth(a,2,"nextSibling")},prev:function(a){return c.nth(a,2,"previousSibling")},nextAll:function(a){return c.dir(a,"nextSibling")},prevAll:function(a){return c.dir(a,"previousSibling")},nextUntil:function(a,b,d){return c.dir(a,"nextSibling",d)},prevUntil:function(a,b,d){return c.dir(a,"previousSibling",d)},siblings:function(a){return c.sibling(a.parentNode.firstChild,a)},children:function(a){return c.sibling(a.firstChild)},contents:function(a){return c.nodeName(a,"iframe")?
+a.contentDocument||a.contentWindow.document:c.makeArray(a.childNodes)}},function(a,b){c.fn[a]=function(d,f){var e=c.map(this,b,d);eb.test(a)||(f=d);if(f&&typeof f==="string")e=c.filter(f,e);e=this.length>1?c.unique(e):e;if((this.length>1||gb.test(f))&&fb.test(a))e=e.reverse();return this.pushStack(e,a,R.call(arguments).join(","))}});c.extend({filter:function(a,b,d){if(d)a=":not("+a+")";return c.find.matches(a,b)},dir:function(a,b,d){var f=[];for(a=a[b];a&&a.nodeType!==9&&(d===w||a.nodeType!==1||!c(a).is(d));){a.nodeType===
+1&&f.push(a);a=a[b]}return f},nth:function(a,b,d){b=b||1;for(var f=0;a;a=a[d])if(a.nodeType===1&&++f===b)break;return a},sibling:function(a,b){for(var d=[];a;a=a.nextSibling)a.nodeType===1&&a!==b&&d.push(a);return d}});var Ja=/ jQuery\d+="(?:\d+|null)"/g,V=/^\s+/,Ka=/(<([\w:]+)[^>]*?)\/>/g,hb=/^(?:area|br|col|embed|hr|img|input|link|meta|param)$/i,La=/<([\w:]+)/,ib=/<tbody/i,jb=/<|&#?\w+;/,ta=/<script|<object|<embed|<option|<style/i,ua=/checked\s*(?:[^=]|=\s*.checked.)/i,Ma=function(a,b,d){return hb.test(d)?
+a:b+"></"+d+">"},F={option:[1,"<select multiple='multiple'>","</select>"],legend:[1,"<fieldset>","</fieldset>"],thead:[1,"<table>","</table>"],tr:[2,"<table><tbody>","</tbody></table>"],td:[3,"<table><tbody><tr>","</tr></tbody></table>"],col:[2,"<table><tbody></tbody><colgroup>","</colgroup></table>"],area:[1,"<map>","</map>"],_default:[0,"",""]};F.optgroup=F.option;F.tbody=F.tfoot=F.colgroup=F.caption=F.thead;F.th=F.td;if(!c.support.htmlSerialize)F._default=[1,"div<div>","</div>"];c.fn.extend({text:function(a){if(c.isFunction(a))return this.each(function(b){var d=
+c(this);d.text(a.call(this,b,d.text()))});if(typeof a!=="object"&&a!==w)return this.empty().append((this[0]&&this[0].ownerDocument||s).createTextNode(a));return c.text(this)},wrapAll:function(a){if(c.isFunction(a))return this.each(function(d){c(this).wrapAll(a.call(this,d))});if(this[0]){var b=c(a,this[0].ownerDocument).eq(0).clone(true);this[0].parentNode&&b.insertBefore(this[0]);b.map(function(){for(var d=this;d.firstChild&&d.firstChild.nodeType===1;)d=d.firstChild;return d}).append(this)}return this},
+wrapInner:function(a){if(c.isFunction(a))return this.each(function(b){c(this).wrapInner(a.call(this,b))});return this.each(function(){var b=c(this),d=b.contents();d.length?d.wrapAll(a):b.append(a)})},wrap:function(a){return this.each(function(){c(this).wrapAll(a)})},unwrap:function(){return this.parent().each(function(){c.nodeName(this,"body")||c(this).replaceWith(this.childNodes)}).end()},append:function(){return this.domManip(arguments,true,function(a){this.nodeType===1&&this.appendChild(a)})},
+prepend:function(){return this.domManip(arguments,true,function(a){this.nodeType===1&&this.insertBefore(a,this.firstChild)})},before:function(){if(this[0]&&this[0].parentNode)return this.domManip(arguments,false,function(b){this.parentNode.insertBefore(b,this)});else if(arguments.length){var a=c(arguments[0]);a.push.apply(a,this.toArray());return this.pushStack(a,"before",arguments)}},after:function(){if(this[0]&&this[0].parentNode)return this.domManip(arguments,false,function(b){this.parentNode.insertBefore(b,
+this.nextSibling)});else if(arguments.length){var a=this.pushStack(this,"after",arguments);a.push.apply(a,c(arguments[0]).toArray());return a}},remove:function(a,b){for(var d=0,f;(f=this[d])!=null;d++)if(!a||c.filter(a,[f]).length){if(!b&&f.nodeType===1){c.cleanData(f.getElementsByTagName("*"));c.cleanData([f])}f.parentNode&&f.parentNode.removeChild(f)}return this},empty:function(){for(var a=0,b;(b=this[a])!=null;a++)for(b.nodeType===1&&c.cleanData(b.getElementsByTagName("*"));b.firstChild;)b.removeChild(b.firstChild);
+return this},clone:function(a){var b=this.map(function(){if(!c.support.noCloneEvent&&!c.isXMLDoc(this)){var d=this.outerHTML,f=this.ownerDocument;if(!d){d=f.createElement("div");d.appendChild(this.cloneNode(true));d=d.innerHTML}return c.clean([d.replace(Ja,"").replace(/=([^="'>\s]+\/)>/g,'="$1">').replace(V,"")],f)[0]}else return this.cloneNode(true)});if(a===true){ra(this,b);ra(this.find("*"),b.find("*"))}return b},html:function(a){if(a===w)return this[0]&&this[0].nodeType===1?this[0].innerHTML.replace(Ja,
+""):null;else if(typeof a==="string"&&!ta.test(a)&&(c.support.leadingWhitespace||!V.test(a))&&!F[(La.exec(a)||["",""])[1].toLowerCase()]){a=a.replace(Ka,Ma);try{for(var b=0,d=this.length;b<d;b++)if(this[b].nodeType===1){c.cleanData(this[b].getElementsByTagName("*"));this[b].innerHTML=a}}catch(f){this.empty().append(a)}}else c.isFunction(a)?this.each(function(e){var j=c(this),i=j.html();j.empty().append(function(){return a.call(this,e,i)})}):this.empty().append(a);return this},replaceWith:function(a){if(this[0]&&
+this[0].parentNode){if(c.isFunction(a))return this.each(function(b){var d=c(this),f=d.html();d.replaceWith(a.call(this,b,f))});if(typeof a!=="string")a=c(a).detach();return this.each(function(){var b=this.nextSibling,d=this.parentNode;c(this).remove();b?c(b).before(a):c(d).append(a)})}else return this.pushStack(c(c.isFunction(a)?a():a),"replaceWith",a)},detach:function(a){return this.remove(a,true)},domManip:function(a,b,d){function f(u){return c.nodeName(u,"table")?u.getElementsByTagName("tbody")[0]||
+u.appendChild(u.ownerDocument.createElement("tbody")):u}var e,j,i=a[0],o=[],k;if(!c.support.checkClone&&arguments.length===3&&typeof i==="string"&&ua.test(i))return this.each(function(){c(this).domManip(a,b,d,true)});if(c.isFunction(i))return this.each(function(u){var z=c(this);a[0]=i.call(this,u,b?z.html():w);z.domManip(a,b,d)});if(this[0]){e=i&&i.parentNode;e=c.support.parentNode&&e&&e.nodeType===11&&e.childNodes.length===this.length?{fragment:e}:sa(a,this,o);k=e.fragment;if(j=k.childNodes.length===
+1?(k=k.firstChild):k.firstChild){b=b&&c.nodeName(j,"tr");for(var n=0,r=this.length;n<r;n++)d.call(b?f(this[n],j):this[n],n>0||e.cacheable||this.length>1?k.cloneNode(true):k)}o.length&&c.each(o,Qa)}return this}});c.fragments={};c.each({appendTo:"append",prependTo:"prepend",insertBefore:"before",insertAfter:"after",replaceAll:"replaceWith"},function(a,b){c.fn[a]=function(d){var f=[];d=c(d);var e=this.length===1&&this[0].parentNode;if(e&&e.nodeType===11&&e.childNodes.length===1&&d.length===1){d[b](this[0]);
+return this}else{e=0;for(var j=d.length;e<j;e++){var i=(e>0?this.clone(true):this).get();c.fn[b].apply(c(d[e]),i);f=f.concat(i)}return this.pushStack(f,a,d.selector)}}});c.extend({clean:function(a,b,d,f){b=b||s;if(typeof b.createElement==="undefined")b=b.ownerDocument||b[0]&&b[0].ownerDocument||s;for(var e=[],j=0,i;(i=a[j])!=null;j++){if(typeof i==="number")i+="";if(i){if(typeof i==="string"&&!jb.test(i))i=b.createTextNode(i);else if(typeof i==="string"){i=i.replace(Ka,Ma);var o=(La.exec(i)||["",
+""])[1].toLowerCase(),k=F[o]||F._default,n=k[0],r=b.createElement("div");for(r.innerHTML=k[1]+i+k[2];n--;)r=r.lastChild;if(!c.support.tbody){n=ib.test(i);o=o==="table"&&!n?r.firstChild&&r.firstChild.childNodes:k[1]==="<table>"&&!n?r.childNodes:[];for(k=o.length-1;k>=0;--k)c.nodeName(o[k],"tbody")&&!o[k].childNodes.length&&o[k].parentNode.removeChild(o[k])}!c.support.leadingWhitespace&&V.test(i)&&r.insertBefore(b.createTextNode(V.exec(i)[0]),r.firstChild);i=r.childNodes}if(i.nodeType)e.push(i);else e=
+c.merge(e,i)}}if(d)for(j=0;e[j];j++)if(f&&c.nodeName(e[j],"script")&&(!e[j].type||e[j].type.toLowerCase()==="text/javascript"))f.push(e[j].parentNode?e[j].parentNode.removeChild(e[j]):e[j]);else{e[j].nodeType===1&&e.splice.apply(e,[j+1,0].concat(c.makeArray(e[j].getElementsByTagName("script"))));d.appendChild(e[j])}return e},cleanData:function(a){for(var b,d,f=c.cache,e=c.event.special,j=c.support.deleteExpando,i=0,o;(o=a[i])!=null;i++)if(d=o[c.expando]){b=f[d];if(b.events)for(var k in b.events)e[k]?
+c.event.remove(o,k):Ca(o,k,b.handle);if(j)delete o[c.expando];else o.removeAttribute&&o.removeAttribute(c.expando);delete f[d]}}});var kb=/z-?index|font-?weight|opacity|zoom|line-?height/i,Na=/alpha\([^)]*\)/,Oa=/opacity=([^)]*)/,ha=/float/i,ia=/-([a-z])/ig,lb=/([A-Z])/g,mb=/^-?\d+(?:px)?$/i,nb=/^-?\d/,ob={position:"absolute",visibility:"hidden",display:"block"},pb=["Left","Right"],qb=["Top","Bottom"],rb=s.defaultView&&s.defaultView.getComputedStyle,Pa=c.support.cssFloat?"cssFloat":"styleFloat",ja=
+function(a,b){return b.toUpperCase()};c.fn.css=function(a,b){return X(this,a,b,true,function(d,f,e){if(e===w)return c.curCSS(d,f);if(typeof e==="number"&&!kb.test(f))e+="px";c.style(d,f,e)})};c.extend({style:function(a,b,d){if(!a||a.nodeType===3||a.nodeType===8)return w;if((b==="width"||b==="height")&&parseFloat(d)<0)d=w;var f=a.style||a,e=d!==w;if(!c.support.opacity&&b==="opacity"){if(e){f.zoom=1;b=parseInt(d,10)+""==="NaN"?"":"alpha(opacity="+d*100+")";a=f.filter||c.curCSS(a,"filter")||"";f.filter=
+Na.test(a)?a.replace(Na,b):b}return f.filter&&f.filter.indexOf("opacity=")>=0?parseFloat(Oa.exec(f.filter)[1])/100+"":""}if(ha.test(b))b=Pa;b=b.replace(ia,ja);if(e)f[b]=d;return f[b]},css:function(a,b,d,f){if(b==="width"||b==="height"){var e,j=b==="width"?pb:qb;function i(){e=b==="width"?a.offsetWidth:a.offsetHeight;f!=="border"&&c.each(j,function(){f||(e-=parseFloat(c.curCSS(a,"padding"+this,true))||0);if(f==="margin")e+=parseFloat(c.curCSS(a,"margin"+this,true))||0;else e-=parseFloat(c.curCSS(a,
+"border"+this+"Width",true))||0})}a.offsetWidth!==0?i():c.swap(a,ob,i);return Math.max(0,Math.round(e))}return c.curCSS(a,b,d)},curCSS:function(a,b,d){var f,e=a.style;if(!c.support.opacity&&b==="opacity"&&a.currentStyle){f=Oa.test(a.currentStyle.filter||"")?parseFloat(RegExp.$1)/100+"":"";return f===""?"1":f}if(ha.test(b))b=Pa;if(!d&&e&&e[b])f=e[b];else if(rb){if(ha.test(b))b="float";b=b.replace(lb,"-$1").toLowerCase();e=a.ownerDocument.defaultView;if(!e)return null;if(a=e.getComputedStyle(a,null))f=
+a.getPropertyValue(b);if(b==="opacity"&&f==="")f="1"}else if(a.currentStyle){d=b.replace(ia,ja);f=a.currentStyle[b]||a.currentStyle[d];if(!mb.test(f)&&nb.test(f)){b=e.left;var j=a.runtimeStyle.left;a.runtimeStyle.left=a.currentStyle.left;e.left=d==="fontSize"?"1em":f||0;f=e.pixelLeft+"px";e.left=b;a.runtimeStyle.left=j}}return f},swap:function(a,b,d){var f={};for(var e in b){f[e]=a.style[e];a.style[e]=b[e]}d.call(a);for(e in b)a.style[e]=f[e]}});if(c.expr&&c.expr.filters){c.expr.filters.hidden=function(a){var b=
+a.offsetWidth,d=a.offsetHeight,f=a.nodeName.toLowerCase()==="tr";return b===0&&d===0&&!f?true:b>0&&d>0&&!f?false:c.curCSS(a,"display")==="none"};c.expr.filters.visible=function(a){return!c.expr.filters.hidden(a)}}var sb=J(),tb=/<script(.|\s)*?\/script>/gi,ub=/select|textarea/i,vb=/color|date|datetime|email|hidden|month|number|password|range|search|tel|text|time|url|week/i,N=/=\?(&|$)/,ka=/\?/,wb=/(\?|&)_=.*?(&|$)/,xb=/^(\w+:)?\/\/([^\/?#]+)/,yb=/%20/g,zb=c.fn.load;c.fn.extend({load:function(a,b,d){if(typeof a!==
+"string")return zb.call(this,a);else if(!this.length)return this;var f=a.indexOf(" ");if(f>=0){var e=a.slice(f,a.length);a=a.slice(0,f)}f="GET";if(b)if(c.isFunction(b)){d=b;b=null}else if(typeof b==="object"){b=c.param(b,c.ajaxSettings.traditional);f="POST"}var j=this;c.ajax({url:a,type:f,dataType:"html",data:b,complete:function(i,o){if(o==="success"||o==="notmodified")j.html(e?c("<div />").append(i.responseText.replace(tb,"")).find(e):i.responseText);d&&j.each(d,[i.responseText,o,i])}});return this},
+serialize:function(){return c.param(this.serializeArray())},serializeArray:function(){return this.map(function(){return this.elements?c.makeArray(this.elements):this}).filter(function(){return this.name&&!this.disabled&&(this.checked||ub.test(this.nodeName)||vb.test(this.type))}).map(function(a,b){a=c(this).val();return a==null?null:c.isArray(a)?c.map(a,function(d){return{name:b.name,value:d}}):{name:b.name,value:a}}).get()}});c.each("ajaxStart ajaxStop ajaxComplete ajaxError ajaxSuccess ajaxSend".split(" "),
+function(a,b){c.fn[b]=function(d){return this.bind(b,d)}});c.extend({get:function(a,b,d,f){if(c.isFunction(b)){f=f||d;d=b;b=null}return c.ajax({type:"GET",url:a,data:b,success:d,dataType:f})},getScript:function(a,b){return c.get(a,null,b,"script")},getJSON:function(a,b,d){return c.get(a,b,d,"json")},post:function(a,b,d,f){if(c.isFunction(b)){f=f||d;d=b;b={}}return c.ajax({type:"POST",url:a,data:b,success:d,dataType:f})},ajaxSetup:function(a){c.extend(c.ajaxSettings,a)},ajaxSettings:{url:location.href,
+global:true,type:"GET",contentType:"application/x-www-form-urlencoded",processData:true,async:true,xhr:A.XMLHttpRequest&&(A.location.protocol!=="file:"||!A.ActiveXObject)?function(){return new A.XMLHttpRequest}:function(){try{return new A.ActiveXObject("Microsoft.XMLHTTP")}catch(a){}},accepts:{xml:"application/xml, text/xml",html:"text/html",script:"text/javascript, application/javascript",json:"application/json, text/javascript",text:"text/plain",_default:"*/*"}},lastModified:{},etag:{},ajax:function(a){function b(){e.success&&
+e.success.call(k,o,i,x);e.global&&f("ajaxSuccess",[x,e])}function d(){e.complete&&e.complete.call(k,x,i);e.global&&f("ajaxComplete",[x,e]);e.global&&!--c.active&&c.event.trigger("ajaxStop")}function f(q,p){(e.context?c(e.context):c.event).trigger(q,p)}var e=c.extend(true,{},c.ajaxSettings,a),j,i,o,k=a&&a.context||e,n=e.type.toUpperCase();if(e.data&&e.processData&&typeof e.data!=="string")e.data=c.param(e.data,e.traditional);if(e.dataType==="jsonp"){if(n==="GET")N.test(e.url)||(e.url+=(ka.test(e.url)?
+"&":"?")+(e.jsonp||"callback")+"=?");else if(!e.data||!N.test(e.data))e.data=(e.data?e.data+"&":"")+(e.jsonp||"callback")+"=?";e.dataType="json"}if(e.dataType==="json"&&(e.data&&N.test(e.data)||N.test(e.url))){j=e.jsonpCallback||"jsonp"+sb++;if(e.data)e.data=(e.data+"").replace(N,"="+j+"$1");e.url=e.url.replace(N,"="+j+"$1");e.dataType="script";A[j]=A[j]||function(q){o=q;b();d();A[j]=w;try{delete A[j]}catch(p){}z&&z.removeChild(C)}}if(e.dataType==="script"&&e.cache===null)e.cache=false;if(e.cache===
+false&&n==="GET"){var r=J(),u=e.url.replace(wb,"$1_="+r+"$2");e.url=u+(u===e.url?(ka.test(e.url)?"&":"?")+"_="+r:"")}if(e.data&&n==="GET")e.url+=(ka.test(e.url)?"&":"?")+e.data;e.global&&!c.active++&&c.event.trigger("ajaxStart");r=(r=xb.exec(e.url))&&(r[1]&&r[1]!==location.protocol||r[2]!==location.host);if(e.dataType==="script"&&n==="GET"&&r){var z=s.getElementsByTagName("head")[0]||s.documentElement,C=s.createElement("script");C.src=e.url;if(e.scriptCharset)C.charset=e.scriptCharset;if(!j){var B=
+false;C.onload=C.onreadystatechange=function(){if(!B&&(!this.readyState||this.readyState==="loaded"||this.readyState==="complete")){B=true;b();d();C.onload=C.onreadystatechange=null;z&&C.parentNode&&z.removeChild(C)}}}z.insertBefore(C,z.firstChild);return w}var E=false,x=e.xhr();if(x){e.username?x.open(n,e.url,e.async,e.username,e.password):x.open(n,e.url,e.async);try{if(e.data||a&&a.contentType)x.setRequestHeader("Content-Type",e.contentType);if(e.ifModified){c.lastModified[e.url]&&x.setRequestHeader("If-Modified-Since",
+c.lastModified[e.url]);c.etag[e.url]&&x.setRequestHeader("If-None-Match",c.etag[e.url])}r||x.setRequestHeader("X-Requested-With","XMLHttpRequest");x.setRequestHeader("Accept",e.dataType&&e.accepts[e.dataType]?e.accepts[e.dataType]+", */*":e.accepts._default)}catch(ga){}if(e.beforeSend&&e.beforeSend.call(k,x,e)===false){e.global&&!--c.active&&c.event.trigger("ajaxStop");x.abort();return false}e.global&&f("ajaxSend",[x,e]);var g=x.onreadystatechange=function(q){if(!x||x.readyState===0||q==="abort"){E||
+d();E=true;if(x)x.onreadystatechange=c.noop}else if(!E&&x&&(x.readyState===4||q==="timeout")){E=true;x.onreadystatechange=c.noop;i=q==="timeout"?"timeout":!c.httpSuccess(x)?"error":e.ifModified&&c.httpNotModified(x,e.url)?"notmodified":"success";var p;if(i==="success")try{o=c.httpData(x,e.dataType,e)}catch(v){i="parsererror";p=v}if(i==="success"||i==="notmodified")j||b();else c.handleError(e,x,i,p);d();q==="timeout"&&x.abort();if(e.async)x=null}};try{var h=x.abort;x.abort=function(){x&&h.call(x);
+g("abort")}}catch(l){}e.async&&e.timeout>0&&setTimeout(function(){x&&!E&&g("timeout")},e.timeout);try{x.send(n==="POST"||n==="PUT"||n==="DELETE"?e.data:null)}catch(m){c.handleError(e,x,null,m);d()}e.async||g();return x}},handleError:function(a,b,d,f){if(a.error)a.error.call(a.context||a,b,d,f);if(a.global)(a.context?c(a.context):c.event).trigger("ajaxError",[b,a,f])},active:0,httpSuccess:function(a){try{return!a.status&&location.protocol==="file:"||a.status>=200&&a.status<300||a.status===304||a.status===
+1223||a.status===0}catch(b){}return false},httpNotModified:function(a,b){var d=a.getResponseHeader("Last-Modified"),f=a.getResponseHeader("Etag");if(d)c.lastModified[b]=d;if(f)c.etag[b]=f;return a.status===304||a.status===0},httpData:function(a,b,d){var f=a.getResponseHeader("content-type")||"",e=b==="xml"||!b&&f.indexOf("xml")>=0;a=e?a.responseXML:a.responseText;e&&a.documentElement.nodeName==="parsererror"&&c.error("parsererror");if(d&&d.dataFilter)a=d.dataFilter(a,b);if(typeof a==="string")if(b===
+"json"||!b&&f.indexOf("json")>=0)a=c.parseJSON(a);else if(b==="script"||!b&&f.indexOf("javascript")>=0)c.globalEval(a);return a},param:function(a,b){function d(i,o){if(c.isArray(o))c.each(o,function(k,n){b||/\[\]$/.test(i)?f(i,n):d(i+"["+(typeof n==="object"||c.isArray(n)?k:"")+"]",n)});else!b&&o!=null&&typeof o==="object"?c.each(o,function(k,n){d(i+"["+k+"]",n)}):f(i,o)}function f(i,o){o=c.isFunction(o)?o():o;e[e.length]=encodeURIComponent(i)+"="+encodeURIComponent(o)}var e=[];if(b===w)b=c.ajaxSettings.traditional;
+if(c.isArray(a)||a.jquery)c.each(a,function(){f(this.name,this.value)});else for(var j in a)d(j,a[j]);return e.join("&").replace(yb,"+")}});var la={},Ab=/toggle|show|hide/,Bb=/^([+-]=)?([\d+-.]+)(.*)$/,W,va=[["height","marginTop","marginBottom","paddingTop","paddingBottom"],["width","marginLeft","marginRight","paddingLeft","paddingRight"],["opacity"]];c.fn.extend({show:function(a,b){if(a||a===0)return this.animate(K("show",3),a,b);else{a=0;for(b=this.length;a<b;a++){var d=c.data(this[a],"olddisplay");
+this[a].style.display=d||"";if(c.css(this[a],"display")==="none"){d=this[a].nodeName;var f;if(la[d])f=la[d];else{var e=c("<"+d+" />").appendTo("body");f=e.css("display");if(f==="none")f="block";e.remove();la[d]=f}c.data(this[a],"olddisplay",f)}}a=0;for(b=this.length;a<b;a++)this[a].style.display=c.data(this[a],"olddisplay")||"";return this}},hide:function(a,b){if(a||a===0)return this.animate(K("hide",3),a,b);else{a=0;for(b=this.length;a<b;a++){var d=c.data(this[a],"olddisplay");!d&&d!=="none"&&c.data(this[a],
+"olddisplay",c.css(this[a],"display"))}a=0;for(b=this.length;a<b;a++)this[a].style.display="none";return this}},_toggle:c.fn.toggle,toggle:function(a,b){var d=typeof a==="boolean";if(c.isFunction(a)&&c.isFunction(b))this._toggle.apply(this,arguments);else a==null||d?this.each(function(){var f=d?a:c(this).is(":hidden");c(this)[f?"show":"hide"]()}):this.animate(K("toggle",3),a,b);return this},fadeTo:function(a,b,d){return this.filter(":hidden").css("opacity",0).show().end().animate({opacity:b},a,d)},
+animate:function(a,b,d,f){var e=c.speed(b,d,f);if(c.isEmptyObject(a))return this.each(e.complete);return this[e.queue===false?"each":"queue"](function(){var j=c.extend({},e),i,o=this.nodeType===1&&c(this).is(":hidden"),k=this;for(i in a){var n=i.replace(ia,ja);if(i!==n){a[n]=a[i];delete a[i];i=n}if(a[i]==="hide"&&o||a[i]==="show"&&!o)return j.complete.call(this);if((i==="height"||i==="width")&&this.style){j.display=c.css(this,"display");j.overflow=this.style.overflow}if(c.isArray(a[i])){(j.specialEasing=
+j.specialEasing||{})[i]=a[i][1];a[i]=a[i][0]}}if(j.overflow!=null)this.style.overflow="hidden";j.curAnim=c.extend({},a);c.each(a,function(r,u){var z=new c.fx(k,j,r);if(Ab.test(u))z[u==="toggle"?o?"show":"hide":u](a);else{var C=Bb.exec(u),B=z.cur(true)||0;if(C){u=parseFloat(C[2]);var E=C[3]||"px";if(E!=="px"){k.style[r]=(u||1)+E;B=(u||1)/z.cur(true)*B;k.style[r]=B+E}if(C[1])u=(C[1]==="-="?-1:1)*u+B;z.custom(B,u,E)}else z.custom(B,u,"")}});return true})},stop:function(a,b){var d=c.timers;a&&this.queue([]);
+this.each(function(){for(var f=d.length-1;f>=0;f--)if(d[f].elem===this){b&&d[f](true);d.splice(f,1)}});b||this.dequeue();return this}});c.each({slideDown:K("show",1),slideUp:K("hide",1),slideToggle:K("toggle",1),fadeIn:{opacity:"show"},fadeOut:{opacity:"hide"}},function(a,b){c.fn[a]=function(d,f){return this.animate(b,d,f)}});c.extend({speed:function(a,b,d){var f=a&&typeof a==="object"?a:{complete:d||!d&&b||c.isFunction(a)&&a,duration:a,easing:d&&b||b&&!c.isFunction(b)&&b};f.duration=c.fx.off?0:typeof f.duration===
+"number"?f.duration:c.fx.speeds[f.duration]||c.fx.speeds._default;f.old=f.complete;f.complete=function(){f.queue!==false&&c(this).dequeue();c.isFunction(f.old)&&f.old.call(this)};return f},easing:{linear:function(a,b,d,f){return d+f*a},swing:function(a,b,d,f){return(-Math.cos(a*Math.PI)/2+0.5)*f+d}},timers:[],fx:function(a,b,d){this.options=b;this.elem=a;this.prop=d;if(!b.orig)b.orig={}}});c.fx.prototype={update:function(){this.options.step&&this.options.step.call(this.elem,this.now,this);(c.fx.step[this.prop]||
+c.fx.step._default)(this);if((this.prop==="height"||this.prop==="width")&&this.elem.style)this.elem.style.display="block"},cur:function(a){if(this.elem[this.prop]!=null&&(!this.elem.style||this.elem.style[this.prop]==null))return this.elem[this.prop];return(a=parseFloat(c.css(this.elem,this.prop,a)))&&a>-10000?a:parseFloat(c.curCSS(this.elem,this.prop))||0},custom:function(a,b,d){function f(j){return e.step(j)}this.startTime=J();this.start=a;this.end=b;this.unit=d||this.unit||"px";this.now=this.start;
+this.pos=this.state=0;var e=this;f.elem=this.elem;if(f()&&c.timers.push(f)&&!W)W=setInterval(c.fx.tick,13)},show:function(){this.options.orig[this.prop]=c.style(this.elem,this.prop);this.options.show=true;this.custom(this.prop==="width"||this.prop==="height"?1:0,this.cur());c(this.elem).show()},hide:function(){this.options.orig[this.prop]=c.style(this.elem,this.prop);this.options.hide=true;this.custom(this.cur(),0)},step:function(a){var b=J(),d=true;if(a||b>=this.options.duration+this.startTime){this.now=
+this.end;this.pos=this.state=1;this.update();this.options.curAnim[this.prop]=true;for(var f in this.options.curAnim)if(this.options.curAnim[f]!==true)d=false;if(d){if(this.options.display!=null){this.elem.style.overflow=this.options.overflow;a=c.data(this.elem,"olddisplay");this.elem.style.display=a?a:this.options.display;if(c.css(this.elem,"display")==="none")this.elem.style.display="block"}this.options.hide&&c(this.elem).hide();if(this.options.hide||this.options.show)for(var e in this.options.curAnim)c.style(this.elem,
+e,this.options.orig[e]);this.options.complete.call(this.elem)}return false}else{e=b-this.startTime;this.state=e/this.options.duration;a=this.options.easing||(c.easing.swing?"swing":"linear");this.pos=c.easing[this.options.specialEasing&&this.options.specialEasing[this.prop]||a](this.state,e,0,1,this.options.duration);this.now=this.start+(this.end-this.start)*this.pos;this.update()}return true}};c.extend(c.fx,{tick:function(){for(var a=c.timers,b=0;b<a.length;b++)a[b]()||a.splice(b--,1);a.length||
+c.fx.stop()},stop:function(){clearInterval(W);W=null},speeds:{slow:600,fast:200,_default:400},step:{opacity:function(a){c.style(a.elem,"opacity",a.now)},_default:function(a){if(a.elem.style&&a.elem.style[a.prop]!=null)a.elem.style[a.prop]=(a.prop==="width"||a.prop==="height"?Math.max(0,a.now):a.now)+a.unit;else a.elem[a.prop]=a.now}}});if(c.expr&&c.expr.filters)c.expr.filters.animated=function(a){return c.grep(c.timers,function(b){return a===b.elem}).length};c.fn.offset="getBoundingClientRect"in s.documentElement?
+function(a){var b=this[0];if(a)return this.each(function(e){c.offset.setOffset(this,a,e)});if(!b||!b.ownerDocument)return null;if(b===b.ownerDocument.body)return c.offset.bodyOffset(b);var d=b.getBoundingClientRect(),f=b.ownerDocument;b=f.body;f=f.documentElement;return{top:d.top+(self.pageYOffset||c.support.boxModel&&f.scrollTop||b.scrollTop)-(f.clientTop||b.clientTop||0),left:d.left+(self.pageXOffset||c.support.boxModel&&f.scrollLeft||b.scrollLeft)-(f.clientLeft||b.clientLeft||0)}}:function(a){var b=
+this[0];if(a)return this.each(function(r){c.offset.setOffset(this,a,r)});if(!b||!b.ownerDocument)return null;if(b===b.ownerDocument.body)return c.offset.bodyOffset(b);c.offset.initialize();var d=b.offsetParent,f=b,e=b.ownerDocument,j,i=e.documentElement,o=e.body;f=(e=e.defaultView)?e.getComputedStyle(b,null):b.currentStyle;for(var k=b.offsetTop,n=b.offsetLeft;(b=b.parentNode)&&b!==o&&b!==i;){if(c.offset.supportsFixedPosition&&f.position==="fixed")break;j=e?e.getComputedStyle(b,null):b.currentStyle;
+k-=b.scrollTop;n-=b.scrollLeft;if(b===d){k+=b.offsetTop;n+=b.offsetLeft;if(c.offset.doesNotAddBorder&&!(c.offset.doesAddBorderForTableAndCells&&/^t(able|d|h)$/i.test(b.nodeName))){k+=parseFloat(j.borderTopWidth)||0;n+=parseFloat(j.borderLeftWidth)||0}f=d;d=b.offsetParent}if(c.offset.subtractsBorderForOverflowNotVisible&&j.overflow!=="visible"){k+=parseFloat(j.borderTopWidth)||0;n+=parseFloat(j.borderLeftWidth)||0}f=j}if(f.position==="relative"||f.position==="static"){k+=o.offsetTop;n+=o.offsetLeft}if(c.offset.supportsFixedPosition&&
+f.position==="fixed"){k+=Math.max(i.scrollTop,o.scrollTop);n+=Math.max(i.scrollLeft,o.scrollLeft)}return{top:k,left:n}};c.offset={initialize:function(){var a=s.body,b=s.createElement("div"),d,f,e,j=parseFloat(c.curCSS(a,"marginTop",true))||0;c.extend(b.style,{position:"absolute",top:0,left:0,margin:0,border:0,width:"1px",height:"1px",visibility:"hidden"});b.innerHTML="<div style='position:absolute;top:0;left:0;margin:0;border:5px solid #000;padding:0;width:1px;height:1px;'><div></div></div><table style='position:absolute;top:0;left:0;margin:0;border:5px solid #000;padding:0;width:1px;height:1px;' cellpadding='0' cellspacing='0'><tr><td></td></tr></table>";
+a.insertBefore(b,a.firstChild);d=b.firstChild;f=d.firstChild;e=d.nextSibling.firstChild.firstChild;this.doesNotAddBorder=f.offsetTop!==5;this.doesAddBorderForTableAndCells=e.offsetTop===5;f.style.position="fixed";f.style.top="20px";this.supportsFixedPosition=f.offsetTop===20||f.offsetTop===15;f.style.position=f.style.top="";d.style.overflow="hidden";d.style.position="relative";this.subtractsBorderForOverflowNotVisible=f.offsetTop===-5;this.doesNotIncludeMarginInBodyOffset=a.offsetTop!==j;a.removeChild(b);
+c.offset.initialize=c.noop},bodyOffset:function(a){var b=a.offsetTop,d=a.offsetLeft;c.offset.initialize();if(c.offset.doesNotIncludeMarginInBodyOffset){b+=parseFloat(c.curCSS(a,"marginTop",true))||0;d+=parseFloat(c.curCSS(a,"marginLeft",true))||0}return{top:b,left:d}},setOffset:function(a,b,d){if(/static/.test(c.curCSS(a,"position")))a.style.position="relative";var f=c(a),e=f.offset(),j=parseInt(c.curCSS(a,"top",true),10)||0,i=parseInt(c.curCSS(a,"left",true),10)||0;if(c.isFunction(b))b=b.call(a,
+d,e);d={top:b.top-e.top+j,left:b.left-e.left+i};"using"in b?b.using.call(a,d):f.css(d)}};c.fn.extend({position:function(){if(!this[0])return null;var a=this[0],b=this.offsetParent(),d=this.offset(),f=/^body|html$/i.test(b[0].nodeName)?{top:0,left:0}:b.offset();d.top-=parseFloat(c.curCSS(a,"marginTop",true))||0;d.left-=parseFloat(c.curCSS(a,"marginLeft",true))||0;f.top+=parseFloat(c.curCSS(b[0],"borderTopWidth",true))||0;f.left+=parseFloat(c.curCSS(b[0],"borderLeftWidth",true))||0;return{top:d.top-
+f.top,left:d.left-f.left}},offsetParent:function(){return this.map(function(){for(var a=this.offsetParent||s.body;a&&!/^body|html$/i.test(a.nodeName)&&c.css(a,"position")==="static";)a=a.offsetParent;return a})}});c.each(["Left","Top"],function(a,b){var d="scroll"+b;c.fn[d]=function(f){var e=this[0],j;if(!e)return null;if(f!==w)return this.each(function(){if(j=wa(this))j.scrollTo(!a?f:c(j).scrollLeft(),a?f:c(j).scrollTop());else this[d]=f});else return(j=wa(e))?"pageXOffset"in j?j[a?"pageYOffset":
+"pageXOffset"]:c.support.boxModel&&j.document.documentElement[d]||j.document.body[d]:e[d]}});c.each(["Height","Width"],function(a,b){var d=b.toLowerCase();c.fn["inner"+b]=function(){return this[0]?c.css(this[0],d,false,"padding"):null};c.fn["outer"+b]=function(f){return this[0]?c.css(this[0],d,false,f?"margin":"border"):null};c.fn[d]=function(f){var e=this[0];if(!e)return f==null?null:this;if(c.isFunction(f))return this.each(function(j){var i=c(this);i[d](f.call(this,j,i[d]()))});return"scrollTo"in
+e&&e.document?e.document.compatMode==="CSS1Compat"&&e.document.documentElement["client"+b]||e.document.body["client"+b]:e.nodeType===9?Math.max(e.documentElement["client"+b],e.body["scroll"+b],e.documentElement["scroll"+b],e.body["offset"+b],e.documentElement["offset"+b]):f===w?c.css(e,d):this.css(d,typeof f==="string"?f:f+"px")}});A.jQuery=A.$=c})(window);
diff --git a/javascripts/lib/raphael.js b/javascripts/lib/raphael.js
index 8c45c3d..222f87f 100644
--- a/javascripts/lib/raphael.js
+++ b/javascripts/lib/raphael.js
@@ -3055,6 +3055,24 @@ Raphael = (function () {
     Element[proto].animateWith = function (element, params, ms, easing, callback) {
         animationElements[element.id] && (params.start = animationElements[element.id].start);
         return this.animate(params, ms, easing, callback);
+    };
+	// hack! http://groups.google.com/group/raphaeljs/browse_thread/thread/f5dc3ea149d3540b
+	Element[proto].moveTo = function(x, y){
+            switch (this.type) {
+                    case "path":
+                            var path = pathToRelative(this.attrs.path),
+                                    dim = pathDimensions(path),
+                                    dx = (path[0][1] - dim.x) + x,
+                                    dy = (path[0][2] - dim.y) + y;
+                            path[0][1] = dx;
+                            path[0][2] = dy;
+                            return this.attr({path: path});
+                            break;
+                    default:
+                            return this.attr({x: x, y: y});
+                    break;
+            }
+            return this;
     };
     Element[proto].animateAlong = along();
     Element[proto].animateAlongBack = along(1);
diff --git a/javascripts/main.js b/javascripts/main.js
deleted file mode 100644
index dc3c98b..0000000
--- a/javascripts/main.js
+++ /dev/null
@@ -1,28 +0,0 @@
-// globals
-var EPSILON     = '~';
-var NEXTSTATE   = 0;
-var EMPTYSYMBOL = '%';
-var ALPHABET    = 'abc'+EMPTYSYMBOL;
-var REDELIMITER = '$';
-var regex       = 'a*b|b*a' //(a|b)*'//'a(a|b)*a');
-var word	    = 'ba'; //'abba';
-
-
-function main() {
-	// parse regular expression
-	var parser = new RegexParser();
-	var nfa    = parser.parse(regex);
-	document.write('Parsing: '+parser.getErrorMessage()+'<br />');
-	
-	// simulate
-	var simulator = new NfaSimulator(nfa);
-	document.write('\''+word+'\' in <em>L</em>: '+simulator.simulate(word)+'<br />');
-	
-	// nfa -> dfa
-	document.write('<pre>');
-	var dfa = new Nfa2Dfa(nfa);
-	var ttable = dfa.do();
-	document.write('</pre>');
-	
-	//drawGraph()
-}
diff --git a/javascripts/uifunc.js b/javascripts/uifunc.js
new file mode 100644
index 0000000..48d0095
--- /dev/null
+++ b/javascripts/uifunc.js
@@ -0,0 +1,61 @@
+// 
+function checkLength(el, bId) {
+	if(el.value.length > 0) {
+		enable(bId);
+	} else {
+		disable(bId);
+	};
+};
+
+// 
+function enable(id) {
+		 $(id).removeAttr("disabled");
+};
+
+// 
+function disable(id) {
+	 $(id).attr("disabled","disabled");
+};
+
+// 
+function uiParse() {
+	var parser = new RegexParser();
+	nfa = parser.parse($('#regex').attr('value'));
+	$('#parseMessage').html('Parse: '+parser.getErrorMessage());
+	if (parser.getErrorMessage() != 'Ok') {
+		$('#parseMessage').removeClass('success');	
+		$('#parseMessage').addClass('failure');	
+		$('#regex').addClass('failure');
+	} else {
+		$('#parseMessage').removeClass('failure');
+		$('#regex').removeClass('failure');
+		$('#parseMessage').addClass('success');
+		$('#regex').addClass('success');
+		enable('#word');
+		var dfa = new Nfa2Dfa(nfa);
+		var ttable = dfa.do();
+		graph();
+		disable('#parseButton');
+	};
+	$('#parseMessage').effect("highlight", {}, 1000);
+};
+
+// 
+function uiSimulate() {
+	var simulator = new NfaSimulator(nfa);
+	var check = simulator.simulate($('#word').attr('value'));
+	if (!check) {
+		$('#checkMessage').html('Word not accepted');
+		$('#checkMessage').removeClass('success');
+		$('#word').removeClass('success');	
+		$('#checkMessage').addClass('failure');
+		$('#word').addClass('failure');	
+	} else {
+		$('#checkMessage').html('Word accepted');
+		$('#checkMessage').removeClass('failure');	
+		$('#word').removeClass('failure');	
+		$('#checkMessage').addClass('success');
+		$('#word').addClass('success');
+	};
+	$('#checkMessage').effect("highlight", {}, 1000);	
+};
diff --git a/presentation/simianer-regexvis.bib b/presentation/simianer-regexvis.bib
new file mode 100644
index 0000000..cba9c56
--- /dev/null
+++ b/presentation/simianer-regexvis.bib
@@ -0,0 +1,7 @@
+@booklet{goecke,
+    address = {Wiesbaden},
+    author  = {Goecke, R.},
+    title   = {Kommunikation von F{\"u}hrungskr{\"a}ften. Fallstudien zur Medienanwendung im oberen Management},
+    year    = {1997}
+}
+
diff --git a/presentation/simianer-regexvis.tex b/presentation/simianer-regexvis.tex
new file mode 100644
index 0000000..e361bf5
--- /dev/null
+++ b/presentation/simianer-regexvis.tex
@@ -0,0 +1,170 @@
+% template-beamer.tex
+% Patrick Simianer <p@simianer.de>
+% YYYY-MM-DD
+\documentclass[ignorenonframetext]{beamer}
+
+\mode<presentation>
+{
+  \usetheme{Singapore}
+  \usecolortheme{dolphin}
+  \usefonttheme{professionalfonts}
+  \useinnertheme{circles}
+  \useoutertheme{miniframes}
+  \setbeamertemplate{navigation symbols}{}
+  \beamersetuncovermixins{\opaqueness<1>{5}}{\opaqueness<2->{15}}
+  \setbeamertemplate{footline}[frame number]
+}
+
+\usepackage[utf8]{inputenc}
+\usepackage[T1]{fontenc}
+\usepackage[ngerman]{babel}
+\usepackage{lmodern}
+\usepackage{framed}
+
+
+\title[ktitel]{Autor(en)\\ Titel}
+\author{Patrick~Simianer \tiny 2508483\\\normalsize 1985-01-18}
+\date{Veranstaltung bei Dozent\\ Universitiät Heidelberg im Wintersemester 1985/86}
+
+\AtBeginSection[]{%
+\begin{frame}
+\tableofcontents[currentsection]
+\end{frame}
+}% AtBeginSection
+
+
+
+\begin{document}
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\frame[plain]{\titlepage}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[plain]
+    \frametitle{Gliederung}
+    \tableofcontents
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\section{Pause, Abblenden}
+
+
+\subsection{Pause}
+
+\begin{frame}
+    \frametitle{Test von Pause}
+
+    \begin{itemize}
+        \item Motivation 
+        .....
+        \pause
+        \item Experiment
+        \begin{itemize}
+            \item Aufbau des Experiments
+            .....
+        \end{itemize}
+    \end{itemize}
+\end{frame}
+
+
+\subsection{Abblenden}
+
+\begin{frame}
+    \frametitle{Abblenden}
+    
+    \begin{itemize}
+        \item<1-> Normal LaTeX class.
+        \item<2-> Easy overlays.
+        \item<3-> No external programs needed.      
+    \end{itemize}
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\section{Nur ein Test}
+
+
+\subsection{Test Blocks}
+
+\begin{frame}
+    \frametitle{Test Blocks}
+    
+    \begin{alert}{Titel des Blocks}
+        Dies steht in einem Block
+    \end{alert}
+    
+    \begin{example}{Titel des 2. Blocks}
+        Dies steht in einem Block\\ Das auch ...
+    \end{example}
+    
+    \begin{block}{Titel des 2. Blocks}
+        Dies steht in einem Block\\ Das auch ...
+    \end{block}
+  
+    \begin{framed}
+        \begin{block}{Titel des 2. Blocks}
+            Dies steht in einem Block\\ Das auch ...
+        \end{block}
+    \end{framed}
+\end{frame}
+
+
+\subsection{Nochmal Blocks}
+
+\begin{frame}
+    \frametitle{Nochmal Blocks}
+    
+    \begin{block}{Titel des Blocks}
+        Dies steht in einem Block\\ Das auch ...
+    \end{block}
+    \begin{block}{Titel des 2. Blocks}
+        Dies steht in einem Block\\ Das auch ...
+    \end{block}
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\section{Verbatim}
+
+
+\begin{frame}[fragile]
+\frametitle{Verbatim}
+\begin{verbatim}
+a
+b
+c
+d
+e
+f
+g
+\end{verbatim}
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[allowframebreaks]
+    \frametitle{Literatur}
+    \bibliographystyle{alpha}
+    \bibliography{beamer}
+    \nocite{*}
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+
+\end{document}
+
diff --git a/regexvis.html b/regexvis.html
index e431fe1..a881d82 100644
--- a/regexvis.html
+++ b/regexvis.html
@@ -6,28 +6,81 @@
     <meta http-equiv='Content-Language' content='en_EN' />
     <meta name='author' content='Patrick Simianer' />       
     
-    <title>RegexVis</title>
+    <title>Visualizing Regular Expressions (Patrick Simianer/'Endliche Automaten' SS2010)</title>
     
-    <link rel='stylesheet' type='text/css' href='stylesheets/RegexVis.css' />
+    <link rel='stylesheet' type='text/css' href='stylesheets/styles.css' />
     
-    <script type='text/javascript' src='javascripts/main.js'></script>
+    <script type='text/javascript' src='javascripts/lib/raphael.js'></script>
+    <script type='text/javascript' src='javascripts/lib/jquery.js'></script>
+    <script type='text/javascript' src='javascripts/lib/jquery-ui.js'></script>
+
+    <script type='text/javascript' src='javascripts/globals.js'></script>
     <script type='text/javascript' src='javascripts/NfaState.js'></script>
     <script type='text/javascript' src='javascripts/Nfa.js'></script>
     <script type='text/javascript' src='javascripts/RegexParser.js'></script>
     <script type='text/javascript' src='javascripts/Stack.js'></script>       
     <script type='text/javascript' src='javascripts/NfaSimulator.js'></script>
     <script type='text/javascript' src='javascripts/Nfa2Dfa.js'></script>
-    <script type='text/javascript' src='javascripts/lib/raphael.js'></script>
-    <script type='text/javascript' src='javascripts/lib/graffle.js'></script>
-    <!--<script type='text/javascript' src='javascripts/Dfa2Graph.js'></script>-->
+    <script type='text/javascript' src='javascripts/graph.js'></script>
+	<script type="text/javascript" src='javascripts/uifunc.js'></script>
 </head>
 
 <body>
 
-	<script type="text/javascript">
-		main();
-	</script>
-	<div id="holder"></div>
+	<div id="wrapper">
+		
+		<p style="line-height:1.3em">
+			<a class="message gray" href="#" onclick="$('#desc').toggle();">
+				<strong>Description</strong></a>
+			<span id="desc">&nbsp;Lorem ipsum dolor sit amet,
+			consectetur adipisicing elit, sed do eiusmod tempor incididunt ut
+			labore et dolore magna aliqua. Ut enim ad minim veniam, quis
+			nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo
+			consequat. Duis aute irure dolor in reprehenderit in voluptate
+			velit esse cillum dolore eu fugiat nulla pariatur. Excepteur sint
+			occaecat cupidatat non proident, sunt in culpa qui officia
+			deserunt mollit anim id est laborum.</span>
+		</p>
+		
+		<table>
+			<tr>
+				<td style="text-align:right"><strong style="color:#303030">Alphabet:</strong></td>
+				<td><strong style="color:#303030">
+					<script type="text/javascript" charset="utf-8">
+						document.write(ALPHABET.substr(0,ALPHABET.length-1));
+						</script>
+					</strong>
+				</td>	
+			</tr>
+			<tr>
+				<td style='text-align:right'><strong>Regular Expression:</strong></td>
+				<td><input type="text" name="regex" id="regex" value=""
+						onchange='checkLength(this, "#parseButton")'
+						onmouseout='checkLength(this, "#parseButton")' autocomplete="off" />
+						<input type="button" name="parseButton" id="parseButton"
+						value="Parse" disabled='disabled' autocomplete="off" onclick="uiParse()" />
+				</td>
+			</tr>
+			<tr>
+				<td style='text-align:right'><strong>Word:</strong></td>
+				<td><input type="text" name="word" id="word" value="" disabled='disabled'
+						onchange='checkLength(this, "#checkButton")'
+						onmouseout='checkLength(this, "#checkButton")' autocomplete="off" />
+					<input type="button" name="checkButton" id="checkButton"
+						value="Check" disabled='disabled' autocomplete="off" onclick="uiSimulate()" />
+					</td>
+				</tr>
+		</table>
+			
+		<p>
+			<a class='message gray' href='#' onclick="window.location.reload()"/>Reset</a>
+			<span id="parseMessage" class="message" style="display:none"></span>
+			<span id="checkMessage" class="message" style="display:none"></span>
+		</p>
+		
+		<div id="holder"></div>
+		
+	</div>
 
 </body>
 </html>
diff --git a/resources/RENFADFA.doc b/resources/RENFADFA.doc
deleted file mode 100644
index fb76173..0000000
Binary files a/resources/RENFADFA.doc and /dev/null differ
diff --git a/resources/RegExSource.zip b/resources/RegExSource.zip
deleted file mode 100644
index 6171e3d..0000000
Binary files a/resources/RegExSource.zip and /dev/null differ
diff --git a/resources/fsmnlp.ps b/resources/fsmnlp.ps
deleted file mode 100644
index 34379af..0000000
--- a/resources/fsmnlp.ps
+++ /dev/null
@@ -1,6674 +0,0 @@
-%!PS-Adobe-2.0
-%%Creator: dvips(k) 5.86 Copyright 1999 Radical Eye Software
-%%Pages: 16
-%%PageOrder: Ascend
-%%BoundingBox: 0 0 596 842
-%%DocumentFonts: Palatino-Bold Palatino-Roman CMSY6 Palatino-Italic
-%%+ CMMI10 CMR7 CMSY8 CMR6 Palatino-BoldItalic CMSY7 CMSY10 CMR10 CMMI7
-%%+ CMMI6 CMEX10 Courier CMMI9
-%%DocumentPaperSizes: a4
-%%EndComments
-%DVIPSWebPage: (www.radicaleye.com)
-%DVIPSCommandLine: dvips -f
-%DVIPSParameters: dpi=600, compressed, comments removed
-%DVIPSSource:  TeX output 2003.05.08:1610
-%%BeginProcSet: texc.pro
-/TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S
-N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72
-mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0
-0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{
-landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize
-mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR[
-matrix currentmatrix{A A round sub abs 0.00001 lt{round}if}forall round
-exch round exch]setmatrix}N/@landscape{/isls true N}B/@manualfeed{
-statusdict/manualfeed true put}B/@copies{/#copies X}B/FMat[1 0 0 -1 0 0]
-N/FBB[0 0 0 0]N/nn 0 N/IEn 0 N/ctr 0 N/df-tail{/nn 8 dict N nn begin
-/FontType 3 N/FontMatrix fntrx N/FontBBox FBB N string/base X array
-/BitMaps X/BuildChar{CharBuilder}N/Encoding IEn N end A{/foo setfont}2
-array copy cvx N load 0 nn put/ctr 0 N[}B/sf 0 N/df{/sf 1 N/fntrx FMat N
-df-tail}B/dfs{div/sf X/fntrx[sf 0 0 sf neg 0 0]N df-tail}B/E{pop nn A
-definefont setfont}B/Cw{Cd A length 5 sub get}B/Ch{Cd A length 4 sub get
-}B/Cx{128 Cd A length 3 sub get sub}B/Cy{Cd A length 2 sub get 127 sub}
-B/Cdx{Cd A length 1 sub get}B/Ci{Cd A type/stringtype ne{ctr get/ctr ctr
-1 add N}if}B/id 0 N/rw 0 N/rc 0 N/gp 0 N/cp 0 N/G 0 N/CharBuilder{save 3
-1 roll S A/base get 2 index get S/BitMaps get S get/Cd X pop/ctr 0 N Cdx
-0 Cx Cy Ch sub Cx Cw add Cy setcachedevice Cw Ch true[1 0 0 -1 -.1 Cx
-sub Cy .1 sub]/id Ci N/rw Cw 7 add 8 idiv string N/rc 0 N/gp 0 N/cp 0 N{
-rc 0 ne{rc 1 sub/rc X rw}{G}ifelse}imagemask restore}B/G{{id gp get/gp
-gp 1 add N A 18 mod S 18 idiv pl S get exec}loop}B/adv{cp add/cp X}B
-/chg{rw cp id gp 4 index getinterval putinterval A gp add/gp X adv}B/nd{
-/cp 0 N rw exit}B/lsh{rw cp 2 copy get A 0 eq{pop 1}{A 255 eq{pop 254}{
-A A add 255 and S 1 and or}ifelse}ifelse put 1 adv}B/rsh{rw cp 2 copy
-get A 0 eq{pop 128}{A 255 eq{pop 127}{A 2 idiv S 128 and or}ifelse}
-ifelse put 1 adv}B/clr{rw cp 2 index string putinterval adv}B/set{rw cp
-fillstr 0 4 index getinterval putinterval adv}B/fillstr 18 string 0 1 17
-{2 copy 255 put pop}for N/pl[{adv 1 chg}{adv 1 chg nd}{1 add chg}{1 add
-chg nd}{adv lsh}{adv lsh nd}{adv rsh}{adv rsh nd}{1 add adv}{/rc X nd}{
-1 add set}{1 add clr}{adv 2 chg}{adv 2 chg nd}{pop nd}]A{bind pop}
-forall N/D{/cc X A type/stringtype ne{]}if nn/base get cc ctr put nn
-/BitMaps get S ctr S sf 1 ne{A A length 1 sub A 2 index S get sf div put
-}if put/ctr ctr 1 add N}B/I{cc 1 add D}B/bop{userdict/bop-hook known{
-bop-hook}if/SI save N @rigin 0 0 moveto/V matrix currentmatrix A 1 get A
-mul exch 0 get A mul add .99 lt{/QV}{/RV}ifelse load def pop pop}N/eop{
-SI restore userdict/eop-hook known{eop-hook}if showpage}N/@start{
-userdict/start-hook known{start-hook}if pop/VResolution X/Resolution X
-1000 div/DVImag X/IEn 256 array N 2 string 0 1 255{IEn S A 360 add 36 4
-index cvrs cvn put}for pop 65781.76 div/vsize X 65781.76 div/hsize X}N
-/p{show}N/RMat[1 0 0 -1 0 0]N/BDot 260 string N/Rx 0 N/Ry 0 N/V{}B/RV/v{
-/Ry X/Rx X V}B statusdict begin/product where{pop false[(Display)(NeXT)
-(LaserWriter 16/600)]{A length product length le{A length product exch 0
-exch getinterval eq{pop true exit}if}{pop}ifelse}forall}{false}ifelse
-end{{gsave TR -.1 .1 TR 1 1 scale Rx Ry false RMat{BDot}imagemask
-grestore}}{{gsave TR -.1 .1 TR Rx Ry scale 1 1 false RMat{BDot}
-imagemask grestore}}ifelse B/QV{gsave newpath transform round exch round
-exch itransform moveto Rx 0 rlineto 0 Ry neg rlineto Rx neg 0 rlineto
-fill grestore}B/a{moveto}B/delta 0 N/tail{A/delta X 0 rmoveto}B/M{S p
-delta add tail}B/b{S p tail}B/c{-4 M}B/d{-3 M}B/e{-2 M}B/f{-1 M}B/g{0 M}
-B/h{1 M}B/i{2 M}B/j{3 M}B/k{4 M}B/w{0 rmoveto}B/l{p -4 w}B/m{p -3 w}B/n{
-p -2 w}B/o{p -1 w}B/q{p 1 w}B/r{p 2 w}B/s{p 3 w}B/t{p 4 w}B/x{0 S
-rmoveto}B/y{3 2 roll p a}B/bos{/SS save N}B/eos{SS restore}B end
-
-%%EndProcSet
-%%BeginProcSet: pstricks.pro
-% PostScript prologue for pstricks.tex.
-% Version 97 patch 3, 98/06/01
-% For distribution, see pstricks.tex.
-%
-/tx@Dict 200 dict def tx@Dict begin
-/ADict 25 dict def
-/CM { matrix currentmatrix } bind def
-/SLW /setlinewidth load def
-/CLW /currentlinewidth load def
-/CP /currentpoint load def
-/ED { exch def } bind def
-/L /lineto load def
-/T /translate load def
-/TMatrix { } def
-/RAngle { 0 } def
-/Atan { /atan load stopped { pop pop 0 } if } def
-/Div { dup 0 eq { pop } { div } ifelse } def
-/NET { neg exch neg exch T } def
-/Pyth { dup mul exch dup mul add sqrt } def
-/PtoC { 2 copy cos mul 3 1 roll sin mul } def
-/PathLength@ { /z z y y1 sub x x1 sub Pyth add def /y1 y def /x1 x def }
-def
-/PathLength { flattenpath /z 0 def { /y1 ED /x1 ED /y2 y1 def /x2 x1 def
-} { /y ED /x ED PathLength@ } {} { /y y2 def /x x2 def PathLength@ }
-/pathforall load stopped { pop pop pop pop } if z } def
-/STP { .996264 dup scale } def
-/STV { SDict begin normalscale end STP  } def
-/DashLine { dup 0 gt { /a .5 def PathLength exch div } { pop /a 1 def
-PathLength } ifelse /b ED /x ED /y ED /z y x add def b a .5 sub 2 mul y
-mul sub z Div round z mul a .5 sub 2 mul y mul add b exch Div dup y mul
-/y ED x mul /x ED x 0 gt y 0 gt and { [ y x ] 1 a sub y mul } { [ 1 0 ]
-0 } ifelse setdash stroke } def
-/DotLine { /b PathLength def /a ED /z ED /y CLW def /z y z add def a 0 gt
-{ /b b a div def } { a 0 eq { /b b y sub def } { a -3 eq { /b b y add
-def } if } ifelse } ifelse [ 0 b b z Div round Div dup 0 le { pop 1 } if
-] a 0 gt { 0 } { y 2 div a -2 gt { neg } if } ifelse setdash 1
-setlinecap stroke } def
-/LineFill { gsave abs CLW add /a ED a 0 dtransform round exch round exch
-2 copy idtransform exch Atan rotate idtransform pop /a ED .25 .25
-% DG/SR modification begin - Dec. 12, 1997 - Patch 2
-%itransform translate pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a
-itransform pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a
-% DG/SR modification end
-Div cvi /x1 ED /y2 y2 y1 sub def clip newpath 2 setlinecap systemdict
-/setstrokeadjust known { true setstrokeadjust } if x2 x1 sub 1 add { x1
-% DG/SR modification begin - Jun.  1, 1998 - Patch 3 (from Michael Vulis)
-% a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore }
-% def
-a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore
-pop pop } def
-% DG/SR modification end
-/BeginArrow { ADict begin /@mtrx CM def gsave 2 copy T 2 index sub neg
-exch 3 index sub exch Atan rotate newpath } def
-/EndArrow { @mtrx setmatrix CP grestore end } def
-/Arrow { CLW mul add dup 2 div /w ED mul dup /h ED mul /a ED { 0 h T 1 -1
-scale } if w neg h moveto 0 0 L w h L w neg a neg rlineto gsave fill
-grestore } def
-/Tbar { CLW mul add /z ED z -2 div CLW 2 div moveto z 0 rlineto stroke 0
-CLW moveto } def
-/Bracket { CLW mul add dup CLW sub 2 div /x ED mul CLW add /y ED /z CLW 2
-div def x neg y moveto x neg CLW 2 div L x CLW 2 div L x y L stroke 0
-CLW moveto } def
-/RoundBracket { CLW mul add dup 2 div /x ED mul /y ED /mtrx CM def 0 CLW
-2 div T x y mul 0 ne { x y scale } if 1 1 moveto .85 .5 .35 0 0 0
-curveto -.35 0 -.85 .5 -1 1 curveto mtrx setmatrix stroke 0 CLW moveto }
-def
-/SD { 0 360 arc fill } def
-/EndDot { { /z DS def } { /z 0 def } ifelse /b ED 0 z DS SD b { 0 z DS
-CLW sub SD } if 0 DS z add CLW 4 div sub moveto } def
-/Shadow { [ { /moveto load } { /lineto load } { /curveto load } {
-/closepath load } /pathforall load stopped { pop pop pop pop CP /moveto
-load } if ] cvx newpath 3 1 roll T exec } def
-/NArray { aload length 2 div dup dup cvi eq not { exch pop } if /n exch
-cvi def } def
-/NArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop } if
-f { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def
-/Line { NArray n 0 eq not { n 1 eq { 0 0 /n 2 def } if ArrowA /n n 2 sub
-def n { Lineto } repeat CP 4 2 roll ArrowB L pop pop } if } def
-/Arcto { /a [ 6 -2 roll ] cvx def a r /arcto load stopped { 5 } { 4 }
-ifelse { pop } repeat a } def
-/CheckClosed { dup n 2 mul 1 sub index eq 2 index n 2 mul 1 add index eq
-and { pop pop /n n 1 sub def } if } def
-/Polygon { NArray n 2 eq { 0 0 /n 3 def } if n 3 lt { n { pop pop }
-repeat } { n 3 gt { CheckClosed } if n 2 mul -2 roll /y0 ED /x0 ED /y1
-ED /x1 ED x1 y1 /x1 x0 x1 add 2 div def /y1 y0 y1 add 2 div def x1 y1
-moveto /n n 2 sub def n { Lineto } repeat x1 y1 x0 y0 6 4 roll Lineto
-Lineto pop pop closepath } ifelse } def
-/Diamond { /mtrx CM def T rotate /h ED /w ED dup 0 eq { pop } { CLW mul
-neg /d ED /a w h Atan def /h d a sin Div h add def /w d a cos Div w add
-def } ifelse mark w 2 div h 2 div w 0 0 h neg w neg 0 0 h w 2 div h 2
-div /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx
-setmatrix } def
-% DG modification begin - Jan. 15, 1997
-%/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup 0 eq {
-%pop } { CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2
-%div dup cos exch sin Div mul sub def } ifelse mark 0 d w neg d 0 h w d 0
-%d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx
-%setmatrix } def
-/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup
-CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2
-div dup cos exch sin Div mul sub def mark 0 d w neg d 0 h w d 0
-d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx
-% DG/SR modification begin - Jun.  1, 1998 - Patch 3 (from Michael Vulis)
-% setmatrix } def
-setmatrix pop } def
-% DG/SR modification end
-/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth
-def } def
-/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth
-def } def
-/CC { /l0 l1 def /x1 x dx sub def /y1 y dy sub def /dx0 dx1 def /dy0 dy1
-def CCA /dx dx0 l1 c exp mul dx1 l0 c exp mul add def /dy dy0 l1 c exp
-mul dy1 l0 c exp mul add def /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos
-abs b exp a mul dx dy Pyth Div 2 div def /x2 x l0 dx mul m mul sub def
-/y2 y l0 dy mul m mul sub def /dx l1 dx mul m mul neg def /dy l1 dy mul
-m mul neg def } def
-/IC { /c c 1 add def c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if }
-ifelse /a a 2 mul 3 div 45 cos b exp div def CCA /dx 0 def /dy 0 def }
-def
-/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def
-/NC { CC x1 y1 x2 y2 x y curveto } def
-/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def
-/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def
-/NAC { x2 y2 x y curveto CC x1 y1 } def
-/EAC { x2 y2 x y ArrowB curveto pop pop } def
-/OpenCurve { NArray n 3 lt { n { pop pop } repeat } { BOC /n n 3 sub def
-n { NC } repeat EOC } ifelse } def
-/AltCurve { { false NArray n 2 mul 2 roll [ n 2 mul 3 sub 1 roll ] aload
-/Points ED n 2 mul -2 roll } { false NArray } ifelse n 4 lt { n { pop
-pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse } def
-/ClosedCurve { NArray n 3 lt { n { pop pop } repeat } { n 3 gt {
-CheckClosed } if 6 copy n 2 mul 6 add 6 roll IC CC x y moveto n { NC }
-repeat closepath pop pop } ifelse } def
-/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def
-/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def
-/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore }
-def
-/FontDot { DS 2 mul dup matrix scale matrix concatmatrix exch matrix
-rotate matrix concatmatrix exch findfont exch makefont setfont } def
-/Rect { x1 y1 y2 add 2 div moveto x1 y2 lineto x2 y2 lineto x2 y1 lineto
-x1 y1 lineto closepath } def
-/OvalFrame { x1 x2 eq y1 y2 eq or { pop pop x1 y1 moveto x2 y2 L } { y1
-y2 sub abs x1 x2 sub abs 2 copy gt { exch pop } { pop } ifelse 2 div
-exch { dup 3 1 roll mul exch } if 2 copy lt { pop } { exch pop } ifelse
-/b ED x1 y1 y2 add 2 div moveto x1 y2 x2 y2 b arcto x2 y2 x2 y1 b arcto
-x2 y1 x1 y1 b arcto x1 y1 x1 y2 b arcto 16 { pop } repeat closepath }
-ifelse } def
-/Frame { CLW mul /a ED 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add
-/y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED 1 index 0 eq {
-pop pop Rect } { OvalFrame } ifelse } def
-/BezierNArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop
-} if n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat f { ]
-aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def
-/OpenBezier { BezierNArray n 1 eq { pop pop } { ArrowA n 4 sub 3 idiv { 6
-2 roll 4 2 roll curveto } repeat 6 2 roll 4 2 roll ArrowB curveto }
-ifelse } def
-/ClosedBezier { BezierNArray n 1 eq { pop pop } { moveto n 1 sub 3 idiv {
-6 2 roll 4 2 roll curveto } repeat closepath } ifelse } def
-/BezierShowPoints { gsave Points aload length 2 div cvi /n ED moveto n 1
-sub { lineto } repeat CLW 2 div SLW [ 4 4 ] 0 setdash stroke grestore }
-def
-/Parab { /y0 exch def /x0 exch def /y1 exch def /x1 exch def /dx x0 x1
-sub 3 div def /dy y0 y1 sub 3 div def x0 dx sub y0 dy add x1 y1 ArrowA
-x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB curveto /Points [ x1 y1 x0
-y0 x0 2 mul x1 sub y1 ] def } def
-/Grid { newpath /a 4 string def /b ED /c ED /n ED cvi dup 1 lt { pop 1 }
-if /s ED s div dup 0 eq { pop 1 } if /dy ED s div dup 0 eq { pop 1 } if
-/dx ED dy div round dy mul /y0 ED dx div round dx mul /x0 ED dy div
-round cvi /y2 ED dx div round cvi /x2 ED dy div round cvi /y1 ED dx div
-round cvi /x1 ED /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def /w x2 x1 sub
-0 gt { 1 } { -1 } ifelse def b 0 gt { /z1 b 4 div CLW 2 div add def
-/Helvetica findfont b scalefont setfont /b b .95 mul CLW 2 div add def }
-if systemdict /setstrokeadjust known { true setstrokeadjust /t { } def }
-{ /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add
-exch itransform } bind def } ifelse gsave n 0 gt { 1 setlinecap [ 0 dy n
-div ] dy n div 2 div setdash } { 2 setlinecap } ifelse /i x1 def /f y1
-dy mul n 0 gt { dy n div 2 div h mul sub } if def /g y2 dy mul n 0 gt {
-dy n div 2 div h mul add } if def x2 x1 sub w mul 1 add dup 1000 gt {
-pop 1000 } if { i dx mul dup y0 moveto b 0 gt { gsave c i a cvs dup
-stringwidth pop /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse h 0 gt {b neg}
-{z1} ifelse rmoveto show grestore } if dup t f moveto g t L stroke /i i
-w add def } repeat grestore gsave n 0 gt
-% DG/SR modification begin - Nov. 7, 1997 - Patch 1
-%{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash }
-{ 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash }
-% DG/SR modification end
-{ 2 setlinecap } ifelse /i y1 def /f x1 dx mul
-n 0 gt { dx n div 2 div w mul sub } if def /g x2 dx mul n 0 gt { dx n
-div 2 div w mul add } if def y2 y1 sub h mul 1 add dup 1000 gt { pop
-1000 } if { newpath i dy mul dup x0 exch moveto b 0 gt { gsave c i a cvs
-dup stringwidth pop /z2 ED w 0 gt {z1 z2 add neg} {z1} ifelse h 0 gt
-{z1} {b neg} ifelse rmoveto show grestore } if dup f exch t moveto g
-exch t L stroke /i i h add def } repeat grestore } def
-/ArcArrow { /d ED /b ED /a ED gsave newpath 0 -1000 moveto clip newpath 0
-1 0 0 b grestore c mul /e ED pop pop pop r a e d PtoC y add exch x add
-exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c
-mul neg d } def
-/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def
-/Rot { CP CP translate 3 -1 roll neg rotate NET  } def
-/RotBegin { tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 }
-def } if /TMatrix [ TMatrix CM ] cvx def /a ED a Rot /RAngle [ RAngle
-dup a add ] cvx def } def
-/RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ]
-cvx def } def
-/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def
-/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def
-/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def
-/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b s
-abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b
-div w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } {
-h1 abs h sub dup s mul abs } ifelse } def
-/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div s
-mul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q
-{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 add
-exch } def
-/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible
-/IfVisible true def } if } { IfVisible { Invisible /IfVisible false def
-} if } ifelse } def
-/InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def
-/Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnit
-neg exch neg exch idtransform T moveto } def /BOL { BeginOL } def
-/IfVisible true def } def
-end
-% END pstricks.pro
-
-%%EndProcSet
-%%BeginProcSet: pst-dots.pro
-10 dict dup begin
-  /FontType 3 def
-  /FontMatrix [ .001 0 0 .001 0 0 ] def
-  /FontBBox [ 0 0 0 0 ] def
-  /Encoding 256 array def
-  0 1 255 { Encoding exch /.notdef put } for
-  Encoding
-    dup (b) 0 get /Bullet put
-    dup (c) 0 get /Circle put
-    dup (C) 0 get /BoldCircle put
-    dup (u) 0 get /SolidTriangle put
-    dup (t) 0 get /Triangle put
-    dup (T) 0 get /BoldTriangle put
-    dup (r) 0 get /SolidSquare put
-    dup (s) 0 get /Square put
-    dup (S) 0 get /BoldSquare put
-    dup (q) 0 get /SolidPentagon put
-    dup (p) 0 get /Pentagon put
-    (P) 0 get /BoldPentagon put
-  /Metrics 13 dict def
-  Metrics begin
-    /Bullet 1000 def
-    /Circle 1000 def
-    /BoldCircle 1000 def
-    /SolidTriangle 1344 def
-    /Triangle 1344 def
-    /BoldTriangle 1344 def
-    /SolidSquare 886 def
-    /Square 886 def
-    /BoldSquare 886 def
-    /SolidPentagon 1093.2 def
-    /Pentagon 1093.2 def
-    /BoldPentagon 1093.2 def
-    /.notdef 0 def
-  end
-  /BBoxes 13 dict def
-  BBoxes begin
-    /Circle { -550 -550 550 550 } def
-    /BoldCircle /Circle load def
-    /Bullet /Circle load def
-    /Triangle { -571.5 -330 571.5 660 } def
-    /BoldTriangle /Triangle load def
-    /SolidTriangle /Triangle load def
-    /Square { -450 -450 450 450 } def
-    /BoldSquare /Square load def
-    /SolidSquare /Square load def
-    /Pentagon { -546.6 -465 546.6 574.7 } def
-    /BoldPentagon /Pentagon load def
-    /SolidPentagon /Pentagon load def
-    /.notdef { 0 0 0 0 } def
-  end
-  /CharProcs 20 dict def
-  CharProcs begin
-    /Adjust {
-      2 copy dtransform floor .5 add exch floor .5 add exch idtransform
-      3 -1 roll div 3 1 roll exch div exch scale
-    } def
-    /CirclePath { 0 0 500 0 360 arc closepath } def
-    /Bullet { 500 500 Adjust CirclePath fill } def
-    /Circle { 500 500 Adjust CirclePath .9 .9 scale CirclePath eofill } def
-    /BoldCircle { 500 500 Adjust CirclePath .8 .8 scale CirclePath eofill } def
-    /BoldCircle { CirclePath .8 .8 scale CirclePath eofill } def
-    /TrianglePath {
-      0  660 moveto -571.5 -330 lineto 571.5 -330 lineto closepath
-    } def
-    /SolidTriangle { TrianglePath fill } def
-    /Triangle { TrianglePath .85 .85 scale TrianglePath eofill } def
-    /BoldTriangle { TrianglePath .7 .7 scale TrianglePath eofill } def
-    /SquarePath {
-      -450 450 moveto 450 450 lineto 450 -450 lineto -450 -450 lineto
-      closepath
-    } def
-    /SolidSquare { SquarePath fill } def
-    /Square { SquarePath .89 .89 scale SquarePath eofill } def
-    /BoldSquare { SquarePath .78 .78 scale SquarePath eofill } def
-    /PentagonPath {
-      -337.8 -465   moveto
-       337.8 -465   lineto
-       546.6  177.6 lineto
-         0    574.7 lineto
-      -546.6  177.6 lineto
-      closepath
-    } def
-    /SolidPentagon { PentagonPath fill } def
-    /Pentagon { PentagonPath .89 .89 scale PentagonPath eofill } def
-    /BoldPentagon { PentagonPath .78 .78 scale PentagonPath eofill } def
-    /.notdef { } def
-  end
-  /BuildGlyph {
-    exch
-    begin
-      Metrics 1 index get exec 0
-      BBoxes 3 index get exec
-      setcachedevice
-      CharProcs begin load exec end
-    end
-  } def
-  /BuildChar {
-    1 index /Encoding get exch get
-    1 index /BuildGlyph get exec
-  } bind def
-end
-/PSTricksDotFont exch definefont pop
-% END pst-dots.pro
-
-%%EndProcSet
-%%BeginProcSet: pst-node.pro
-% PostScript prologue for pst-node.tex.
-% Version 97 patch 1, 97/05/09.
-% For distribution, see pstricks.tex.
-%
-/tx@NodeDict 400 dict def tx@NodeDict begin
-tx@Dict begin /T /translate load def end
-/NewNode { gsave /next ED dict dup 3 1 roll def exch { dup 3 1 roll def }
-if begin tx@Dict begin STV CP T exec end /NodeMtrx CM def next end
-grestore } def
-/InitPnode { /Y ED /X ED /NodePos { NodeSep Cos mul NodeSep Sin mul } def
-} def
-/InitCnode { /r ED /Y ED /X ED /NodePos { NodeSep r add dup Cos mul exch
-Sin mul } def } def
-/GetRnodePos { Cos 0 gt { /dx r NodeSep add def } { /dx l NodeSep sub def
-} ifelse Sin 0 gt { /dy u NodeSep add def } { /dy d NodeSep sub def }
-ifelse dx Sin mul abs dy Cos mul abs gt { dy Cos mul Sin div dy } { dx
-dup Sin mul Cos Div } ifelse } def
-/InitRnode { /Y ED /X ED X sub /r ED /l X neg def Y add neg /d ED Y sub
-/u ED /NodePos { GetRnodePos } def } def
-/DiaNodePos { w h mul w Sin mul abs h Cos mul abs add Div NodeSep add dup
-Cos mul exch Sin mul } def
-/TriNodePos { Sin s lt { d NodeSep sub dup Cos mul Sin Div exch } { w h
-mul w Sin mul h Cos abs mul add Div NodeSep add dup Cos mul exch Sin mul
-} ifelse } def
-/InitTriNode { sub 2 div exch 2 div exch 2 copy T 2 copy 4 index index /d
-ED pop pop pop pop -90 mul rotate /NodeMtrx CM def /X 0 def /Y 0 def d
-sub abs neg /d ED d add /h ED 2 div h mul h d sub Div /w ED /s d w Atan
-sin def /NodePos { TriNodePos } def } def
-/OvalNodePos { /ww w NodeSep add def /hh h NodeSep add def Sin ww mul Cos
-hh mul Atan dup cos ww mul exch sin hh mul } def
-/GetCenter { begin X Y NodeMtrx transform CM itransform end } def
-/XYPos { dup sin exch cos Do /Cos ED /Sin ED /Dist ED Cos 0 gt { Dist
-Dist Sin mul Cos div } { Cos 0 lt { Dist neg Dist Sin mul Cos div neg }
-{ 0 Dist Sin mul } ifelse } ifelse Do } def
-/GetEdge { dup 0 eq { pop begin 1 0 NodeMtrx dtransform CM idtransform
-exch atan sub dup sin /Sin ED cos /Cos ED /NodeSep ED NodePos NodeMtrx
-dtransform CM idtransform end } { 1 eq {{exch}} {{}} ifelse /Do ED pop
-XYPos } ifelse } def
-/AddOffset { 1 index 0 eq { pop pop } { 2 copy 5 2 roll cos mul add 4 1
-roll sin mul sub exch } ifelse } def
-/GetEdgeA { NodeSepA AngleA NodeA NodeSepTypeA GetEdge OffsetA AngleA
-AddOffset yA add /yA1 ED xA add /xA1 ED } def
-/GetEdgeB { NodeSepB AngleB NodeB NodeSepTypeB GetEdge OffsetB AngleB
-AddOffset yB add /yB1 ED xB add /xB1 ED } def
-/GetArmA { ArmTypeA 0 eq { /xA2 ArmA AngleA cos mul xA1 add def /yA2 ArmA
-AngleA sin mul yA1 add def } { ArmTypeA 1 eq {{exch}} {{}} ifelse /Do ED
-ArmA AngleA XYPos OffsetA AngleA AddOffset yA add /yA2 ED xA add /xA2 ED
-} ifelse } def
-/GetArmB { ArmTypeB 0 eq { /xB2 ArmB AngleB cos mul xB1 add def /yB2 ArmB
-AngleB sin mul yB1 add def } { ArmTypeB 1 eq {{exch}} {{}} ifelse /Do ED
-ArmB AngleB XYPos OffsetB AngleB AddOffset yB add /yB2 ED xB add /xB2 ED
-} ifelse } def
-/InitNC { /b ED /a ED /NodeSepTypeB ED /NodeSepTypeA ED /NodeSepB ED
-/NodeSepA ED /OffsetB ED /OffsetA ED tx@NodeDict a known tx@NodeDict b
-known and dup { /NodeA a load def /NodeB b load def NodeA GetCenter /yA
-ED /xA ED NodeB GetCenter /yB ED /xB ED } if } def
-/LPutLine { 4 copy 3 -1 roll sub neg 3 1 roll sub Atan /NAngle ED 1 t sub
-mul 3 1 roll 1 t sub mul 4 1 roll t mul add /Y ED t mul add /X ED } def
-/LPutLines { mark LPutVar counttomark 2 div 1 sub /n ED t floor dup n gt
-{ pop n 1 sub /t 1 def } { dup t sub neg /t ED } ifelse cvi 2 mul { pop
-} repeat LPutLine cleartomark } def
-/BezierMidpoint { /y3 ED /x3 ED /y2 ED /x2 ED /y1 ED /x1 ED /y0 ED /x0 ED
-/t ED /cx x1 x0 sub 3 mul def /cy y1 y0 sub 3 mul def /bx x2 x1 sub 3
-mul cx sub def /by y2 y1 sub 3 mul cy sub def /ax x3 x0 sub cx sub bx
-sub def /ay y3 y0 sub cy sub by sub def ax t 3 exp mul bx t t mul mul
-add cx t mul add x0 add ay t 3 exp mul by t t mul mul add cy t mul add
-y0 add 3 ay t t mul mul mul 2 by t mul mul add cy add 3 ax t t mul mul
-mul 2 bx t mul mul add cx add atan /NAngle ED /Y ED /X ED } def
-/HPosBegin { yB yA ge { /t 1 t sub def } if /Y yB yA sub t mul yA add def
-} def
-/HPosEnd { /X Y yyA sub yyB yyA sub Div xxB xxA sub mul xxA add def
-/NAngle yyB yyA sub xxB xxA sub Atan def } def
-/HPutLine { HPosBegin /yyA ED /xxA ED /yyB ED /xxB ED HPosEnd  } def
-/HPutLines { HPosBegin yB yA ge { /check { le } def } { /check { ge } def
-} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { dup Y check { exit
-} { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark HPosEnd 
-} def
-/VPosBegin { xB xA lt { /t 1 t sub def } if /X xB xA sub t mul xA add def
-} def
-/VPosEnd { /Y X xxA sub xxB xxA sub Div yyB yyA sub mul yyA add def
-/NAngle yyB yyA sub xxB xxA sub Atan def } def
-/VPutLine { VPosBegin /yyA ED /xxA ED /yyB ED /xxB ED VPosEnd  } def
-/VPutLines { VPosBegin xB xA ge { /check { le } def } { /check { ge } def
-} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { 1 index X check {
-exit } { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark
-VPosEnd  } def
-/HPutCurve { gsave newpath /SaveLPutVar /LPutVar load def LPutVar 8 -2
-roll moveto curveto flattenpath /LPutVar [ {} {} {} {} pathforall ] cvx
-def grestore exec /LPutVar /SaveLPutVar load def } def
-/NCCoor { /AngleA yB yA sub xB xA sub Atan def /AngleB AngleA 180 add def
-GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 xA1 yA1 ] cvx def /LPutPos {
-LPutVar LPutLine } def /HPutPos { LPutVar HPutLine } def /VPutPos {
-LPutVar VPutLine } def LPutVar } def
-/NCLine { NCCoor tx@Dict begin ArrowA CP 4 2 roll ArrowB lineto pop pop
-end } def
-/NCLines { false NArray n 0 eq { NCLine } { 2 copy yA sub exch xA sub
-Atan /AngleA ED n 2 mul dup index exch index yB sub exch xB sub Atan
-/AngleB ED GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 n 2 mul 4 add 4 roll xA1
-yA1 ] cvx def mark LPutVar tx@Dict begin false Line end /LPutPos {
-LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def }
-ifelse } def
-/NCCurve { GetEdgeA GetEdgeB xA1 xB1 sub yA1 yB1 sub Pyth 2 div dup 3 -1
-roll mul /ArmA ED mul /ArmB ED /ArmTypeA 0 def /ArmTypeB 0 def GetArmA
-GetArmB xA2 yA2 xA1 yA1 tx@Dict begin ArrowA end xB2 yB2 xB1 yB1 tx@Dict
-begin ArrowB end curveto /LPutVar [ xA1 yA1 xA2 yA2 xB2 yB2 xB1 yB1 ]
-cvx def /LPutPos { t LPutVar BezierMidpoint } def /HPutPos { { HPutLines
-} HPutCurve } def /VPutPos { { VPutLines } HPutCurve } def } def
-/NCAngles { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate
-def xA2 yA2 mtrx transform pop xB2 yB2 mtrx transform exch pop mtrx
-itransform /y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA2
-yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end /LPutVar [ xB1
-yB1 xB2 yB2 x0 y0 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { LPutLines } def
-/HPutPos { HPutLines } def /VPutPos { VPutLines } def } def
-/NCAngle { GetEdgeA GetEdgeB GetArmB /mtrx AngleA matrix rotate def xB2
-yB2 mtrx itransform pop xA1 yA1 mtrx itransform exch pop mtrx transform
-/y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA1 yA1
-tx@Dict begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA1 yA1 ]
-cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos {
-VPutLines } def } def
-/NCBar { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate def
-xA2 yA2 mtrx itransform pop xB2 yB2 mtrx itransform pop sub dup 0 mtrx
-transform 3 -1 roll 0 gt { /yB2 exch yB2 add def /xB2 exch xB2 add def }
-{ /yA2 exch neg yA2 add def /xA2 exch neg xA2 add def } ifelse mark ArmB
-0 ne { xB1 yB1 } if xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict
-begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx
-def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos {
-VPutLines } def } def
-/NCDiag { GetEdgeA GetEdgeB GetArmA GetArmB mark ArmB 0 ne { xB1 yB1 } if
-xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end
-/LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def /LPutPos {
-LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def }
-def
-/NCDiagg { GetEdgeA GetArmA yB yA2 sub xB xA2 sub Atan 180 add /AngleB ED
-GetEdgeB mark xB1 yB1 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin
-false Line end /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def /LPutPos {
-LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def }
-def
-/NCLoop { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate
-def xA2 yA2 mtrx transform loopsize add /yA3 ED /xA3 ED /xB3 xB2 yB2
-mtrx transform pop def xB3 yA3 mtrx itransform /yB3 ED /xB3 ED xA3 yA3
-mtrx itransform /yA3 ED /xA3 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2
-xB3 yB3 xA3 yA3 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false
-Line end /LPutVar [ xB1 yB1 xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 xA1 yA1 ]
-cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos {
-VPutLines } def } def
-% DG/SR modification begin - May 9, 1997 - Patch 1
-%/NCCircle { 0 0 NodesepA nodeA \tx@GetEdge pop xA sub 2 div dup 2 exp r
-%r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add
-%exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360
-%mul add dup 5 1 roll 90 sub \tx@PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED
-/NCCircle { NodeSepA 0 NodeA 0 GetEdge pop 2 div dup 2 exp r
-r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add
-exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360
-mul add dup 5 1 roll 90 sub PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED
-% DG/SR modification end
-} def /HPutPos { LPutPos } def /VPutPos { LPutPos } def r AngleA 90 sub a add
-AngleA 270 add a sub tx@Dict begin /angleB ED /angleA ED /r ED /c 57.2957 r
-Div def /y ED /x ED } def
-/NCBox { /d ED /h ED /AngleB yB yA sub xB xA sub Atan def /AngleA AngleB
-180 add def GetEdgeA GetEdgeB /dx d AngleB sin mul def /dy d AngleB cos
-mul neg def /hx h AngleB sin mul neg def /hy h AngleB cos mul def
-/LPutVar [ xA1 hx add yA1 hy add xB1 hx add yB1 hy add xB1 dx add yB1 dy
-add xA1 dx add yA1 dy add ] cvx def /LPutPos { LPutLines } def /HPutPos
-{ xB yB xA yA LPutLine } def /VPutPos { HPutPos } def mark LPutVar
-tx@Dict begin false Polygon end } def
-/NCArcBox { /l ED neg /d ED /h ED /a ED /AngleA yB yA sub xB xA sub Atan
-def /AngleB AngleA 180 add def /tA AngleA a sub 90 add def /tB tA a 2
-mul add def /r xB xA sub tA cos tB cos sub Div dup 0 eq { pop 1 } if def
-/x0 xA r tA cos mul add def /y0 yA r tA sin mul add def /c 57.2958 r div
-def /AngleA AngleA a sub 180 add def /AngleB AngleB a add 180 add def
-GetEdgeA GetEdgeB /AngleA tA 180 add yA yA1 sub xA xA1 sub Pyth c mul
-sub def /AngleB tB 180 add yB yB1 sub xB xB1 sub Pyth c mul add def l 0
-eq { x0 y0 r h add AngleA AngleB arc x0 y0 r d add AngleB AngleA arcn }
-{ x0 y0 translate /tA AngleA l c mul add def /tB AngleB l c mul sub def
-0 0 r h add tA tB arc r h add AngleB PtoC r d add AngleB PtoC 2 copy 6 2
-roll l arcto 4 { pop } repeat r d add tB PtoC l arcto 4 { pop } repeat 0
-0 r d add tB tA arcn r d add AngleA PtoC r h add AngleA PtoC 2 copy 6 2
-roll l arcto 4 { pop } repeat r h add tA PtoC l arcto 4 { pop } repeat }
-ifelse closepath /LPutVar [ x0 y0 r AngleA AngleB h d ] cvx def /LPutPos
-{ LPutVar /d ED /h ED /AngleB ED /AngleA ED /r ED /y0 ED /x0 ED t 1 le {
-r h add AngleA 1 t sub mul AngleB t mul add dup 90 add /NAngle ED PtoC }
-{ t 2 lt { /NAngle AngleB 180 add def r 2 t sub h mul t 1 sub d mul add
-add AngleB PtoC } { t 3 lt { r d add AngleB 3 t sub mul AngleA 2 t sub
-mul add dup 90 sub /NAngle ED PtoC } { /NAngle AngleA 180 add def r 4 t
-sub d mul t 3 sub h mul add add AngleA PtoC } ifelse } ifelse } ifelse
-y0 add /Y ED x0 add /X ED } def /HPutPos { LPutPos } def /VPutPos {
-LPutPos } def } def
-/Tfan { /AngleA yB yA sub xB xA sub Atan def GetEdgeA w xA1 xB sub yA1 yB
-sub Pyth Pyth w Div CLW 2 div mul 2 div dup AngleA sin mul yA1 add /yA1
-ED AngleA cos mul xA1 add /xA1 ED /LPutVar [ xA1 yA1 m { xB w add yB xB
-w sub yB } { xB yB w sub xB yB w add } ifelse xA1 yA1 ] cvx def /LPutPos
-{ LPutLines } def /VPutPos@ { LPutVar flag { 8 4 roll pop pop pop pop }
-{ pop pop pop pop 4 2 roll } ifelse } def /VPutPos { VPutPos@ VPutLine }
-def /HPutPos { VPutPos@ HPutLine } def mark LPutVar tx@Dict begin
-/ArrowA { moveto } def /ArrowB { } def false Line closepath end } def
-/LPutCoor { NAngle tx@Dict begin /NAngle ED end gsave CM STV CP Y sub neg
-exch X sub neg exch moveto setmatrix CP grestore } def
-/LPut { tx@NodeDict /LPutPos known { LPutPos } { CP /Y ED /X ED /NAngle 0
-def } ifelse LPutCoor  } def
-/HPutAdjust { Sin Cos mul 0 eq { 0 } { d Cos mul Sin div flag not { neg }
-if h Cos mul Sin div flag { neg } if 2 copy gt { pop } { exch pop }
-ifelse } ifelse s add flag { r add neg } { l add } ifelse X add /X ED }
-def
-/VPutAdjust { Sin Cos mul 0 eq { 0 } { l Sin mul Cos div flag { neg } if
-r Sin mul Cos div flag not { neg } if 2 copy gt { pop } { exch pop }
-ifelse } ifelse s add flag { d add } { h add neg } ifelse Y add /Y ED }
-def
-end
-% END pst-node.pro
-
-%%EndProcSet
-%%BeginProcSet: 8r.enc
-% @@psencodingfile@{
-%   author = "S. Rahtz, P. MacKay, Alan Jeffrey, B. Horn, K. Berry",
-%   version = "0.6",
-%   date = "1 July 1998",
-%   filename = "8r.enc",
-%   email = "tex-fonts@@tug.org",
-%   docstring = "Encoding for TrueType or Type 1 fonts
-%                to be used with TeX."
-% @}
-% 
-% Idea is to have all the characters normally included in Type 1 fonts
-% available for typesetting. This is effectively the characters in Adobe
-% Standard Encoding + ISO Latin 1 + extra characters from Lucida.
-% 
-% Character code assignments were made as follows:
-% 
-% (1) the Windows ANSI characters are almost all in their Windows ANSI
-% positions, because some Windows users cannot easily reencode the
-% fonts, and it makes no difference on other systems. The only Windows
-% ANSI characters not available are those that make no sense for
-% typesetting -- rubout (127 decimal), nobreakspace (160), softhyphen
-% (173). quotesingle and grave are moved just because it's such an
-% irritation not having them in TeX positions.
-% 
-% (2) Remaining characters are assigned arbitrarily to the lower part
-% of the range, avoiding 0, 10 and 13 in case we meet dumb software.
-% 
-% (3) Y&Y Lucida Bright includes some extra text characters; in the
-% hopes that other PostScript fonts, perhaps created for public
-% consumption, will include them, they are included starting at 0x12.
-% 
-% (4) Remaining positions left undefined are for use in (hopefully)
-% upward-compatible revisions, if someday more characters are generally
-% available.
-% 
-% (5) hyphen appears twice for compatibility with both 
-% ASCII and Windows.
-% 
-/TeXBase1Encoding [
-% 0x00 (encoded characters from Adobe Standard not in Windows 3.1)
-  /.notdef /dotaccent /fi /fl
-  /fraction /hungarumlaut /Lslash /lslash
-  /ogonek /ring /.notdef
-  /breve /minus /.notdef 
-% These are the only two remaining unencoded characters, so may as
-% well include them.
-  /Zcaron /zcaron 
-% 0x10
- /caron /dotlessi 
-% (unusual TeX characters available in, e.g., Lucida Bright)
- /dotlessj /ff /ffi /ffl 
- /.notdef /.notdef /.notdef /.notdef
- /.notdef /.notdef /.notdef /.notdef
- % very contentious; it's so painful not having quoteleft and quoteright
- % at 96 and 145 that we move the things normally found there to here.
- /grave /quotesingle 
-% 0x20 (ASCII begins)
- /space /exclam /quotedbl /numbersign
- /dollar /percent /ampersand /quoteright
- /parenleft /parenright /asterisk /plus /comma /hyphen /period /slash
-% 0x30
- /zero /one /two /three /four /five /six /seven
- /eight /nine /colon /semicolon /less /equal /greater /question
-% 0x40
- /at /A /B /C /D /E /F /G /H /I /J /K /L /M /N /O
-% 0x50
- /P /Q /R /S /T /U /V /W
- /X /Y /Z /bracketleft /backslash /bracketright /asciicircum /underscore
-% 0x60
- /quoteleft /a /b /c /d /e /f /g /h /i /j /k /l /m /n /o
-% 0x70
- /p /q /r /s /t /u /v /w
- /x /y /z /braceleft /bar /braceright /asciitilde
- /.notdef % rubout; ASCII ends
-% 0x80
- /.notdef /.notdef /quotesinglbase /florin
- /quotedblbase /ellipsis /dagger /daggerdbl
- /circumflex /perthousand /Scaron /guilsinglleft
- /OE /.notdef /.notdef /.notdef
-% 0x90
- /.notdef /.notdef /.notdef /quotedblleft
- /quotedblright /bullet /endash /emdash
- /tilde /trademark /scaron /guilsinglright
- /oe /.notdef /.notdef /Ydieresis
-% 0xA0
- /.notdef % nobreakspace
- /exclamdown /cent /sterling
- /currency /yen /brokenbar /section
- /dieresis /copyright /ordfeminine /guillemotleft
- /logicalnot
- /hyphen % Y&Y (also at 45); Windows' softhyphen
- /registered
- /macron
-% 0xD0
- /degree /plusminus /twosuperior /threesuperior
- /acute /mu /paragraph /periodcentered
- /cedilla /onesuperior /ordmasculine /guillemotright
- /onequarter /onehalf /threequarters /questiondown
-% 0xC0
- /Agrave /Aacute /Acircumflex /Atilde /Adieresis /Aring /AE /Ccedilla
- /Egrave /Eacute /Ecircumflex /Edieresis
- /Igrave /Iacute /Icircumflex /Idieresis
-% 0xD0
- /Eth /Ntilde /Ograve /Oacute
- /Ocircumflex /Otilde /Odieresis /multiply
- /Oslash /Ugrave /Uacute /Ucircumflex
- /Udieresis /Yacute /Thorn /germandbls
-% 0xE0
- /agrave /aacute /acircumflex /atilde
- /adieresis /aring /ae /ccedilla
- /egrave /eacute /ecircumflex /edieresis
- /igrave /iacute /icircumflex /idieresis
-% 0xF0
- /eth /ntilde /ograve /oacute
- /ocircumflex /otilde /odieresis /divide
- /oslash /ugrave /uacute /ucircumflex
- /udieresis /yacute /thorn /ydieresis
-] def
-
-%%EndProcSet
-%%BeginProcSet: texps.pro
-TeXDict begin/rf{findfont dup length 1 add dict begin{1 index/FID ne 2
-index/UniqueID ne and{def}{pop pop}ifelse}forall[1 index 0 6 -1 roll
-exec 0 exch 5 -1 roll VResolution Resolution div mul neg 0 0]/Metrics
-exch def dict begin Encoding{exch dup type/integertype ne{pop pop 1 sub
-dup 0 le{pop}{[}ifelse}{FontMatrix 0 get div Metrics 0 get div def}
-ifelse}forall Metrics/Metrics currentdict end def[2 index currentdict
-end definefont 3 -1 roll makefont/setfont cvx]cvx def}def/ObliqueSlant{
-dup sin S cos div neg}B/SlantFont{4 index mul add}def/ExtendFont{3 -1
-roll mul exch}def/ReEncodeFont{CharStrings rcheck{/Encoding false def
-dup[exch{dup CharStrings exch known not{pop/.notdef/Encoding true def}
-if}forall Encoding{]exch pop}{cleartomark}ifelse}if/Encoding exch def}
-def end
-
-%%EndProcSet
-%%BeginProcSet: special.pro
-TeXDict begin/SDict 200 dict N SDict begin/@SpecialDefaults{/hs 612 N
-/vs 792 N/ho 0 N/vo 0 N/hsc 1 N/vsc 1 N/ang 0 N/CLIP 0 N/rwiSeen false N
-/rhiSeen false N/letter{}N/note{}N/a4{}N/legal{}N}B/@scaleunit 100 N
-/@hscale{@scaleunit div/hsc X}B/@vscale{@scaleunit div/vsc X}B/@hsize{
-/hs X/CLIP 1 N}B/@vsize{/vs X/CLIP 1 N}B/@clip{/CLIP 2 N}B/@hoffset{/ho
-X}B/@voffset{/vo X}B/@angle{/ang X}B/@rwi{10 div/rwi X/rwiSeen true N}B
-/@rhi{10 div/rhi X/rhiSeen true N}B/@llx{/llx X}B/@lly{/lly X}B/@urx{
-/urx X}B/@ury{/ury X}B/magscale true def end/@MacSetUp{userdict/md known
-{userdict/md get type/dicttype eq{userdict begin md length 10 add md
-maxlength ge{/md md dup length 20 add dict copy def}if end md begin
-/letter{}N/note{}N/legal{}N/od{txpose 1 0 mtx defaultmatrix dtransform S
-atan/pa X newpath clippath mark{transform{itransform moveto}}{transform{
-itransform lineto}}{6 -2 roll transform 6 -2 roll transform 6 -2 roll
-transform{itransform 6 2 roll itransform 6 2 roll itransform 6 2 roll
-curveto}}{{closepath}}pathforall newpath counttomark array astore/gc xdf
-pop ct 39 0 put 10 fz 0 fs 2 F/|______Courier fnt invertflag{PaintBlack}
-if}N/txpose{pxs pys scale ppr aload pop por{noflips{pop S neg S TR pop 1
--1 scale}if xflip yflip and{pop S neg S TR 180 rotate 1 -1 scale ppr 3
-get ppr 1 get neg sub neg ppr 2 get ppr 0 get neg sub neg TR}if xflip
-yflip not and{pop S neg S TR pop 180 rotate ppr 3 get ppr 1 get neg sub
-neg 0 TR}if yflip xflip not and{ppr 1 get neg ppr 0 get neg TR}if}{
-noflips{TR pop pop 270 rotate 1 -1 scale}if xflip yflip and{TR pop pop
-90 rotate 1 -1 scale ppr 3 get ppr 1 get neg sub neg ppr 2 get ppr 0 get
-neg sub neg TR}if xflip yflip not and{TR pop pop 90 rotate ppr 3 get ppr
-1 get neg sub neg 0 TR}if yflip xflip not and{TR pop pop 270 rotate ppr
-2 get ppr 0 get neg sub neg 0 S TR}if}ifelse scaleby96{ppr aload pop 4
--1 roll add 2 div 3 1 roll add 2 div 2 copy TR .96 dup scale neg S neg S
-TR}if}N/cp{pop pop showpage pm restore}N end}if}if}N/normalscale{
-Resolution 72 div VResolution 72 div neg scale magscale{DVImag dup scale
-}if 0 setgray}N/psfts{S 65781.76 div N}N/startTexFig{/psf$SavedState
-save N userdict maxlength dict begin/magscale true def normalscale
-currentpoint TR/psf$ury psfts/psf$urx psfts/psf$lly psfts/psf$llx psfts
-/psf$y psfts/psf$x psfts currentpoint/psf$cy X/psf$cx X/psf$sx psf$x
-psf$urx psf$llx sub div N/psf$sy psf$y psf$ury psf$lly sub div N psf$sx
-psf$sy scale psf$cx psf$sx div psf$llx sub psf$cy psf$sy div psf$ury sub
-TR/showpage{}N/erasepage{}N/copypage{}N/p 3 def @MacSetUp}N/doclip{
-psf$llx psf$lly psf$urx psf$ury currentpoint 6 2 roll newpath 4 copy 4 2
-roll moveto 6 -1 roll S lineto S lineto S lineto closepath clip newpath
-moveto}N/endTexFig{end psf$SavedState restore}N/@beginspecial{SDict
-begin/SpecialSave save N gsave normalscale currentpoint TR
-@SpecialDefaults count/ocount X/dcount countdictstack N}N/@setspecial{
-CLIP 1 eq{newpath 0 0 moveto hs 0 rlineto 0 vs rlineto hs neg 0 rlineto
-closepath clip}if ho vo TR hsc vsc scale ang rotate rwiSeen{rwi urx llx
-sub div rhiSeen{rhi ury lly sub div}{dup}ifelse scale llx neg lly neg TR
-}{rhiSeen{rhi ury lly sub div dup scale llx neg lly neg TR}if}ifelse
-CLIP 2 eq{newpath llx lly moveto urx lly lineto urx ury lineto llx ury
-lineto closepath clip}if/showpage{}N/erasepage{}N/copypage{}N newpath}N
-/@endspecial{count ocount sub{pop}repeat countdictstack dcount sub{end}
-repeat grestore SpecialSave restore end}N/@defspecial{SDict begin}N
-/@fedspecial{end}B/li{lineto}B/rl{rlineto}B/rc{rcurveto}B/np{/SaveX
-currentpoint/SaveY X N 1 setlinecap newpath}N/st{stroke SaveX SaveY
-moveto}N/fil{fill SaveX SaveY moveto}N/ellipse{/endangle X/startangle X
-/yrad X/xrad X/savematrix matrix currentmatrix N TR xrad yrad scale 0 0
-1 startangle endangle arc savematrix setmatrix}N end
-
-%%EndProcSet
-%%BeginProcSet: color.pro
-TeXDict begin/setcmykcolor where{pop}{/setcmykcolor{dup 10 eq{pop
-setrgbcolor}{1 sub 4 1 roll 3{3 index add neg dup 0 lt{pop 0}if 3 1 roll
-}repeat setrgbcolor pop}ifelse}B}ifelse/TeXcolorcmyk{setcmykcolor}def
-/TeXcolorrgb{setrgbcolor}def/TeXcolorgrey{setgray}def/TeXcolorgray{
-setgray}def/TeXcolorhsb{sethsbcolor}def/currentcmykcolor where{pop}{
-/currentcmykcolor{currentrgbcolor 10}B}ifelse/DC{exch dup userdict exch
-known{pop pop}{X}ifelse}B/GreenYellow{0.15 0 0.69 0 setcmykcolor}DC
-/Yellow{0 0 1 0 setcmykcolor}DC/Goldenrod{0 0.10 0.84 0 setcmykcolor}DC
-/Dandelion{0 0.29 0.84 0 setcmykcolor}DC/Apricot{0 0.32 0.52 0
-setcmykcolor}DC/Peach{0 0.50 0.70 0 setcmykcolor}DC/Melon{0 0.46 0.50 0
-setcmykcolor}DC/YellowOrange{0 0.42 1 0 setcmykcolor}DC/Orange{0 0.61
-0.87 0 setcmykcolor}DC/BurntOrange{0 0.51 1 0 setcmykcolor}DC
-/Bittersweet{0 0.75 1 0.24 setcmykcolor}DC/RedOrange{0 0.77 0.87 0
-setcmykcolor}DC/Mahogany{0 0.85 0.87 0.35 setcmykcolor}DC/Maroon{0 0.87
-0.68 0.32 setcmykcolor}DC/BrickRed{0 0.89 0.94 0.28 setcmykcolor}DC/Red{
-0 1 1 0 setcmykcolor}DC/OrangeRed{0 1 0.50 0 setcmykcolor}DC/RubineRed{
-0 1 0.13 0 setcmykcolor}DC/WildStrawberry{0 0.96 0.39 0 setcmykcolor}DC
-/Salmon{0 0.53 0.38 0 setcmykcolor}DC/CarnationPink{0 0.63 0 0
-setcmykcolor}DC/Magenta{0 1 0 0 setcmykcolor}DC/VioletRed{0 0.81 0 0
-setcmykcolor}DC/Rhodamine{0 0.82 0 0 setcmykcolor}DC/Mulberry{0.34 0.90
-0 0.02 setcmykcolor}DC/RedViolet{0.07 0.90 0 0.34 setcmykcolor}DC
-/Fuchsia{0.47 0.91 0 0.08 setcmykcolor}DC/Lavender{0 0.48 0 0
-setcmykcolor}DC/Thistle{0.12 0.59 0 0 setcmykcolor}DC/Orchid{0.32 0.64 0
-0 setcmykcolor}DC/DarkOrchid{0.40 0.80 0.20 0 setcmykcolor}DC/Purple{
-0.45 0.86 0 0 setcmykcolor}DC/Plum{0.50 1 0 0 setcmykcolor}DC/Violet{
-0.79 0.88 0 0 setcmykcolor}DC/RoyalPurple{0.75 0.90 0 0 setcmykcolor}DC
-/BlueViolet{0.86 0.91 0 0.04 setcmykcolor}DC/Periwinkle{0.57 0.55 0 0
-setcmykcolor}DC/CadetBlue{0.62 0.57 0.23 0 setcmykcolor}DC
-/CornflowerBlue{0.65 0.13 0 0 setcmykcolor}DC/MidnightBlue{0.98 0.13 0
-0.43 setcmykcolor}DC/NavyBlue{0.94 0.54 0 0 setcmykcolor}DC/RoyalBlue{1
-0.50 0 0 setcmykcolor}DC/Blue{1 1 0 0 setcmykcolor}DC/Cerulean{0.94 0.11
-0 0 setcmykcolor}DC/Cyan{1 0 0 0 setcmykcolor}DC/ProcessBlue{0.96 0 0 0
-setcmykcolor}DC/SkyBlue{0.62 0 0.12 0 setcmykcolor}DC/Turquoise{0.85 0
-0.20 0 setcmykcolor}DC/TealBlue{0.86 0 0.34 0.02 setcmykcolor}DC
-/Aquamarine{0.82 0 0.30 0 setcmykcolor}DC/BlueGreen{0.85 0 0.33 0
-setcmykcolor}DC/Emerald{1 0 0.50 0 setcmykcolor}DC/JungleGreen{0.99 0
-0.52 0 setcmykcolor}DC/SeaGreen{0.69 0 0.50 0 setcmykcolor}DC/Green{1 0
-1 0 setcmykcolor}DC/ForestGreen{0.91 0 0.88 0.12 setcmykcolor}DC
-/PineGreen{0.92 0 0.59 0.25 setcmykcolor}DC/LimeGreen{0.50 0 1 0
-setcmykcolor}DC/YellowGreen{0.44 0 0.74 0 setcmykcolor}DC/SpringGreen{
-0.26 0 0.76 0 setcmykcolor}DC/OliveGreen{0.64 0 0.95 0.40 setcmykcolor}
-DC/RawSienna{0 0.72 1 0.45 setcmykcolor}DC/Sepia{0 0.83 1 0.70
-setcmykcolor}DC/Brown{0 0.81 1 0.60 setcmykcolor}DC/Tan{0.14 0.42 0.56 0
-setcmykcolor}DC/Gray{0 0 0 0.50 setcmykcolor}DC/Black{0 0 0 1
-setcmykcolor}DC/White{0 0 0 0 setcmykcolor}DC end
-
-%%EndProcSet
-%%BeginFont: CMMI9
-%!PS-AdobeFont-1.1: CMMI9 1.100
-%%CreationDate: 1996 Jul 23 07:53:55
-
-% Copyright (C) 1997 American Mathematical Society.  All Rights Reserved.
-
-11 dict begin
-/FontInfo 7 dict dup begin
-/version (1.100) readonly def
-/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
-/FullName (CMMI9) readonly def
-/FamilyName (Computer Modern) readonly def
-/Weight (Medium) readonly def
-/ItalicAngle -14.04 def
-/isFixedPitch false def
-end readonly def
-/FontName /CMMI9 def
-/PaintType 0 def
-/FontType 1 def
-/FontMatrix [0.001 0 0 0.001 0 0] readonly def
-/Encoding 256 array
-0 1 255 {1 index exch /.notdef put} for
-dup 15 /epsilon1 put
-readonly def
-/FontBBox{-29 -250 1075 750}readonly def
-/UniqueXX 5087384 def
-currentdict end
-currentfile eexec
-80347982ab3942d930e069a70d0d48311d725e830d1c76fba12e12486e989c98
-74c2b527f0925722787027f44470d484262c360cdfdddf3657533a57bb16f730
-48bfbbfcb73a650484015441fdc837add94ac8fbd2022e3ec8f115d4b4bb7b7f
-15388f22cc6198efe768bd9fceb3446ee4a8dc27d6cd152485384ef5f59381ff
-da43f2d20c8fb08aa27ab2015b774db10dacfdcd33e60f178c461553146ab427
-bdd7da12534ba078ad3d780414930da4f8d58abefd45db119b10eb409dd89792
-3c6e705479464a4b33ae3d31bfe98efe259f07f7950237bbaee4f7b64ffea83a
-757fa717d50c3298392891bfd60e34a056b0d6021da3fd9b8b01bf78b0b23dc4
-ea3b0605150d20b27ff9ea5f2524661019d982a2e47cd7c21ee5ca9ed9227821
-f8d07119397de26838c11d7b35bcedc43e011626e300f8249ed846d7b5ccbd89
-02550cda17ddf113df658fb13f8162681013766863784efac128e01ef997e1a4
-30312afac8f3d948edecd7d5090ab5c864b91d7f6e80256f0e1fc99f1102b74c
-61cc456e2e1bedf0e627d5f70f738f963a13666405c51ebf23ca077e97570a2f
-1118536b92e585cf1dbd5fbf36a0a5d197538c05304e93a15f3c931168d91d42
-483ef428b1a3f1b7e548fd1d23b80f5523c8b8bf450b02804fb689f915c86693
-f7dfb1c43f681627c7f027021aa3a8179148f1819cd94b8890a9ac63dc1e8a68
-f254b64f6f173c3d02e3ebc037da05074017c8b113e94f4e2d26b467ef9da07e
-afd7ea7c86e025af52c5ceeb835951e67e02a38daf1e9e698bd21996c1071e84
-ff7fbe77f6ddf9d06fa92b16ecebcbe0370b5cd9d450d0f2906a105cadf93ed0
-0abc7fcf2c996e7c15e452006e35390d99b9cfc59925f1444c20d9c3e1fc2910
-32cf9fa9d580eac1bc956334da391b870a757c3bee6aa3e005b20988d8587876
-3ced20c6edf2ac2b22890e37ff7aedeb0986d85ae05bc84339bf2116df48c5d1
-cc888bb33d409b06dd70ffd0618b2080442aac439aeb39c20a87ad74ef10629c
-f1604db8611e8e4224c5b21ab0c7ebddc77fe9a283b3a8c6a2a9508f6836e3fc
-3eae1366b4da4f44cb7a77fd81d278c17775d56cb28b70f18d894bfd1ec1827f
-fb16b0d4c1a4ce155da066810170fea53e0d24874d69366a46873838b82ece2e
-bb961c260c67b449acd29dd7613c555bdb2105bdddc2924c6064486a50e936ee
-a8c6ea5be6ee8441652dd81f930cb7c529ddee172f25588eeec791ff03753b9a
-80c10598425b6a0886d6aad2d1d973454b9c6319ac29be6b1fa97f8bbbb1c9fd
-acbda78d04e5891f78b85fcd173a827effee79a2fe5df00d2b1b4526b1858fed
-dbd207bf886ef031cdf61ad3fadfbc26cb8eb879dd17b9999d8735ee9fde3ba9
-24ce7786237f6c624563022da4d9174a9ef26e2b6baf5b3248761805f2dd2429
-7375b95ecebc05a109d87220a4e2b06b31e2c87f2f892e10c01c3801be734fac
-04300c4f912ab08adcb21b68b3fe97230cf30214cab7fe65753c1db70b401dc0
-c3
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-cleartomark
-
-%%EndFont 
-%%BeginFont: CMEX10
-%!PS-AdobeFont-1.1: CMEX10 1.00
-%%CreationDate: 1992 Jul 23 21:22:48
-
-% Copyright (C) 1997 American Mathematical Society.  All Rights Reserved.
-
-11 dict begin
-/FontInfo 7 dict dup begin
-/version (1.00) readonly def
-/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
-/FullName (CMEX10) readonly def
-/FamilyName (Computer Modern) readonly def
-/Weight (Medium) readonly def
-/ItalicAngle 0 def
-/isFixedPitch false def
-end readonly def
-/FontName /CMEX10 def
-/PaintType 0 def
-/FontType 1 def
-/FontMatrix [0.001 0 0 0.001 0 0] readonly def
-/Encoding 256 array
-0 1 255 {1 index exch /.notdef put} for
-dup 83 /uniontext put
-readonly def
-/FontBBox{-24 -2960 1454 772}readonly def
-/UniqueXX 5000774 def
-currentdict end
-currentfile eexec
-80347982ab3942d930e069a70d0d48311d7190fa2d133a583138f76695558e7a
-e9348d37cac6651806d08527c1bb4a062a4835ac37784cc39ad8841404e438b4
-d52d3901e47a1de4f7924e0fb3daf442499175bab1226edf692a4956739f8828
-e80592f450c5d5c22ac88bcfbe9748f61d18243a16f4a4467f084e8e2be46ef4
-7fc51c3a8199e3cda62ff9c4fb73956dab8b6683d2156377808cb35026073e80
-523f59a30d195fcf9b9fce4ffafc6d5649664203ab24acb938d58d246707ffe7
-d62f04bec4b70c21ef75beb2b812622b3c74e969d72d3cd11bd7106294a99caf
-0b1629bc7d4de6b96ca82930831d64575f23f4ad06a0e45e315b1d392411be8d
-6d73c998789ff258a07a3c8c2057325784514c845500bfd1a971310cfc11d41c
-1a167dbd5ff012c60add4e87325f6e5299032a839de65fb1473a166aae1876a4
-414a434f22c1d241591fb36f857df6fa930608750ffc0c54f44994662b1f00f1
-400bf752ea8d83ffc4cb77a290bc2d99981ae59a191748ba5c7ba1a9d2583fd2
-1398452b6ff5d83a059f7eadcd2ef744e9dd22bdf9c79d049bf06835e878c32b
-7765c69bdd8ef4deb4ea7cfff4cf9354a4ddffa689de961d16772491c7afbd7f
-ffde42400764c68e954ee5c455a5687959829bc3b319b2147deaab3628662c80
-30c5e02fea09609abe4eaa12e217bc3af673f1bc36a7039eb13fcacb4218fe0f
-c5a3f9452d4edf46cc91db67b624d4f2d37502fb9f11af4da18ca40b61097f95
-d44329375467ed13c5cb585ec53f62b83ef9502cc755af44bf32b87b8ae9f3f2
-f8dbf72dab90acafbacd280db6aaffaefdff6d5eff26669bac56280a950560e3
-d01714ba38659b0e4e28bf8cdc1f15ff7e3ea9d95a6afbbe3d8e6905aa6d531d
-6b6dcab89e2036cc492c65f76ddcc3cfcff33fde3d9ffd10f7a90530fd5c7683
-4329baa902e701ca42717476298c9ff511b1941244bb1dfd0e5cab92a43970cd
-1bdb292eadd055c97972844fdcdb0aa06401e7b2632b9d134f96bce0064860f3
-9859da7a9a82be0a840672a1331212752ae1b521b693b384a72dba8d37a86eaf
-a0341e7fc5f6ef7a8c566aacb91e8bf5005c18837894c4eacff41dba54e071ca
-83fe249b6aa6921340879a644a43e13b3ef9b1db789c61b5927c967d6bf493ca
-0c722a7ba6762fda1dcdfeb814981973f4273f9a2220e0fc2e6daa1a100ba89f
-a91fba83b432117b682a73d3e36ba6a079c103a03999424264222e5b1040a79e
-96bba57dc7d01a8d79396179040acc9c522adc949683542abe58fba208c69e67
-0cce82866c38aff4e1da5771809955c3023c40c6caeee0a28cbc5a2d3f30e340
-345e624bdfbb5f23994d566225a7890711ed54d1dc68411a67f70b73c7bc3083
-683abbfcc8ed1a3caf3ef8b751f1533b359fbc1b029a3c1902d943759319a1e9
-ba7f48b6a34717410abdb15e68c227b0d480ab5a7288426e827bbc9a641200a7
-fca27ee30c2aee6f42b3b29c573be209
-
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-cleartomark
-
-%%EndFont 
-%%BeginFont: CMMI6
-%!PS-AdobeFont-1.1: CMMI6 1.100
-%%CreationDate: 1996 Jul 23 07:53:52
-
-% Copyright (C) 1997 American Mathematical Society.  All Rights Reserved.
-
-11 dict begin
-/FontInfo 7 dict dup begin
-/version (1.100) readonly def
-/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
-/FullName (CMMI6) readonly def
-/FamilyName (Computer Modern) readonly def
-/Weight (Medium) readonly def
-/ItalicAngle -14.04 def
-/isFixedPitch false def
-end readonly def
-/FontName /CMMI6 def
-/PaintType 0 def
-/FontType 1 def
-/FontMatrix [0.001 0 0 0.001 0 0] readonly def
-/Encoding 256 array
-0 1 255 {1 index exch /.notdef put} for
-dup 59 /comma put
-dup 97 /a put
-dup 99 /c put
-dup 115 /s put
-dup 116 /t put
-readonly def
-/FontBBox{11 -250 1241 750}readonly def
-/UniqueXX 5087381 def
-currentdict end
-currentfile eexec
-80347982ab3942d930e069a70d0d48311d725e830d1c76fba12e12486e989c98
-74c2b527f0925722787027f44470d484262c360cdfdddf3657533a57bb16f730
-48bfbbfcb73a650484015441fdc837add94ac8fbd2022e3ec8f115d4b4bb7b7f
-15388f22cc6198efe768bd9fceb3446ee4a8dc27d6cd152485384ef5f59381ff
-da43f2d20c8fb08aa27ab2015b774db10dacfdcd33e60f178c461553146ab427
-bdd7da12534ba078ad3d780414930e72218b3075925ce1192f11fc8530fcd5e3
-038e3a6a6db2dcfbae3b4653e7e02730314e02b54a1e296d2bef8a79411d9225
-dad7b4e6d6f9cf0688b69ba21193bf1495807e7a1e67ed7e41cc25acc04702f6
-8ef703e3d45722c1a91fdef7100a48631a02a6f02a08c6b1f9b4df8310385b86
-8632718fd87119a233f219d9411383b7fa9f3e4780d8c27e2e89e0cae883d664
-c3eac57a3aef8988a2e9f0f8c7f53e0a80bdfc4620e21287d0390e1975398544
-7f3ea66401024bea75e1b4c4437b7bb188f76f96b918ac7c6ad7e8ae7f21d8c2
-790f08cccec904fe48ef39e597ed4d4237c1d1f596f5906b19ea308020f7a35c
-168e327ec3246b1dfabe912f6b6daac09974876d3996e57d180261110db05f15
-e3e8eebba3d90b5764c03df3033a1ed678ebc679569a2fb297378b25434c0f20
-5313ecb8a952f07242d3ee731b0cdc086a4481178a3d65129c47c09b22e9c431
-e11b3747b94c26a757c38d06001798c6a568303d541385244b967d3b1786edea
-f65bb53c4c2fe75e4b1b15c2c78d930b4296c80f08bad86012451edc8e9f0854
-c3b390a16e27b11b3d45a9f72eff8baded2242dc928a61685d79e09681c97425
-5b90a498614cf560fa5b1718981388268ba206a96989e6d0b5d485d9aca5594a
-e67dd7b34d8a369adb06647f8aff8814d6d9cdc04a4835918e557174c5bc0f3f
-bcea9907a04cf93c12727ec40db3f2f77596dca477862747435bdedacd9b2311
-6cc97fa47ffdd7d897fb6bdd5572e35d34e7e1cb5e7273a4ffd86525323ace4a
-84e1297028c2bd5469baa2e75d19360c2c9042139d5e7dd4390a6a3935424711
-de21910126d750ae279916ceb71da3591d60dc62db333c5021e2c1cd61ade51e
-9395804fa8f124b194547de13ddc8ce157d5d0de6ed12ffbfc67bff54c817919
-0d0a07b371965275e62be6a0a177be27972dca5212214fbfb473c9a99d2e8ef8
-02dc76d6a57a2b7496a4df89213b422ac457b844e6e965229a421d83cf444959
-2410dcc1b0e7f1626d1f62759f286c9f5e18b7134d30231d696a1db921544385
-106bed821dd146507164b2a3b30b24e4e20b98f0530aa680f1f9486b47111c18
-8fad0bdc5b2f7a3b5413e21b0949ab099fe4d4b0b279915e932c7e2c5847c583
-a8276cf361449b30941b58f722bb505dd717772666c08a788dbc005cc8da3244
-83a70d422e5babd5080625826bce045b168d253465c3a045bc0f56fcd6e2f96e
-76b5937ca16e463cd1a97ec08a53f7a50dc3c43d77fc3da62d9b97ae6011ff6a
-e32aa6f456435f616af79a96db7509734650f9c3b263f052dee49a7b3770c6c5
-e8fd1a2a941214ded27cb5881cb1abd6dc267ae4942205692fa37890f0539ba5
-b72b188aa91d0401b71a4b7e66c826781936845144068e54f694f07c23c54992
-7b7e33e3114534e8ad553cad8fa4021454b26a74f80254ffbea755f73638b241
-53ad0bf28f299062c9f174d349c78dbc95d4a7611297cabcbfaebb9b75a2a14e
-36630b909bec9c0da30b0164c70c4b974ebb3fdcfa6dbca188c498eaa5e59a8d
-9342f5d43e6dda23bd45c4600a9c3e3033aaae9ec1b897b12e6775520c7c598f
-e66d63a9c5fad7fd4bd96f9e676dd48c319f9dee38761f4dc30de718a83e19bb
-eda092f766c26ea6d458036e2cd23d11340a4b4f80875d81d73df69cfa34eab5
-d489802f782958c4d591c32be26b587cb4b35d20a5db418c6bfa50882deffd58
-aba8c69335e69f2f9e2b863d9d0249a2ebbfcbba1a31c3c5134c8b42e99f2d42
-539e2a0373f861f2aec07cd820c963193f024f672c6bc5d28e93e36f48b38e06
-1617dee4d26838455046ba678a97cf2940d7897bd83d50a4a7fee3298f59128a
-3da093b2a913376c46cb1995aef8065aecb0db36c1b1b700247b76d2813a59d5
-20abf8974b8310bf63278ed31a9e247f65fa3131ab73c21cbef668bd9da5f6cf
-6808fe5c04b2d9615098f382487ff6da3200c1710c3e00503e00325100165525
-e75979f9211d5cff808c0fa4ce75e005bd817b5eb7f32692135003252fab42e9
-9a584fd7534beb3d916c042c816e3d209242a0348292c3af78483a62c44adb2d
-77ec304517b2259ef46b82a1c7df01c981042096e02cad52f2c7839e9946c715
-a311293e5f6ba3aed88222c0c06580676372b467c076f1b155541b883c1cac9f
-15bb9e6c2998b3bb56
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-cleartomark
-
-%%EndFont 
-%%BeginFont: CMMI7
-%!PS-AdobeFont-1.1: CMMI7 1.100
-%%CreationDate: 1996 Jul 23 07:53:53
-
-% Copyright (C) 1997 American Mathematical Society.  All Rights Reserved.
-
-11 dict begin
-/FontInfo 7 dict dup begin
-/version (1.100) readonly def
-/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
-/FullName (CMMI7) readonly def
-/FamilyName (Computer Modern) readonly def
-/Weight (Medium) readonly def
-/ItalicAngle -14.04 def
-/isFixedPitch false def
-end readonly def
-/FontName /CMMI7 def
-/PaintType 0 def
-/FontType 1 def
-/FontMatrix [0.001 0 0 0.001 0 0] readonly def
-/Encoding 256 array
-0 1 255 {1 index exch /.notdef put} for
-dup 59 /comma put
-dup 80 /P put
-dup 81 /Q put
-dup 85 /U put
-dup 88 /X put
-dup 97 /a put
-dup 99 /c put
-dup 105 /i put
-dup 106 /j put
-dup 112 /p put
-dup 115 /s put
-dup 116 /t put
-dup 117 /u put
-readonly def
-/FontBBox{0 -250 1171 750}readonly def
-/UniqueXX 5087382 def
-currentdict end
-currentfile eexec
-80347982ab3942d930e069a70d0d48311d725e830d1c76fba12e12486e989c98
-74c2b527f0925722787027f44470d484262c360cdfdddf3657533a57bb16f730
-48bfbbfcb73a650484015441fdc837add94ac8fbd2022e3ec8f115d4b4bb7b7f
-15388f22cc6198efe768bd9fceb3446ee4a8dc27d6cd152485384ef5f59381ff
-da43f2d20c8fb08aa27ab2015b774db10dacfdcd33e60f178c461553146ab427
-bdd7da12534ba078ad3d780414930f01bdaae649990604a33aa9eaffbe5b5489
-e5c7c9ff9d9be01b08220832c41caac64816b53bbc087ae4b621d2b44b21ae5e
-3f7fe4ddb05c675abfe30510eee4a7c874bb57b2ffe521a6875eddfdfd18c781
-25bfca5a097aad361dd94df46f14026c25ea988194899b95001209cb7009cead
-4b4ea03473ea120e7a7e341d4e3926796347fdb3a124c29660ac09f4648b313c
-b58e824884382f24ce08d2edc686923acace1201c16a07a42803288cd0b946f7
-546510e95b1fa1cc96f0bf72aa823d8e83d7c68c752c82a54c752eed2b1e699d
-e9db1830272ffbf2f4996ccc2d6fe2ae272798989525ef3b67b0d09bffcef749
-a805e5f76578222b9c4a8a09b13189a16ab746ddef7875f1ecf83e568f493d82
-ff729baa1e0834dbec30a35d3c49c9b10c5e1d90c6e3c8fb737df5ceb3299d96
-0fb79632f91f257753b4d2e34e3f54a26c7b950981fb7fe4dee3315db63e75b0
-24b4d318baec8aac9cde186f6d65767df1dba35124287c2e805bc660a3a22772
-0ae4fa097f1d75107441c0a0fbb9eec17d5516fa03b98756b7df7ac7eff9c7a2
-364b9f691ed5cb692dfff9dd80c761e9c4d5d6061782b327302c053ce1cd09ba
-0605ebf761cf9b730524e1994e7dfaa956799d522ec53d5acba27a35c4d28279
-617771938ece58c5ab664aa00c1bc4efba2d15504247a68e3af0f9bd59a387b3
-80db88cca083b06f5af70d768d1699826fb12ce12efc2b4c70923e052dbb964f
-5fa957c3ce225c0fda64d9b5321ee1ade207c1cc93105096cc73118f4082594c
-8ecddeb0d7bfde6f70bc62f10407c26a476ed88be7999d64a15912493829a9de
-62c71f5a34fbf5a843e311873cd98817dc9f8a4aeb7e0738b5de10043f5cfea7
-147c926ba6ce84d344ec60682b4d85913695c25e77231a7e950f4241bfa1dd50
-a25c96d21ba767fd8804d1448c7311088347264c062d3a70b6b89dde975ffb8c
-65f950f04f3b7ffd9075bfdb43ff5918fb8ace4273bf29524d9c9ba59c7abdc8
-c41e98d969d238bb6d1370e1b71f129e276bdc26838c54da8780280a4f39194d
-3075865d5264815eca65beb7f78f4af22dee08efa9775a9b16be602f28139b1a
-22ca65b9a6cdfca8c5d233a4286e320bf6d39c19a6dfcb3994dbf412d10289bf
-e6c542ef3d68bb9e560e5750958813fdf19b0bc0abbfdaa6bae8408063af47b0
-a226b3ae30442af91c80af26bd1bf6fe97f56a9271ac2922ed41ef471593c4d3
-536d2d2888e1b030bc0061c8475af14bb9b2b1668e36dbe8051390e0d7aa2740
-47e4bb90a068901f3a0b420e85d5f251ac3ad298e2332c48463a204c05651acf
-8e4222ceb1d73ea7876cc4c7bd54d641d570455a930ec79d1158281316f67fd7
-dace8abba26619264e523c5e98f45945553a15f7d8a00d9709589f6a76b37179
-e996625ac67c29dc45d42dd9561c373b7e4a2f0d6f8a8ba12e12237bd45f488c
-e2354ed5b048d900d9b28119beff12871f600ab02b516d35607bb65c802c04be
-ee08f03bc43d5f9b4253ddac00e55f79ddb2d8febd4d25cf62de4568e2dda882
-3f30d0b9e864473012126ee279ea2624dfa1f7b95cfb453d0badf3a26a8242db
-56907465f7828662f4fb011b6bd60982f326493a07795f2a862d388c23d58ef0
-9ce6e58bda6bfc142a822770583f818db619c528dc568cf60f7aa9818f63ad2d
-1233942a1b4b543706f144581320c976ec1f2f1effbfb64714a770172041b001
-69699bede2caafa71dae2a6e163daa4bf3d43f537fbca0104d645879a3c3ebc4
-9f2c3a9efb651457aeaab4dd214529b7b0cce4653a33defc68065f8c14c953fe
-e97774977368c0661dffbef71acf1759706b899e9ba7b12a53b52d9f53dbc14e
-8322e472966744022eebe349f6cb7c0bee577112f2c376ca23f6f789c08f7167
-61147762e1068424ccd9b61510802c29ee62ddfdbe6d47828699da5da409f562
-aabc270d880bd6a04437400f6067b836ae893cc60c77bb4cba347249d38cb655
-e67ea619302ff0d929cf844ff933110108f83db8799e8fcfe60ce2796adb945d
-ba4c2bd8b13d40bac60b082aa49b54c711885020fe8d43ff91a3f3cfb57df5df
-c296ab07ca2b342cc6efb63288874b57fc8c58b2784415c4d035c3c9c1bcda2e
-4d70fa651224ce09afb6a34b454a1d9104390983dfb9641117fce3e23bfa267a
-0d96fa97101cb5479ad421d21fbfd75f8c0b2143ee4c3eaf80ff5b995f16ee0a
-b7c8bfd6a7253d2239921507477d2770104370bffd49cbead54b19ee08a8c417
-2beef445c0cd1e9748aac2f94bc0b6b981e7ea3c47af5a931d0ba333e807c751
-0f9cc782ba0e543a01674f8247fa6e573e71dce65b75e532471fd67f91ab09ef
-1f046f4e97dd6ddff3834bcaa36f38fd337a442394249724b92e9bcb39c77232
-5e81b11e75fd9e93b4fd5cb434066462b507cffff7571117f6069885582d8f57
-06e1684b2904b3a534d972f70091bd48fb19fc44be5a7cdef8b5189b6f25e37c
-a31056256a78cd175f0202b6e45e76b10ca015efcd165c88199a8023aca239a5
-4e64f8b8c1c7294aa46a541bfa0dfbe4a534e88d5e463812d5afce4158f07adc
-e2b7bcbc692e26ca0187dd0ce76506f9e44eba7a3afe7f09c5fb02af4d9e944a
-92814704368c54f89a39cfd266236ef553113d293d3d68f3b6f913fcb1c7dda9
-4a1f39e94f232c362e9da28c9c80f64bc948d59ab391312f4dd5dd8e40bd8a5b
-76666eb1673d704f35d9774a5e5e8a21061a0414651a19839997ee0e19f2c4a9
-136197ef1b53ef3141c74beb59b186e96f81f27a3393dbae26cd5a3a049d246c
-b418ff4ac753dd2806386961f48a5a0f06f439ed42a594e4ed372704dcbe060e
-490ca08a144945edfb250f591ec89cba259e0d2df3ba283152ee1853aeea6b1f
-fae156d02a4275dcfe33c16acdc2ce7c139992643f68e9fbf88c2dc86d94e3da
-ad2f64261a294226cc8e6f61b3426bea2ef7de92641e727ec9d9b7e02f35438a
-13114f2c14fac8ea8c40fd32b979af0ca4d223c39d07ca45822d1a27c666afcc
-ce0c55e04306575fee24db16264f645d9a26541b015c58af7aff7c6ad39987a0
-ed3ba6da32bca17363872deb91105132270d0cab0a9c5ed064f95ff5c5b8d3d0
-03d20063742357595fb0760e460ed07c8bc9f22e46ff6603f19fd5b76a280aa8
-7f4f395d0ebea24edbba17bba51c7c9a1b82ddd674e97fadc70d2df98b3ce850
-08081f9428f9e93d4982ce72ba6e5255701f595d08f46e1152be0b3ac0676626
-708d481b430b02234d3a5c5aa4f9807714d7fc48ba0fc01277e89671a0272c17
-478e7e64fe10c5df195ec37f1932606c4feec57ecf632b94b4c82efe940c65aa
-082eee703485930a801545c9c5ba1c686813c7a2876ad1e90fd7f081deed04b3
-c5a781808aa6048c87df86625cdb22d6c7c2de9f8d06bb8218b5e9ff2cd5c022
-cda27896222ac4fa3fe7ae166017375cfb1c143bf957af52e578302557a8af0d
-8090969cf926163d23ff3f58f27583e8b3d76e0dc661e5bb77c1358cf0ed855b
-765ae295d873dac304cd4e8df8a952294128f212ec11c300df6d80d72ffd181c
-cebf24f00d1dc62a2db6845e9f524ad93cd92d30b7c55e34422814ececac7fa9
-7cd78cecc4becd25ef0b7038594fc555d801a303e71bbc078e8fb2bafefc62b0
-fbd9bb507f130814df586fb1014c34a60561f1da43213adec0e96a561ab088e2
-e5ff4a797ec4635d84ad200be5e582ded21160cea45b4e5fa30a6e1bfcb87276
-b21f391137c84c84dd9ba79ae80d4332c29ff3d8f67d6e6cac50013b5d6b60c7
-4a375bf59f7e9796d38b7e5a7e1c18c4a9b11cac11e2e76c0acb39e353a9eed6
-e846ae26b47bc775f9458c11b8821a4ff5a59c85322dabe7ca9dc17ad73e73be
-2fd023164c99a30001f1905b782e63fdffcfab6d11c29b609e13205b3cd28495
-6f11c34617f068a33e7453b26894b762f5b950e30d7c55f836133814c24ef6b0
-66b626475ae63a118f7828a812a317379c217518d06b0dc96ff76e54df280648
-ae3f39eb0351d30d3d66de361534ec14d0583ca6de242d6747769548ffe91463
-55818a4390d53d10fa5d123b757f66dbde495e885a5e3d28df17e71027958b1a
-6274469ab3eec14c916f6eee602b0d2c27ec3c9b96ae9bdf709c4d14c1a86846
-3c99fd206e7a1d294f5354e0ce9899e56665edde9b2732767d1b37ad436d6530
-fd55f6623b1242e7547cfb22ba76baf711cac6a2a7a3b3e59b6852a9814a0824
-34837fcc9a5b910613e09a7ce2dea2d560effab80828d6ce6a8741d46307aba2
-87fdd3b51b03d9a4ed73af2a5a4eb9ee501a29260f84950d3909f31fce971b86
-8d93526095e400d4228bb59a83fe88c9d1e056258ae883da2ce1ad7e65dbae35
-009306189cfbb8c00ddea59ad1076ea99a19029d1071b02a4797dc215f513516
-e6561f968124ea2ca6ecd0b156871fd4d0f618db9df5b33c3ff13a8a4e777771
-25bb72af3ea22db7c3c65a807ca695f7991df4d3d8e8b34c832cbbbdb61af548
-3bae21be70ababc2793f140947e755b38bc72065c21eaebb2a1bbf8149ae36ee
-96a8868bc494ca542c22c62387635984b1096549d6bfbd2b842d09e2caaa76af
-345aee3dd5152c9a03af9f4d00b78f6288a0a0eaf35081dcba906d165b3ea575
-35f5087b447c6693c4584a9250beef04d7e9991ec656e44d911ffa98eb41c852
-a5f10a610fc9bed6803a3497f70cee94305f0fe69eeee2130696f129b17402e5
-6f92ef35bb8728d4ec580a61eadd51d6a3d6bee02e17865514288e000758846c
-aaef14eb30d6b61fa7dc062cef6d6726d50dd58410f984dcfa299cc036066724
-9ba2e28a88a3f13bcfb930fcc91f74e8829b
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-cleartomark
-
-%%EndFont 
-%%BeginFont: CMR10
-%!PS-AdobeFont-1.1: CMR10 1.00B
-%%CreationDate: 1992 Feb 19 19:54:52
-
-% Copyright (C) 1997 American Mathematical Society.  All Rights Reserved.
-
-11 dict begin
-/FontInfo 7 dict dup begin
-/version (1.00B) readonly def
-/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
-/FullName (CMR10) readonly def
-/FamilyName (Computer Modern) readonly def
-/Weight (Medium) readonly def
-/ItalicAngle 0 def
-/isFixedPitch false def
-end readonly def
-/FontName /CMR10 def
-/PaintType 0 def
-/FontType 1 def
-/FontMatrix [0.001 0 0 0.001 0 0] readonly def
-/Encoding 256 array
-0 1 255 {1 index exch /.notdef put} for
-dup 6 /Sigma put
-dup 40 /parenleft put
-dup 41 /parenright put
-dup 49 /one put
-dup 50 /two put
-dup 51 /three put
-dup 52 /four put
-dup 53 /five put
-dup 54 /six put
-dup 58 /colon put
-dup 59 /semicolon put
-dup 61 /equal put
-dup 91 /bracketleft put
-dup 93 /bracketright put
-readonly def
-/FontBBox{-251 -250 1009 969}readonly def
-/UniqueXX 5000793 def
-currentdict end
-currentfile eexec
-8053514d28ec28da1630165fab262882d3fca78881823c5537fe6c3dda8ee5b8
-97e17cb027f5c73fdbb56b0a7c25fc3512b55fe8f3acfbffcc7f4a382d8299cc
-8fd37d3cea49dabdca92847af0560b404ef71134b0f3d99934fc9d0b4e602011
-b9cfb856c23f958f3c5a2fbe0ef8587d1f5774879c324e51fcb22888b74f2415
-50d7401eb990d4f3a7af635198422283cac1b6cd446ddbcbd915db9bff88844e
-784c6bf7389803d9450b0c21756a017306457c7e62c1d269f306bd3402e266de
-fc3b5e7d8a8d2f5bf0fe6ddd40d07391df4fad4a6018dce29a2b8f692b29f202
-3a7c0e66de8ed85c14f1f8492167357f51a7e84cc5d92e0fee4d81cf7fbc8de5
-2d2e7bb57142033993f9c08c315abade8dbc4a732e84e142d3bee51557910e12
-cd8aa37c459a5e6b7f5269f59078aba3be4641a11ac48d0b625c8325b38ec08e
-4c9e5e7fed976a5650d99d82114f449b9ca14c4ec957702295a39a93ef93f618
-99b8ea06b092c3c1e503e6e436e0a9fa22576c8930ab3dc8c20f5d82b69cddf8
-ff4dacfa9c54bed5a3aa3ea5b129fe96be632843b9b6bc91b615581a985db56b
-1e01ca60ee69ca92cf5c0882ece62edad3e106d835348822400f0b66af658f2a
-e56ed08f8b0010571807009b73ab12a8cf14ca6c71f03c2a48c500f9d62266af
-154a6375ff600d9bac3f05ce34142d6867a79581c533176bb2f3117336671e2e
-44638a97167e2ea9644e31ea16c2ad2990ea33c54001e0c8156e6de8ab6a4d40
-a7137ba275f39589fea2e2db8256adc103d6f9cc038037a47e8fd469c5f98a5e
-3c15bd4ace40d340018b1cff7d1ed8abb0ac57b5b5a2c20a51957b96c453edb7
-dae5affd91a46d938fe0a13363001d844ded4323f1ee6d30012aea19b024a552
-315505535c85dc26bad31e09c50e6512802976d298c4e90d0044c362e6bf3ab3
-62a454ee93de25ce54411090c29e9d75c80ce26a84404bd9de3aee0e3f921ac5
-87f907572b8354a5c3165eea7e8b2ba4e155f60e5ea763348a68b1555c02ad7d
-7dbf7316889a222ff9e91a46568b2ada7a721bdc74c01285a4d2da9e68a45294
-59165bf752b1c65f96c8c782a1c5b0e85e61ae98fa9e1a75b3713bb0f9dc5c40
-59474f76d6b5adb96221d0387e31a31793d314e7807f205fd779f84ce8f01c78
-362f20f481b1df7ca50fe86df11e304c0ae7abae013fbdeb1fe7f4553c608ba5
-aaea38980169fc15eb0718eca3051fea142c6eae24e51b0470b1c9d20361ad1f
-ec8c0a799fabb8e11ed97bef296fc10b39ed96503d408758c6ecc63492f3d3de
-4defb94289cb05412204c3d36c428e7697212ab9c24a05ec13d27b017d1f7fb3
-15dbe2563fb00b7d7706a64cd22ad45db96fedc41d3022eaa2df55d6e65d40c3
-9d501e4575718cf7c784c6c724734e0dc598a95a997a6545628fda277fb75f7b
-0c1761e3e0408c38e7972ada405012301b919f9ce925bc451644fad90efb6fa1
-62819061ad78992aac07d8a60ccd3033ddf10dffc9fb29921e5790b9c6f502c9
-0f71f63898ffe2d1bbb773ab17d27756c13cfcc0ecd5893926997ce318ba6716
-e463187beea13224650ae855571905ef1b4a6dff435b6afc43d464a3e3ce3188
-5a24fbf28db8e892833f24be491cab7e48cf2c0b69ebc9c7667f703ea3e1b7eb
-982af736f2d10496dc2c358d16fc8316c3b1ba061d682232e87b09b541e18b0d
-c06b7e8bcdc04bc22f53ec668844c22dbc4ea5b756a9288fb08711d1e2474fd0
-f544579e3331d9f9315c4002dde371235d804259804ba18bf27e2bc843cad136
-cd20b676570f74e4084773063d0a09f1c97078922af2f5360a8159c2ae17ec27
-c64d8d72b533a62b0bca6326e963d9c58759a400a8b71bc2a60ee79fabc76611
-82fd1c626cbb9d7304bd8d363d9900e8777cac47defd8caf09038f23494dceda
-13bf53661dbd183259a23c8d65caf3ef45a69533cb2d48b3ca3b7046b6a8389d
-5fc1c3857222c428959526c99d773e23cbf305d9bc616bac57a0d2d713daf3c2
-43d9b56c944e4748466c5be464e5adde746599cce30180e4d2768046c3e7e508
-60888ba0b61159d1ee984fd3d37b68e39acdb248e6b1f3951940a3a60070e701
-5f53dd3cd8e36dd7896f75c5023dc629736901c5b46319c26ae6c19f2f80d489
-be7a5a92e7f8bc716727fe000d3a8a4213a2ac5f6c1c9a96ca5654bbed40b44a
-d2414d25a29786de2e5b0efd5a01727bc54bd041e4abc6a920b4e1fc857fb1de
-ab75ab41b2dd7e7deaac6af802cad689a866c7c425ba1876500b5456864fc05b
-21b883eff82c96f4dced5c0c733367d4a1fca966f471386cccbdf2d95d386dd2
-d79e43b03cfdff4a9c369bdc248392db702167458eaaf318871d639722977752
-44c5e3f5c45ae0f5788c15422c646747f7a586007a7d636060ccc11c3285be86
-fb54e493d71c79f32c1e0324b5812a7d4506eeb0199ca8fdf8c17e27cb4e3801
-ca4378469645ed4cd6e438a9d4579c9811b921084e94542d8bca618919ae962a
-b18cde0353fe47bb836d8d6e4dd56a297711873d9101c6f8f7d1a5075a6d840a
-e48cc4c70d5232baba5af46499a4c82958d8a6fbbfef86ca1b50fad89e97d1c3
-b3cda28d1e66ccf2f1c0f8150be73db6fcdde760715ae9fdf2bb24687400f4c5
-41c9ed695aa923e152f92f7becd9e85d41d0d8e2e6692a14bd5ad5a8dd1a96b5
-a67f8b27cf8b3176b6b2bc785ee2368421dcdf98ccddf2f23d006fe1e02da1e2
-b994457ab691496dba78c15d352189c9fbc94a92a7ddda6a3a450d89163b822b
-356a22ea2f3efbc73b91c12c8c2866d5a7432a2ff6adc54077725235fa4fd89f
-1a38108d4c7668e63e12bb289904e12a97e3a56f2c8480f91f8522a8cef6e688
-c9b07482e0cc7bc6c13dabbf1618a47419a641aaccea0a4bde44044ecdf0c42c
-1bcd725e0a56fac3e020ce42173d2ea945d941a712f214c1cbdd800566cbf968
-967d665e7987786687a8dc75b71d9fd84ea2fb888256a48692615e8631938d4b
-b32a26dcaaa09f35c6ba19588ab0ccf3bb1949813bd5b93e6731f9ffc57227ff
-032861f757c6c754fb773147427ed346649c5e9fdb132cbead7e8aa28822e50f
-4d2684cd68575aef73f0a0bf97cebf08a6dfd58356f977a48d83a42bdd782cf6
-bee009e82602ab8677a337807fd2f9ef8c23b64a041b70bf5ba98b392504d926
-b0aa788478a62aeb5ac518c0f011e55ee8dcd6e2319de1bd74334debe7977da1
-57f2941999299799a448f661e48fa9092036d9777e1dcccc12f1b79c94de069d
-9e6e98facdd66cc1b6e75f8d44f3eb53e26226593f8f48fb3252d030beebf9db
-c998decf56ad7a3cd3e1effe62d605c06320a3744cf4e867b5d7f5f8d47f036d
-5937aac0c7ac8d8f1698f085791045fdc7ce880c8d5176596871cf5f07820230
-68883afc9eaedd182b1f9c60013b92109cfd28cf8740d777307cc2de672c3a66
-001aaac10e422ea3e0573b3afbbc83633b9d103de7b0530625441f39363a804b
-c2e343f19e4e4cd502a88c12e3de1cb382ad9e7310417f7fceefd4bf64cca6a1
-9cead353cd232c064c47237ceee396fb51001bd9fdcec2b3326e0eb49703803d
-0e94e462259ae3f5bdcb0b180923035f9b49ec95a9bcf1a375d81ae2c7aed1bc
-65dbba2dcd3f3652753aaa5d8cc617c6f7ef16a78b3e6307e582208254ea2911
-c79c16f3963013b7ab06688433e5dab3639dfa36d86562b2e496114668651366
-f43758a5a34fb9e46666af146e3c76cc1dca2a489e6e3d3dc89053323887fbb4
-b0983f3df46ed75e98b6f1e5fd8e480ba328215516c50bc4383e18818a0ff50a
-ff0ea5c6579434a51c88558fb1ddeb626fc47ae45b3dbe86e27b3641035502fc
-fd4a20290ff1abaa87658f15d8b4b4614dc516784c2801fb2db4f78ae14deae2
-ed645fcee410f3404095ae7b7929811eaea86a341ef988952c9e98940d224483
-9a48c9a8e4807f6fb49cab06aad1043b5f124da54554bfab1cb601285c803a53
-c00c0983ee483f13b0b9f9020d7169e01b2bc24f77a6fae19755f6be4404fb43
-806c24f1827388475d462d64a55dbd9ba9e15acde222cd44f57b55cfbc2e6561
-62cd87ba55333361f89b3408edbbc14859864f0a65975b003de187b8aaf27058
-84cdeeb1ebbe438aa83c0a47cdb871f5f226e1365b6b7709f7ca194cf2e249d3
-0015245f7e792b1c436d87cb944ceffe7f1ed906c90ccb27876df09f5f8d6b2b
-ddfcf113726d790986b34013773b8d621434b754c1ddc4da14c5c2f1cc3a2194
-1b6bbc159e6f7ec23e279507a5bf71534243f45ddcc2029030d695e82e968808
-0770fa7fe17f1f999fd3c34ced7d
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-cleartomark
-
-%%EndFont 
-%%BeginFont: CMSY10
-%!PS-AdobeFont-1.1: CMSY10 1.0
-%%CreationDate: 1991 Aug 15 07:20:57
-
-% Copyright (C) 1997 American Mathematical Society.  All Rights Reserved.
-
-11 dict begin
-/FontInfo 7 dict dup begin
-/version (1.0) readonly def
-/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
-/FullName (CMSY10) readonly def
-/FamilyName (Computer Modern) readonly def
-/Weight (Medium) readonly def
-/ItalicAngle -14.035 def
-/isFixedPitch false def
-end readonly def
-/FontName /CMSY10 def
-/PaintType 0 def
-/FontType 1 def
-/FontMatrix [0.001 0 0 0.001 0 0] readonly def
-/Encoding 256 array
-0 1 255 {1 index exch /.notdef put} for
-dup 2 /multiply put
-dup 15 /bullet put
-dup 18 /reflexsubset put
-dup 19 /reflexsuperset put
-dup 33 /arrowright put
-dup 50 /element put
-dup 59 /emptyset put
-dup 91 /union put
-dup 92 /intersection put
-dup 102 /braceleft put
-dup 103 /braceright put
-dup 106 /bar put
-readonly def
-/FontBBox{-29 -960 1116 775}readonly def
-/UniqueXX 5000820 def
-currentdict end
-currentfile eexec
-9b9c1569015f2c1d2bf560f4c0d52257bac8ced9b09a275ab231194ecf829352
-05826f4e975dcecec72b2cf3a18899ccde1fd935d09d813b096cc6b83cdf4f23
-b9a60db41f9976ac333263c908dcefcdbd4c8402ed00a36e7487634d089fd45a
-f4a38a56a4412c3b0baffaeb717bf0de9ffb7a8460bf475a6718b0c73c571145
-d026957276530530a2fbefc6c8f67052788e6703bb5ee49533870bca1f113ad8
-3750d597b842d8d96c423ba1273ddd32f3a54a912a443fcd44f7c3a6fe3956b0
-aa1e784aaec6fce08dae0c76da9d0a3eba57b98a6233d9e9f0c3f00fcc6b2c6a
-9ba23af389e6dfff4efec3de05d6276c6be417703ce508377f25960ef4ed83b4
-9b01b873f3a639ce00f356229b6477a081933fef3bb80e2b9dffa7f75567b1fa
-4d739b772f8d674e567534c6c5bbf1cf615372be20b18472f7aa58be8c216dbd
-df81cc0a86b6d8318ca68fe22c8af13b54d7576fe4ca5a7af9005ea5cc4edb79
-c0ab668e4fec4b7f5a9eb5f0e4c088cd818ecc4feb4b40ec8bd2981bf2336074
-b64c4302813551ec0153be72f1f9695b56a658dabe99f8667d0236d0abb09f3c
-ea230c59e6cc255cf32ccdc338aff2bfe51f3521d06c7825b3f99d122ae597e2
-d995b95525325f461af5bfe8eb8c42ac414629a4b0e2887c696966ba8c1b6f3c
-ed5540608d095018fda4f0a224566315eafc70cc46b7f315c2e1139c87645173
-91b7c65ca7517a60d92f76ca2e67dd4b3bdba7aa7b5244e585a71eabb36b2bf4
-fadefdce47a623ba178613eda0b665951ae7136ac733db742f94a871fe68e6d8
-fde47d96669d1102cb4395f209cd0bdd18ecf2b72156283bd9f76175bf1cc9d8
-7001d1bc696cea850a5904fd1fd68ea8ec1d997580e1ad4d6c1b874fd92bb3a4
-ed5f7661ada49c62f8084a7b826810e86c958e00fadb465b2758a8ce6db79a2a
-d2ba4ea210d3170bd2acddea0357aedc5efc7badbdc739259d8562269170ae01
-4b0c24b09735adc253e26937889bcbf00b31817df769dd0594ab3f25ece62e50
-d7128e4137cca7a6bf205919c60946b7ed42f80d00c9b599c2f0fc6ad86d7eea
-0b445529041b481b9b7745e70244385c25255d2f869f8026ce0215b9c55a7e60
-ae8a42ef9700976ba849cecaa5990a1fda9c33feb854e3321beaf9ac23b1bd56
-250ebca1c4336f24042370409e1ec1a7a7dacc212295a43bd621e40a597efe46
-b2eb64b943a9bb0572c4e0d04201ad063899fb3e7559d7403d6c3050ce089454
-ba0d70bc7e1e1795afa62cf4e9eae075a064a6e4c4e36e8308eeb81ef2bea17d
-318a31ca3df6b2adee5ee4071bed0d7efd58e207d818e278b91c8620ef1807ca
-4a2f4ab30a51fe4152006a073a1ccddd1ee8671fd2ca9c54cebd27904a493a48
-ad9cbe731cff093ead2e314d7a54ab0a62cbbe09f084e254b97f8fea39242dc9
-ec087eb96c5538b484b604bb1585e3946b415e33e9ecd2de401bbdcdc789b6a1
-47c42261414dc09a6252422c04b47ad78129112c22dc88eade9e4eb46a3d1525
-a4bbd59c343e189a97e77839f3957c77e532fbda0197c91c6564b5355aebfbf4
-1bcf0a078d1db53b1e89c44a8f6c9a9f68665084b8e1a91429d401dd616f3b02
-b966bb9c419dbfdd8e7ad453ee0aa387eedc1142d815ca28715c2d9c308a1bfc
-1f2035871ab8e411022d3c6fad8f68835b9142a733e89fd82d1eb5a7ebad5318
-66045f06e194525c59250e09c8f04b4302b54b34a065b7251dad0eca830e0072
-4c45f345a97061b261e9221361e80aaa1985dfae610990884a04ed65c26ad1b9
-2a28f4e4161caf23a2b8a364e2bc990b27c1341a1754bf1a032aa69846de6e69
-a42731dc7ec26e1abfe2dd09391f70876beec63c307ef0a8026ffe2bef19244b
-7123ea890ff1eaba8044d3e4f6436862e52dac2b713bdadd9450eb2235d5e008
-0cae2aaa8967cd68e15fa84dda4bcb391ff5cd8b47b8c08c02cbaf16d83a09d9
-fc09b5aadb7abc34e388c7d973a9a03fc02bf6c36a1f79af7ea72e5765686aa4
-4f142fd393638781733c13265a1a5a3b437369171db0a4117cb61a9eb428a0b9
-ef449cd651e3e4ab905e2a295e77ac44cf8507529333fa63e87bf9961645f51e
-8b25e19be7ec03b205474e1f0a19ebeec6f2564d9e19399b27bc0efe6424f017
-6d0f282bca9350a5955d01dbd91cde44e20864a230b76b4cebee653783926293
-4b7f77bdae0d9b0bd14eb611b4da1779b45eb16e329618b9b995cd0fca4af32b
-f077f096ca58c3df8dfff71d562800d5f8185fa52e5a9d205e8e51cd9c014448
-ba782fb6ddc461361b5c3962533f756e392286309b71b0b569c1fbcb2962b7ec
-17fd34f672c2c15cf1ae5b1e49be71f34f158e72fc09f59fa84b3fe0e04830a5
-a398caf61158de3a12c7a56eb709a5c28c080a710dcea99310b8998731b014cd
-ef816a8dc8c73c2b72a23e99998bdd1586c7c31b818a68fb5486041c693d176f
-8b160d0329de85cc89a286b485d374fe10129a3ec0b5c087451b8efb7cf08f19
-300a18921401498b580307342ba7df251cfdbd4f5637114eeefc113937263e85
-aa59c840597def86297aa1deaff84e5ee13e406ca73a8b06aab2857a906a8acf
-a4862b6c7df139c840ecb800d35cfed13f2697ac8c440287a6a8f56de44ec244
-d30a5c2d704a61699a63af9227e8fda255a36601f0909c9b0ce371c5f8e4e226
-655ec4be0c3dca5b0b2391c3babff3e0f8519273b95001affe12b58ad78b1f07
-83d1db49bee439f5981c2fce2dd7a1b447d02eca534a692293f45ce732c7d69c
-bf58aee97f85435b5a81795cc5d91b8b6ee35401dc646087542373f71d8a0b8b
-041b134339e6bd073e86a7b2d31ecdaa578e34b53a3de9c93b17a9ea82206547
-4816ef66e8464a04f4a99f76a8b58739871f61f44c98fd7b85f8fe46806e8ee7
-df462a01df21ba6061011810493793b01cc4b58440f5c2c6cf0c2e9de5c286d3
-eed7c590d33ba72d7c76b759ff8e7cc48cbe5623545bf96638a408f3a29e4486
-2e153410f15a6c9b4dba97f2397f7cfe61a83fb4f46f988a9e67f3aef2794335
-5ce0be6d5bba3e2a256df3e0b59abf08b375acaa02388d7ee73510283c482134
-8fe809b097d77099329a79db6843e9e3036d59352efed7f3156d9583f2f30805
-932583c68f2ffdc00ca416
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-cleartomark
-
-%%EndFont 
-%%BeginFont: CMSY7
-%!PS-AdobeFont-1.1: CMSY7 1.0
-%%CreationDate: 1991 Aug 15 07:21:52
-
-% Copyright (C) 1997 American Mathematical Society.  All Rights Reserved.
-
-11 dict begin
-/FontInfo 7 dict dup begin
-/version (1.0) readonly def
-/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
-/FullName (CMSY7) readonly def
-/FamilyName (Computer Modern) readonly def
-/Weight (Medium) readonly def
-/ItalicAngle -14.035 def
-/isFixedPitch false def
-end readonly def
-/FontName /CMSY7 def
-/PaintType 0 def
-/FontType 1 def
-/FontMatrix [0.001 0 0 0.001 0 0] readonly def
-/Encoding 256 array
-0 1 255 {1 index exch /.notdef put} for
-dup 0 /minus put
-dup 3 /asteriskmath put
-dup 48 /prime put
-dup 50 /element put
-dup 106 /bar put
-readonly def
-/FontBBox{-15 -951 1252 782}readonly def
-/UniqueXX 5000817 def
-currentdict end
-currentfile eexec
-9b9c1569015f2c1d2bf560f4c0d52257bac8ced9b09a275ab231194ecf829352
-05826f4e975dcecec72b2cf3a18899ccde1fd935d09d813b096cc6b83cdf4f23
-b9a60db41f9976ac333263c908dcefcdbd4c8402ed00a36e7487634d089fd45a
-f4a38a56a4412c3b0baffaeb717bf0de9ffb7a8460bf475a6718b0c73c571145
-d026957276530530a2fbefc6c8f73e9b697ddc0351763500e23c4d170ea8a2d2
-75ad0b6b23097f02fa803c1f46f9ac10fe0e527c431b11b1b9a50e874896cca6
-17fe3e255960846bc319ca68b9b930a45d5d0fc36b352c3443ab6f7793b38d2c
-7fb9c409ab7980ead55e9f8f6b83c70088d1fa6d7f2214da8928e40b96334ad2
-72d1b5db9d1355a579b26a8dac21f021e393d7d837a95deb8de92ed818a8b80b
-98ee9cdd8a3c57ad7d6eb7a82f43eaa6ec520eefa7302e750edc4b495f70bba2
-24a2182eec37f1a1c5dc8e20973007150237daa6bf03d498826777eeebe09014
-ebfe05a8731e1a421cfc513d47d673e3d94d805f5d0668ffa265e0962cb5a75a
-4a93d9b8763c70f88a5d87e970994617fc62f70fb0ed32c459934f23a9f150fa
-083cf9eda2757efdfc0ffcf2a563927bbad06da9fbd2cc59328c0d1cbf948664
-ff7eb9e71e42dd9eab74f6d8385bec475fbbbc5d26a9c90ef6e6050ec283a71e
-6922d272c3c23863007a9f53cbc7cdf50d3ea31622542858c80e08699eb84656
-ea41df4a8c71471000d202dff2b633a0cf98d403af763ed5240b7e301f14beb6
-0059d1ad4f936e4a3db3338958feb1fa736b970f7b9c0317b9ab2220802aea08
-22f4823816d7cdba7d977abfa1b68382e8ba20c656708ea6599d9912329b2292
-b1672afc5f9806e3aca1e593d770dc728a8798e5e26e536b128c23c131b686d7
-82a279a89e0ff3eb32ef20e5df240933d65f58bd8c79ca297191de63af012daa
-658b56745ffaf752d97f342d9ac6c2976fa2a7b56ae33f609451258b9a0cdd1c
-f78e711f1878ccbd46489c78534da7ef61aafc7b174d0ec47b78c884b5382993
-8dd2dfffd077c9e38719cb128beefbc65bb2619383071ef0041b8c85762fdba1
-2ab9ae506dd348e40ad87b15727c6729329a2a4f5b674cf802feca3cd12d7b9e
-455534b2831cd4cc04a13b890f9dafaded255d79844df6622c203cb82f840afb
-8364e5c1e72f39179d7e9dbd4b0778d82840d7ac819be3fbbb93975b34f5a2c1
-874d4112f660462027eb6912f64c049598067ddd0c51e4674034636c4bb0a833
-d50ef70b7b5889cb44a40e8173421082a5058846bde25252254f3258cd8356bc
-205f5a2ab23b1babbfe628f2b40753979b7631d163c2a94dc27092273f0382e7
-615a09eeac272e51ddbfb633f1c503ba8f2036c3fbf0608a4e523a12e1613a65
-99149acf52c8b0a077e52551fd08bcb8e7b1d2111f682425deb1e34f227e4103
-06725b89ee10a10996d0aae0d765896f910f97363b9464914c1627d6336bb8f0
-9187f280096696f0e83f7067ac2bb763046b58c206b664d37ca9afe9925055a0
-0c997a12a28cabce6e96d97f782e030ccb2c728053abc09f42
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-cleartomark
-
-%%EndFont 
-%%BeginFont: CMR6
-%!PS-AdobeFont-1.1: CMR6 1.0
-%%CreationDate: 1991 Aug 20 16:39:02
-
-% Copyright (C) 1997 American Mathematical Society.  All Rights Reserved.
-
-11 dict begin
-/FontInfo 7 dict dup begin
-/version (1.0) readonly def
-/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
-/FullName (CMR6) readonly def
-/FamilyName (Computer Modern) readonly def
-/Weight (Medium) readonly def
-/ItalicAngle 0 def
-/isFixedPitch false def
-end readonly def
-/FontName /CMR6 def
-/PaintType 0 def
-/FontType 1 def
-/FontMatrix [0.001 0 0 0.001 0 0] readonly def
-/Encoding 256 array
-0 1 255 {1 index exch /.notdef put} for
-dup 49 /one put
-dup 50 /two put
-dup 51 /three put
-dup 52 /four put
-dup 53 /five put
-dup 54 /six put
-readonly def
-/FontBBox{-20 -250 1193 750}readonly def
-/UniqueXX 5000789 def
-currentdict end
-currentfile eexec
-9b9c1569015f2c1d2bf560f4c0d52257bacdd6500abda5ed9835f6a016cfc8f0
-0b6c052ed76a87856b50f4d80dfaeb508c97f8281f3f88b17e4d3b90c0f65ec3
-79791aacdc162a66cbbc5be2f53aad8de72dd113b55a022fbfee658cb95f5bb3
-2ba0357b5e050fddf264a07470bef1c52119b6fbd5c77ebed964ac5a2bbec9d8
-b3e48ae5bb003a63d545774b922b9d5ff6b0066ece43645a131879b032137d6d
-823385fe55f3402d557fd3b4486858b2a4b5a0cc2e1bf4e2a4a0e748483c3bcf
-5de47cc5260a3a967cac70a7a35b88b54315191d0423b4065c7a432987938c6b
-edad3b72ad63c2918b6e5a2017457e0d4ebc204b031f3fc6c13d7da7277a94ba
-018e9998b3dd888011a5d7c4204989f30f908b95533bda845746b673ab71ea57
-65a0d14f4350707e47c8276305b28513cbe1bb0dbd269a53719bda46e536685d
-df78ca0146b6b93e760256b74d939d4e35b5e77238f04c92298dfdd188feea30
-e053eefbcbb52f2011772b3aae39f5805597bbc1e8bb75a446ce014030f4f2f0
-f49f9e962ee4a1024a746fa92a3628db5270732b54e43fe5ecfa524f127e5fcc
-788e77e66098336ad67fe4cccaf0253272d5df79864bf4b734cb9a5859d557d8
-bc11b8e00221ebc12e97de4b1f466ead83a4c894709363bca9040410a52d592e
-34ee40cc7e5efa920546b981aa659513a24b1b85c221a1875b62d0b89e57a368
-321b8043a5b094e0379760a443d632892b14ad6d19dacc8c78093243ad67e6a3
-08e56e6b68412ee690b10dac6e17708754a00d51fc957b500eb80175716eef4b
-2ca1ef867614659bee3f2b7319e97b6fdf1efc847bf3cee3156f72f21751da8e
-5fb6898919e6799820d3de0642d756e09d6fae4ff08dd3deda3173bff4bb11f7
-9109c97ddc05897af709ea199a90fcee8ce4c7a3c15b18170c41c04de2d3fba8
-f34296a95b8e1e8de3739b17273f8f2c85e914615e8eac5e8bd2387ba3b1edf4
-7968f06e2067d836d0f9f3e085cdfd2de06a62c81d786b304326f7002e83160a
-36598589228b4dddddc43c85e1d126f8fe81b828028e26317af5894aaccf4f69
-6301e1a9fc45935d8a414957f08febebbc3a72ada80f101e47447d019ade56e9
-f4fab969bba2b44e47399fedf5caa1bcea216d7ba713d523da5d7776ec0bb452
-fc23761a3e881b097d783e6608a001eae5a6b8bb69589902e05d9dbc92f27c27
-2348ae1f0ca880d6428de6fc0eed6c08a0a7814bd38e9bd9ea8abac49d5455ad
-f6eb7b914537823b7d84f63fceb9b4b655dc671dd1f5bbb2c0565fb9841d8f88
-c25332d81167dd2e49cbf91b8ff9aaec3caff6f74b9d057de435f022e7bce755
-85dd57330b4a524700b0a0e39d0697795b55e7b1aa507019f565f02f1d67de5f
-353296ef3feb20647e28e6e2e380bfa1ee330fe17e58c44ae95716c6a2f09f4d
-646a81965cecb7620e62b0b72a5a432364cd0560da0db5a4af5b0e8b4905fcba
-b791ddcd766688f158da449332daa27ef2ef2998b0946101bdd4a521433e0c2c
-b3ee2aa43022952dd34509c8cb57975a5332ff89b4c150ea14529eb9e7323d34
-f9a1adbb512ad2b78172df0cfb85be7f73d31fe0ac0d6cf98d7e25192196f519
-b57e599040f7c29a34a661bfbe350cbb4c050d22e10acf5380b450d073164518
-a0bf97017d5ca7f23c8b245a90b0c5876e270cd583ce2ef6932c64b9ab57109c
-3c10d0ad9e58346513442514d9f7f9829bf36a5cd2a0a4c41fcc029b3abd86e2
-342d2d4f5ad996a02b9d931b09d9b960650fc66dac32b561eddfe9f2852619bc
-a885cd130b5cdf131a421a2ceecac3cf636e8a091850e5967052f80bdc72d5a4
-40f35b29e65532db482f07d9ae5b7bf9d49064156f644072de2962c8b73b9d4a
-6814b98a16af84222ab2fb12f82b3e936036ee316f01a782734ba7285aea2ed0
-df5875cd0a781978aa6c55d34c2067529cee81accfb090c9e9ca4654cd6a9a29
-3695138f98362a46be6c8a507fc5dea916d9c64a8cda8bf3b996e6faac2358e9
-9fbb29ae326d6b3fd434957c41cb6e8b54eb000003103170093d2f927f266ce1
-f7fe2b5147028c4d41a36277f534b801aa1b28ca6aa004a692dcb5f22348c2fb
-2c25faef9ed78cad84ff3d52b3c83d2b56c4a0c2702eb526a2006b52fde7b619
-e1627a170be9eb71f2559520707ccd737002471ee8a5089040d0731a667dcabb
-bb30a6e5595695aad80742dac5ceb37924132116791565d50d86b692ce777412
-21b45baebd359adda98c084a0102d6d52f9f774c5798b0bea1ad3ae86111126a
-50da58673572778d3bec5fc0161341ad43f221713fcf5d783cc2855d7d17b376
-ee7b97b5452c7cc87c2be2fe187420969facd599b10de1578b0bad79cda626fe
-45851f43b5785ba8989cd8290791a8f40931ad8353ac077bd58cc2a99bc95f32
-fbe74ad2e8c2dad4db14612aed39c9c9fdf558eb80e6a92ee5d2fa5ff8ae4a21
-2d3cb19ef141679106b28f30dffd06d9e3a8a592f67a0407eccea6921c55d0bf
-961036adb22fbdce5a84feb3dcf64c4408087516edda733b4240e607e26607e1
-ce8b691b28d2c1741caf5d252c97831594479ac0ae2d2261d21a0f45266a9862
-d4ce67aac80573d4132a6cf7472bd3fa17f2c3deef3c7f23e7b5bfd640d4cdea
-79331fe5cfad5822352b68c29d18088367d063837b4a6c78ef1e4c3dc3795a4e
-3b2cfa5cd67c94aa65c210572001b9fef4a37bd2e557c0353e24857fc5bfb7ab
-49e709218905235efa101cde008f98f6cf896186e780ac8877bd4b0935a6
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-cleartomark
-
-%%EndFont 
-%%BeginFont: CMSY8
-%!PS-AdobeFont-1.1: CMSY8 1.0
-%%CreationDate: 1991 Aug 15 07:22:10
-
-% Copyright (C) 1997 American Mathematical Society.  All Rights Reserved.
-
-11 dict begin
-/FontInfo 7 dict dup begin
-/version (1.0) readonly def
-/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
-/FullName (CMSY8) readonly def
-/FamilyName (Computer Modern) readonly def
-/Weight (Medium) readonly def
-/ItalicAngle -14.035 def
-/isFixedPitch false def
-end readonly def
-/FontName /CMSY8 def
-/PaintType 0 def
-/FontType 1 def
-/FontMatrix [0.001 0 0 0.001 0 0] readonly def
-/Encoding 256 array
-0 1 255 {1 index exch /.notdef put} for
-dup 3 /asteriskmath put
-dup 13 /circlecopyrt put
-readonly def
-/FontBBox{-30 -955 1185 779}readonly def
-/UniqueXX 5000818 def
-currentdict end
-currentfile eexec
-9b9c1569015f2c1d2bf560f4c0d52257bac8ced9b09a275ab231194ecf829352
-05826f4e975dcecec72b2cf3a18899ccde1fd935d09d813b096cc6b83cdf4f23
-b9a60db41f9976ac333263c908dcefcdbd4c8402ed00a36e7487634d089fd45a
-f4a38a56a4412c3b0baffaeb717bf0de9ffb7a8460bf475a6718b0c73c571145
-d026957276530530a2fbefc6c8f059084178f5ab59e11b66566ca5ba42b1911a
-5d7f1bf343015eece988b7a93bce0c7aa61344d48aed9c92c8698d4b7c9951c8
-7d103f2414b39e1437f9d2e50c4ee5f218f2e6716926a79ea978f13b1f855345
-191dd7d31d8f82c2e3343c7a5894d95bdc492c28226834efcb5c12fea36ac5cc
-430e0aa604961e34888adf6c1f3954cbc2498e225d953cf5685852162346f474
-5a2a7087d5d7ad486de16d2ca8e15cee26e012671ba3bdc7d95cc8c98bb774f5
-08625e968aee27ff7d1a06e63bcfb5aa4876c3f8f13b30ccccee73c3caf4e70d
-98e6ed2f422dbb4950bf789680e064150995941a9f4dd68a575949847a7d012b
-b910bf03a69374e341e8036ff92c949f3dc6e86aaa7a2b79532b36ca1496c973
-3f5e789fa3754f83951039e765b6ef8d37389a18ca2655d971ea0ab2f6131886
-1d71a694f55fc3186d85d232f23b49634341f3d4279a84def32013aabbb89fa4
-20ba8b5a82ec05c02340bfc3e91a5db9a027ddccd503a463a6bf851d16d578a6
-b0a76a6efb49266813508e17c5b74b2890d4c8dad59c3a09170f03dc0265a344
-3356687a0d87b14590aafdc0739693bb5e81d1a98faa93a01a1b550d6ff8f53f
-06b1c4158d18ebfd24cf56f2a597d93da619a4034396e94a01a3c6b9f05cc22f
-2737d96e86155384cb35c41e2b9f34256e7d2765d1981b70b6e4937f7c0ee777
-e2b72dd324b0de03ffb857bc2d97dc2013e0a7c0a796a2ce060a1ae00065ff25
-de3f1433f60a0027f873dde7228f44d5bec99f2090494867fa9dc172a5c6b303
-5547be2f6ade63192e3cced295b049b7b61283a13eeb7a1541f72f6b1f464df9
-a6ba7d783987b571200b314418c8f132f0acc95ee967aaec1c8ee0d734dbf8cd
-6ca9e20df809650d5e92b4a48e854ec9d24e1f9a0b0d8fe52779156dabe22ce5
-11ed2afc265c8fdd73c8f73e5de20dcac79671963a66b0967d0c83f5f62240b7
-322bbd4a6f4a4532b6997ea91071c95cfab937f912ade36507ac53e60904ee66
-cd828d58a502e0dc
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-cleartomark
-
-%%EndFont 
-%%BeginFont: CMR7
-%!PS-AdobeFont-1.1: CMR7 1.0
-%%CreationDate: 1991 Aug 20 16:39:21
-
-% Copyright (C) 1997 American Mathematical Society.  All Rights Reserved.
-
-11 dict begin
-/FontInfo 7 dict dup begin
-/version (1.0) readonly def
-/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
-/FullName (CMR7) readonly def
-/FamilyName (Computer Modern) readonly def
-/Weight (Medium) readonly def
-/ItalicAngle 0 def
-/isFixedPitch false def
-end readonly def
-/FontName /CMR7 def
-/PaintType 0 def
-/FontType 1 def
-/FontMatrix [0.001 0 0 0.001 0 0] readonly def
-/Encoding 256 array
-0 1 255 {1 index exch /.notdef put} for
-dup 48 /zero put
-dup 49 /one put
-dup 50 /two put
-dup 51 /three put
-readonly def
-/FontBBox{-27 -250 1122 750}readonly def
-/UniqueXX 5000790 def
-currentdict end
-currentfile eexec
-9b9c1569015f2c1d2bf560f4c0d52257bacdd6500abda5ed9835f6a016cfc8f0
-0b6c052ed76a87856b50f4d80dfaeb508c97f8281f3f88b17e4d3b90c0f65ec3
-79791aacdc162a66cbbc5be2f53aad8de72dd113b55a022fbfee658cb95f5bb3
-2ba0357b5e050fddf264a07470bef1c52119b6fbd5c77ebed964ac5a2bbec9d8
-b3e48ae5bb003a63d545774b922b9d5ff6b0066ece43645a131879b032137d6d
-823385fe55f3402d557fd3b448685940729e6e22f4be0e08c6505cba868f7950
-93f556b64b808dd710eb936d3ac83e5783b5f7e56d363a59a026a5619a357d21
-c4e77bea121eb24b09027d1aad93158edf912940e91cd2f17922b35885894644
-7773730bb19af9e70453e1b78d5edc123b273a979891d6d5e624f4a388f3897e
-13b045e34b4ee2f5e4fc5e996d3549640010c671de14d18b0b3cd300e57dac03
-22e59bfbf7b29422230870f5897fcfaad4b50c7c1c58edcd119218163d6f6e56
-25ccb882db7b6d09a1586508e8cb642a11c29a46915e4a96e282079cb21922c1
-c2e360b487a45302fd22ec8c5fab63e54b5e844d4b17ca2fff37c69c366dd72a
-d02922c14c0932f65ed03e4219c117962edbad2dcdeaa9c10ce8af38a4ae52e2
-b377245b0be19a77d6c936e7530cc4d0b78d0cc4a92698fa2870fa54f2d8503e
-2d17b3d52fb2febb09f2b2af0c2a1892039ebe19a690098799a858e3d39631bd
-6925a154d161df3918074ada6bd52baddd0adc3f07e2d9f15e27cbf7fe8b98c4
-07205c811121fa91e059f2f99322fed63f359ac9da97aec383f067f23e5de331
-51e80f0a88ab50fe8fdae4a5de93c1ae2fdca06150b37246140c0e87cb2325a6
-0d2349162ae3ac93144eee1e665a1289105318fdfe86b6e76251cb25adc967d3
-d0b97fe5e279e1161736ab22b4ca510b964342383a840defd38f96a7280e6ac1
-34e48d740607ff2e7804164a16d47735864db847c97335e6d4215cb99911a1ec
-015a3edaac1f28fedd56d2467130d07bae9416c15f0827d27c6c79f59054282a
-418c12c157c91223a829947f47592f7cafd93ca182b25a73a9419127e3b12a9e
-5167ac3963f2b019b338ac46d63880f94dda4b538835884d2a5538c85528d6bd
-977f844d32b43b0e48caed5a4bdabcefe71695d69ca784db55ff8fd5c5c42e30
-40097ef70580328190679602afd080901928e98fe6d2dc73cac402e4e1ca6f7f
-432df214ec854aad9718714bdb6ba5281a79414d38ff3b5d49b6265ac26d3e4e
-a6c10279881a342085ea3e9bb3dd7f89bcbcfd367ff35c8e711da5022dce9399
-016902f1575ce159c868f1f9ecac906f7a5e7f60fea3c2e71a2548de75ddaf9e
-f3bd912397302b349d1897aca3279b170aee052fb7f473ac38ad55bdb638421a
-8ebb6dc9887fe398c58ff86217a35ad1bfc089e8a1dd89af1972e100ee0a289f
-4cd724cbd37d89e7b30ff19887f6dfd9332f5efe43d6cb6b4e42d9e70c79face
-5741a2d96458bb62f8ab9e12848d9bd05d0c1795a0a45b188762163a0ee14418
-476631c149aa9cc61c746cdaf335337be1e733e652d4650291d864efb26b07f2
-63644ba180e34e0fa0eccbb4f7d0372c7288301dd46dd34fb5d055757f818dd0
-e20ae31124469e7e9a345e0e6be9a0c797c9a3c726b17b1550ba3937203f5764
-2d4d44ce8dba5a13c8cbd99e44015855f93084aa67bae6fb9114361be84268fe
-6430900fa1fe389b22da19b6c3437999c1365f39c2bb6abd92eadf93c6d9fa1e
-ccdd217fc6d1c2842b5187cff6da02b1c3a9a316c414f8dffc71f0e34c35167c
-2a2514a30bb7617e533fdc4bcc453d684f5dc7a290b400c57e87a8719901c077
-4ca32a5e311fe7dab79bfe6036621b6831f817c4d7ba447997e12442fe33cfef
-f94e68847de78230a79e2841e73382efaca832c888b25d2bb81b4916dbd747fc
-172616ae399eed5be00ffcdd22a2d965ebb2adc7d97156efe60c3fb86399ba49
-ba0223ebd12c75a4d2a9cdea372376993f80992e0122f71f4f23992269b1a21e
-b6732d9f6ee4a9e584fa56dbeb6147d098ea6144be68211dd20a9c6b688bb5b6
-c9303d9e39fece40bf91e134b3811568dc7444200faf6a60e0e784df471ef31d
-de12b813811fc69ed7de6f1d8aaf407db2339d2ad24696e086d14038feec0f66
-d2e7649fc57a6396a480935be9cb7c54ec870169ce7e6c4431deb30a3e577750
-cf914d9c0c5a83919bca88f5d6f9e579
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-cleartomark
-
-%%EndFont 
-%%BeginFont: CMMI10
-%!PS-AdobeFont-1.1: CMMI10 1.100
-%%CreationDate: 1996 Jul 23 07:53:57
-
-% Copyright (C) 1997 American Mathematical Society.  All Rights Reserved.
-
-11 dict begin
-/FontInfo 7 dict dup begin
-/version (1.100) readonly def
-/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
-/FullName (CMMI10) readonly def
-/FamilyName (Computer Modern) readonly def
-/Weight (Medium) readonly def
-/ItalicAngle -14.04 def
-/isFixedPitch false def
-end readonly def
-/FontName /CMMI10 def
-/PaintType 0 def
-/FontType 1 def
-/FontMatrix [0.001 0 0 0.001 0 0] readonly def
-/Encoding 256 array
-0 1 255 {1 index exch /.notdef put} for
-dup 14 /delta put
-dup 15 /epsilon1 put
-dup 58 /period put
-dup 59 /comma put
-dup 61 /slash put
-dup 68 /D put
-dup 70 /F put
-dup 77 /M put
-dup 80 /P put
-dup 81 /Q put
-dup 83 /S put
-dup 84 /T put
-dup 85 /U put
-dup 97 /a put
-dup 98 /b put
-dup 110 /n put
-dup 112 /p put
-dup 113 /q put
-dup 114 /r put
-dup 115 /s put
-dup 116 /t put
-dup 117 /u put
-readonly def
-/FontBBox{-32 -250 1048 750}readonly def
-/UniqueXX 5087385 def
-currentdict end
-currentfile eexec
-80347982ab3942d930e069a70d0d48311d725e830d1c76fba12e12486e989c98
-74c2b527f0925722787027f44470d484262c360cdfdddf3657533a57bb16f730
-48bfbbfcb73a650484015441fdc837add94ac8fbd2022e3ec8f115d4b4bb7b7f
-15388f22cc6198efe768bd9fceb3446ee4a8dc27d6cd152485384ef5f59381ff
-da43f2d20c8fb08aa27ab2015b774db10dacfdcd33e60f178c461553146ab427
-bdd7da12534ba078ad3d780414930da4f8d58abefd45db119b10eb409dd89792
-3c6e705479464a4b310b58348c4b42393988fef4925cf984423aaf65fea9f0e6
-4629953bcf50b919d968d99bd185f83112b2759cc411764e9bde677f57c5ee5a
-c555448d5f81a16259ded1e11bf4119d53e8ab07a802df900d3a2d5ccc1c6876
-d29c5e9effb7af3ef83400b0910c07873a8c56fa7b1eb1ba426043b00cc95dbe
-dc6e136cbbbcb3f67509964f9f281ebf81fe5b018122eaf66c4a838487e82e18
-6e006093042848a903efb3469ab6b4049767aadb95c30408dfd58d8a10f4cb22
-168decd9f3ee100f07b49aa44c92139b669cc312ba20192454eb2375be6284b0
-26659d964b96ae82d4942e758027fcf23c25ed01115af27ce7f20efe2a822bb6
-84004f20243a49c9e93301fc21b80815c033c3e2ba58ef53da2157d524b395f2
-b37abca13bc6a2f42e824ab7e47106176b0d6db267fbb795ac7425582df2e3dc
-55863468a9200742bd7b552c48f8cf58bc21343bd3b95abfa140f33f37c6f3f7
-8b0d8a5154eb7c1f62ec598267f13e841a3e64172663935ac8b665d86540d316
-ddece329c008049c5e74b27d59022c5515059bc3b89370b1bc6a169c888bb325
-e0b74282d6f053a50da4024ed1e433271a32ab8c17d41c632b41cf9f3ecd5fe1
-24daf7aea7ce8a63047b245822930d517df7baaafa69d2d17f7d93cebd45416d
-f3459365434123a76ccf883a4973bab19807e1f0c4bab03a45f7ed69ff2660ff
-3963e4def11001eec4238c368a39d874fd30b3c14f4186ec7700fbce22abe468
-eb32baf7b0164f8f21a9b5e706b91411faaa44467cb2180ab03de375c1ab93e9
-76e11ab92fdd4a7280a6d1a8dc65c4c89d04c8ed6988045a2a3de9a4c7b1efd3
-75b78d2ee00e6c955ee2c3e0ec7817ca1274bdc3b510be7ebd1e500d0bff5eed
-52eb9de4ece6e5e061cbfc0389d458cd198e9ad3eed9b58053df2bb41bd22495
-e9b2be46eca74062f2ffeb08f7034288d43da11b503e0e11b8713c301f0852f7
-ee440cbd0aae1e0c9d7f4f33441d17878cdf154f4e4cf5ae71891da59f0ebbc8
-2d29bc393f4e4544b672ec732662634845cc437be64fcec560d466c7c171c7eb
-621d13bf0bca0f672c520e67316b2d95c6f0668a4ab4356aad64ccaef7aee840
-6c9317d8b1c66519a96eea4f1d2db6f27179d209444094ddff0c95d066634f33
-853e7622219ffa825b81ae2faee14921bc58d620daa87b86bfc29baffd8087ea
-62790b6eb6436d0a569898d82b85a51eea2e6d3fd15b2710e3b26b8a22028472
-94845e9ede5259e6639068c86f1ecf5d1a8be634f06b9ab919af14c836e8169d
-e3948538566cae3f89c7f8e6beeb314a7f530331bb8ece57b901f6b601a7abb2
-1e956fb7313b501923ada1a69c27f09529a4e75540baf813aab4243493850325
-66842f8d1f693da1e9a4a8a3038580e723304c6d34f202a73836f49516daacf3
-b55e276f75f9d398bda2ec531e40a9e17c568c3194f1a8876629e891855d0ae7
-b397ebfcbb553083b79debcc7da4a9d890fc76da60b7de055a9a0cf04eaee382
-671aa1fa6f491a98a19a5903a85e755968751d177410dfdbc392404073dae859
-9fee3175f23b491334d84d3c91f3aea8524804154af668826b942a46f3cc7110
-178ef3935a1d84055ee41a86d936160656aae13f80720835e93e19dc430b695b
-67c07dc6a1b319ef0c5f89d818dc890647ecc07e3a047213aeb351c4b5a8c202
-52e121390061bbc50600e4bdce87461a38b75aaa76e1d573783e4a9a9d4f2b4e
-15ae1b384b621825eeee6213bef83c49aaeaa543700534b84335e56e2e9a25b7
-156125518069cda1c245ff062e76b418a17a80b2102ba631be200a8c59b0a661
-6a43a8ff790ba582610c24a2dc5175fe865a21cd020a4fd2310102ca7de41fbb
-7b8508ef3945e42c2a09da2558cc9a0cb3eb5ddfe92be82a2306a74e138561a3
-18eeae2c92f71a1b3d41e48c3c9addf084765a25eaa2e0881998565dfa999b13
-d413d4a592e1c07b6453a06e6f82a4f8f570f8225f0ac8ba63bcefa2aee1778a
-4e3c1ea25f6d50b45af124a70981610f428f7035d09aac792898de54f002ad6a
-1877614d6516c8c824f549055a7d87ff2de308378d1ca151b353fec551c5e7db
-18752fa603d9d3daefb62c6b2ec6b694cf5cb0115b5341f80fb7a2390463e73a
-6c9157bb5adb21eb082869a6993ba7c38da8962cba3388181f2702c411a48c3f
-9ffd684cdc15439727fe75fd8f18c8374d75886cf739a799dcd5a2647eea7480
-859da8a3bcd71094629afd1997a05fc1d71762b9abf18dd20e419a412a28d48a
-77363b7a9ca6d473f7d177cf19deba5c32fd0132d5f4ea1183e987412ceb85d2
-4f74ab0488174b2e0b820f72bde92874fb79f879319a78021d7b24ecc0758732
-5ab344fdd02c8d356f6a7723c1794c6e77af502b8fd5f06bcb7053ea9ee045cf
-a567f2170f31a6ff5d060d81289e2cb6eee427845584a9ed30010898766e31bc
-c82c079a8d77df87b49492faa0664ca420b0c50ff01000aced86866083653c1d
-dd4835e6dc95b0bcceea56f035a9f7feaf8456fbd9b63227052cbc2f043c8c0b
-ea81b79f5e3044fd9e9340f991e67a4751c718a72c90eb0c6bbfd7d31c63ef84
-13b5bbee3924af80a7c27715384debdc1325d21897494c9ad934b26bdc22380e
-b5b0ad11f8e2117909ea99b0cdc17de09143ce8e719d975a430caf57414d70e6
-389b8f525e09abeef5c65c977b460062e12db05b7a7333360431dcb7d811f849
-8efd04fbb81193478c8da7d296e2faec6b2c3d0cbb0b550831f830b5022f442d
-80de3beb8b0bdac26887e4995909a4769ea2d372a1cb14a8a34387f10337a489
-2bc0736fdcc9731191627f328c49a1593b8f70c64c71076fef587b0208e8ad3f
-7eec3f1285ee9f458b024574e4b77f1df1353ecf533b6d75b57889c1f1ded74c
-8769080a8ca167833a898f064f55644e5005e6caedde40b40a4b313f4325d933
-c5c94c72e76685289a7887fe046e2ee03c4a7a4f7f94240175ce4efacc2d18ec
-d3e3137b1b6e94b50126c5442d3dc7a8a6298d4dacdfb10823087e8ad3ca8ecb
-2c24d23bd72590b6ba951378adc0f8d635d8e35bcaf04261788dbf14322eb433
-8ed1096538c12a637e4d5bf1337ab704fdeafd33e83ba58846adbce55d1515cd
-039a6413101daea6a4f49d586daa3375873f5accd4b1867f1bd31f91ca6f9329
-ba44f07df61996c7073de8879e6d38959756ea7b19908cf5a081f08b391a9cb8
-a75f6671b9eade89e7289490d41252d987b3499dfa87b31c935ab00f9559cfee
-0c0a004a35e2fa0e4f0d44695dbe0b17a6ab6a8d935c500bcce07cbf2853ab4b
-15f69779c96c5c9755885a3fb2e0938252c0b5fb85b6a41e95a6b2f420e6ce73
-d8709ecbbee494877df4e26396eb0e854c3ad399588b6d1f213c954dba95ea51
-f3344a8fb5f3d08e3c615036c005d1828c9d4401455ebf6daf11909490ae989a
-77884137c9ca94cc33e717d440bdf67dce128af6ffa51cedb61f87f83eff5f84
-0c349d4d7f6e867e9ad941666ff5c632bfc4c2acba7828f6e856b7fef9b08a69
-e090eb5d4c81e59a1df26fe728efea4a99effcf10fa8489c582173f360af7237
-55774b49e17fdb1799412808d9fd071a9d54f89aaa9323246a67e4abe8058c40
-0b1a602938249bd23c95b063b342e7a6771f50c5ba91026dcf3a0108d7d100e6
-eaaa081f6045af8f21da33dee154674c4d3c65780ab9004f26e0b9e729c78f6a
-22e9ff47716d11f5d76f92ae0f0f1c43f96af6553eed8693236cb7171e0517f0
-9ccd019c700bc75a6ae72fa99d602041aa95b4572e4c4546db13c86bfc891978
-cb1cbc059aa05b380cacb07f7a8d2850a07c0f5e584d34733a6ed490da861181
-dd723a89e5c607236c523c439fe8141f25cf7dbc9a13ed6584f19819b0b9f0c4
-005fb7f185a172b7c8c984fef306a563ca6d200b36295e0125862a1b0e5859f4
-7915347008fc3a6408293cacb55b5c987a5b23066ad2425597c5e45c7353dd25
-8f84a49fb2f8eb58fb9015b09e509e16b4b88b2fe5da72feefba8d4eeebaf494
-e90f4dbaf8650fa7aa2f8b7ae44a4a8f08816cf7644db8d196b767831bcfa125
-bbcfa4b7ee1aa8a7b22a9829defd1ff7303b8001e385282fc38d9b1ffe04342b
-04f46e28acd9c21a1eb95e5289f3ffb4dfa571c28107266b675a1769ddfeb7be
-bc3f07e019d70efa77231c1dfe11dc8b768151c4c2a001f7f711f91b8e289024
-5929b163cb5698a9958e144effb0d153e075d6116a1a2bed8c36df672e17018c
-74493d29619c639dbe7480eef00285ebe816b667887fee771652ae1f3772d594
-a47cb2d3246631cf0d2e6ac3c5e03ec42a963f5b378c5262e50fc975f2b4c660
-c3c359efd103b41a62d4538d4c6a927c16e21666be203878c5b14dca81ecf757
-775dec363e840cf6fd074bdba5108f6a81c7991a3f40cf8d9a7101f93fb9dca5
-4074c7207984c47048b335e6e7d87f12c17fd282c3831b9c2ac7a07580056bac
-b16399b6c211e1aa49753965bb3bc9eac89462f8804b4e51a615a816d2578308
-e845390132d4e32fbc1f65576e85d81f53cc6402868b78eb05b8028862fd80ce
-847ca511a3421904482fe693c124d6978e3abdb1eb934806fa0b3a64ae01f4be
-f0a37235ebf3b24d50081e3208380c223ed25a8ab1055f2af6e871e78707bad1
-f04acff5fb4ca29411dd4925f748a020cb1fabab9a29ac50e3d8fd430e3775f9
-e624ab77ca4b05e92fae75d3f06d76a2575f3ae3f7fa83806b954c4cbced6cfc
-38130874b52cd910c2eb365271d268ab23cd4fa29d2abb407a37678b360d9a90
-3090749b52f4247dc71659733030b2ce8b409fc38e32b931f001ee3350ce9c07
-b46c792a5f7754070690564c2dc9317bf3958e637b78b551a2aaba577bbad52b
-e1c5ac15ee46eaa0ca038ac562d657ce24b565f29b8119ca19e8b7e9f997f31a
-22ff33e5f1095f5769889b5e9991c41827d10978629a235fa86db7f5139219b5
-06fef252548772985a491a43f4b46ea6c6efbfc8fb73ffd4b0fbe84eb2dffd5f
-2d04f66442434b99abf2875a9d5207d611f37d35ccff144d797ada8ea68fccdb
-cb95745101bfc5da9558d9678fd04388fe6f2239e19edc692948edf253fd71d0
-438b1cafc02bcb29417307e6665dc117c9f0e82ece7337479e123842f65fec31
-3b5274d569d8f6b27a2fcbb83632b6c539e102d5bc0dc984aaa746f0e1de1db5
-28a15895b58233aa013885defdbbd8fd64a262a8993d3cb516ba368daef29885
-f377240a5af10e5e05789cee83e54b3094667382c0a6998f9816293429a2fae5
-5a2217df27e3d0b9aadf0b5b6a1e3c4cd4ffbeebe429f86ae02f3971e6b15b35
-68b49a3b44fce3478dc6a110f29e2a933f3abea7a37466141568baabd7411a52
-756217e28078fb66133be285fd24877953cd4c39412ca20692e653a9e7d23f1d
-231635687a1e35422c5c2343a3946ab5c51356c21f51a64115b2b3e7df1813ff
-25ee91c931807c02e640375aba7c9a059ad18c953aa1d233a03e1b0cc46f76c7
-ca0ff71e55aa175d7651f0df2fd880942528a7cd836e8c5b89ab3b0334d425a6
-1acac212587be5e5a7c5d93417747c7094f7bc379e8e956c42df9f29b938abd0
-b7713ad2630f3488f623d70c88a85dca14a0761cdc4b7b9bbd2ebee9b0a6c038
-50aeb5e4b0535b842d09497af5fa481b671a8c644858cefbc63d189c28a83007
-c766fe23f7992d0720b66c1a1bcd96330445e0e2ffd14a4eb3eea827b3730001
-872e82cccb9a2a503d85e95076d0f53969425836ec7a3571fdb0fa817682835c
-6babce55981cb1854267ab7f89e696cec60ecea00fd7d5abe69709c95dc8898a
-47c1349e72218b6dd5abc6df734c37995756984b26c0571ca730cdcc864714c9
-ed5c11d5005ab9b15b0e4e6e6fb1609d3cc751572a625c448646ca04c955b7cc
-7ebca59337f9d880109150feed4cdd1eb37d3b22f213fc43e73829be38479352
-5e3ef510de8086fd01f331b3ffb07cd3bbffe56cd21c439bd567d51bfc1ebb8a
-22a6d0d19467958947c0e3a956fb9beedb594f5c7e060b812c12997883c12d1f
-fba4e766c72fb0bcbaab290d3787ccbf411da60170bebd7b749f52bf5977c8a8
-b6644df6622e5206530a3785afa2873ea696d5b467b4c3b09c06dfc6cfbee520
-621580f0211c7594839071d28a36ffa22b46907b380d1b71f9d6670868289bd6
-d641e4c43540e9f29d9edbd72deea4e2e4d16fa441fa1b46f73608715194d40b
-b3ce6c918c31a4dd573202205eea2f7232ed59a43a81b053190d8b1e9e0097b3
-8ea091ffb9e27942a5bca1637611e56e5028fd66f28991c571e16fbca14f3406
-7fb2e1876516f81d0960f0ab356f372407d1a02b6afbff927932437e5bbb5425
-1c2f24352eaa48f3ed3e963e7c8f2115d13816e80ef7f12e91b226dd7632b655
-439f10b8413d7a15758d9eedc2cc612d042bfb2698143e11c8dee61c78c8cc5a
-f313aaf35e665a2fbc28da960e2a8e58bc76b488ce3c74cd3480b584a1588ae5
-207d2ccf3d72f00c8b0c49aa15dc69a650c8203fffd1ff7eb4c766d2ecf5c9e1
-373a479a7c1192e92288c16b2be7c46a096687af1fd2e766899dba63e8153b2f
-2a78c48a5363789a1baf924f4802bbc411b10e3abac5e10e04ae7bf53394fead
-23dcc6bb0c03978b9c6f9436b182c3634bb29f4e94477d7b745e9247cebcdbfe
-94d2810a15529bbaaa2a57ac8255e03a33bf30d633668328503444a2f8fa5bc5
-c02c97f942e325ce92770ebea0b783bc1106c3e021f5f2738665717580344c6b
-5d1cbb142a40e2b863a4356b07149c021471f20c282615e997df7c74783b523c
-8d90f000d7a6a6f45fdff7d1e0276246bfa6885bb67c317c8f2a8ba36e31f6f0
-a8799d0ee485f2d33041f03d98c4d33de3d6602f23bb09d234d6b71c6688198e
-b6217ef1088abf762140a442ccf0767685129ae52bca01389229478fa02432c6
-bb126be105d248
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-cleartomark
-
-%%EndFont 
-%%BeginFont: CMSY6
-%!PS-AdobeFont-1.1: CMSY6 1.0
-%%CreationDate: 1991 Aug 15 07:21:34
-
-% Copyright (C) 1997 American Mathematical Society.  All Rights Reserved.
-
-11 dict begin
-/FontInfo 7 dict dup begin
-/version (1.0) readonly def
-/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
-/FullName (CMSY6) readonly def
-/FamilyName (Computer Modern) readonly def
-/Weight (Medium) readonly def
-/ItalicAngle -14.035 def
-/isFixedPitch false def
-end readonly def
-/FontName /CMSY6 def
-/PaintType 0 def
-/FontType 1 def
-/FontMatrix [0.001 0 0 0.001 0 0] readonly def
-/Encoding 256 array
-0 1 255 {1 index exch /.notdef put} for
-dup 3 /asteriskmath put
-readonly def
-/FontBBox{-4 -948 1329 786}readonly def
-/UniqueXX 5000816 def
-currentdict end
-currentfile eexec
-9b9c1569015f2c1d2bf560f4c0d52257bac8ced9b09a275ab231194ecf829352
-05826f4e975dcecec72b2cf3a18899ccde1fd935d09d813b096cc6b83cdf4f23
-b9a60db41f9976ac333263c908dcefcdbd4c8402ed00a36e7487634d089fd45a
-f4a38a56a4412c3b0baffaeb717bf0de9ffb7a8460bf475a6718b0c73c571145
-d026957276530530a2fbefc6c8f059084178f5ab59e11b6a18979f258b8c6ed3
-ccafbc21aca420c9c83eea371adc20e038b4d7b8ac303004b0aa205f04135140
-76407216032fdd22e6219da8f16b28ca12524deb7bca073cc5eba65c102a5e85
-fd48e6d062cd4283ee570a7774597e5bf0e3400b6be72db0115f3cb12db70ce0
-83722870cddfadee715f10f1fcaf20e06f3c54afe5ca238539bfe2b596116e83
-f5371ff18fa5003d8543226cfd4025f9940365b392a858d27f078d3abcffe4a1
-54e78c7692d1a32bf935967c64f01b24788ff8325d61145e2d4a489fd986fb77
-38e6b254522c77ca2797a504a9ce4676a77ebacb026eca94dde5922c936f8e90
-c43e28519671e8def84a1526a8b89450ef2bd624857da91e76994317b723923a
-47cb7b71e71550262a4a4eeef7e0d2eba371584b12b189f38fdb9feabf33b900
-d528bea06075d4e71d7696aa2ce7a5bf900014283045468c2625de16e2000219
-15074a97c681b3c6eee6d67ec3e481e174b53d1a3dd58da4507f93fa57f4f715
-e5df982321fae7682dcd02c3e977327fa2b9b80ef30e834269bba9c69dcd694b
-b055398be8186c0a2d19f9c101f67b30c506d8fe62dd7da5dc0d4c7abd32f9c3
-c64e081ca3cda88b1949fa64f70da6cb7a544360778ed200f21b04958bdbd70f
-044e7e611a28443d0c7b8049413c0ac989dd986086bb0b8a304c185458138b9f
-6c929aec9a804d4422ce5429d29a5c03b8a7916ed162a368650de8db6d9961ab
-cf373b396ed91d0289d26958cce7318fd7cde1bedb07347b1990557b33352b61
-b18672a53c81d8766a5260d28b9a2aaa542368e2c307cfedbb67e7a5a2b0fdfe
-8ee5f5f0c0f3cb9e7744b87ceee63dab32
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-0000000000000000000000000000000000000000000000000000000000000000
-cleartomark
-
-%%EndFont 
-TeXDict begin 39158280 55380996 1000 600 600 () @start
-/Fa 240[31 15[{}1 74.7198 /CMMI9 rf /Fb 131[50 1[50 5[50
-50 50 1[50 50 50 50 50 2[50 50 1[50 50 50 2[50 44[50
-4[50 47[{TeXBase1Encoding ReEncodeFont}18 83.022 /Courier
-rf /Fc 134[37 37 2[42 25 29 29 35 37 33 42 58 21 33 1[21
-37 37 21 29 37 30 35 33 9[71 54 58 46 42 50 1[46 58 58
-71 42 2[25 58 54 42 46 1[50 1[54 5[19 1[37 37 37 37 37
-1[37 37 37 2[19 25 19 4[21 39[{TeXBase1Encoding ReEncodeFont}53
-74.7198 /Palatino-Italic rf /Fd 136[62 1[46 25 33 29
-2[42 46 66 25 46 1[25 1[42 29 37 46 33 46 37 12[50 1[54
-11[42 4[58 7[37 37 37 37 37 37 37 37 37 49[{
-TeXBase1Encoding ReEncodeFont}31 74.7198 /Palatino-Bold
-rf /Fe 172[69 83[{}1 83.022 /CMEX10 rf /Ff 135[43 2[50
-27 35 33 1[50 45 48 73 24 46 1[24 1[46 1[40 51 37 46
-42 12[51 44 12[46 28[28 28 40[{
-.167 SlantFont TeXBase1Encoding ReEncodeFont}23 83.022
-/Palatino-Roman rf /Fg 139[24 29 15[28 1[34 37[19 59[{}5
-49.8132 /CMMI6 rf /Fh 134[33 3[37 22 26 26 1[33 29 37
-52 18 2[18 33 33 1[26 33 27 31 29 97[{TeXBase1Encoding ReEncodeFont}18
-66.4176 /Palatino-Italic rf /Fi 138[39 25 31 2[34 5[27
-23 5[30 1[36 8[54 2[45 3[52 42 20[20 59[{}13 58.1154
-/CMMI7 rf /Fj 162[23 1[23 29[65 1[23 23 3[42 42 42 42
-42 42 7[32 32 33[60 6[{}14 83.022 /CMR10 rf /Fk 149[23
-2[42 42 9[55 55 31[42 8[55 16[83 13[65 65 2[42 12[65
-2[{}12 83.022 /CMSY10 rf /Fl 149[20 55[45 1[19 44[34
-2[52{}5 58.1154 /CMSY7 rf /Fm 138[46 32 37 32 1[46 7[46
-42 1[37 2[45 46 97[{TeXBase1Encoding ReEncodeFont}10
-83.022 /Palatino-BoldItalic rf /Fn 201[30 30 30 30 30
-30 49[{}6 49.8132 /CMR6 rf /Fo 103[25 1[37 27[37 42 39
-62 42 45 24 32 30 42 45 41 43 66 22 42 17 22 43 42 25
-36 46 33 41 37 21 6[50 1[75 54 58 46 39 50 1[45 59 62
-71 46 54 25 25 62 57 42 46 58 53 46 58 5[19 19 37 37
-37 37 37 37 37 37 37 37 45 19 25 19 2[25 25 21 58 35[45
-2[{TeXBase1Encoding ReEncodeFont}73 74.7198 /Palatino-Roman
-rf /Fp 103[22 30[37 34 55 38 40 22 28 26 37 40 36 39
-59 19 37 1[19 39 37 22 32 41 29 37 33 9[66 2[41 1[44
-2[52 55 63 41 1[22 22 55 1[37 41 51 47 41 52 50 5[17
-33 33 1[33 33 33 33 33 33 33 40 17 22 17 2[22 22 18 52
-35[40 2[{TeXBase1Encoding ReEncodeFont}61 66.4176 /Palatino-Roman
-rf /Fq 242[71 9[35 3[{}2 66.4176 /CMSY8 rf /Fr 204[33
-33 33 33 48[{}4 58.1154 /CMR7 rf /Fs 135[42 69 46 51
-28 37 32 1[51 46 51 74 28 1[28 28 51 46 32 42 51 37 51
-42 10[65 2[51 2[51 2[83 51 2[32 2[46 51 1[60 1[65 11[42
-42 42 42 42 2[21 28 42[51 2[{TeXBase1Encoding ReEncodeFont}40
-83.022 /Palatino-Bold rf /Ft 138[48 30 39 37 37 42 1[50
-11[36 44 11[57 49 51 1[66 53 2[81 6[53 1[69 6[42 1[23
-23 42[34 37 14[{}22 83.022 /CMMI10 rf /Fu 133[37 42 42
-60 42 46 28 32 32 1[42 37 46 65 23 37 23 23 42 42 23
-32 42 34 38 37 11[65 51 46 55 4[78 6[46 51 65 55 1[60
-6[21 11[21 28 21 41[44 2[{TeXBase1Encoding ReEncodeFont}40
-83.022 /Palatino-Italic rf /Fv 103[28 83 28[42 46 43
-69 47 50 27 35 33 46 50 45 48 73 24 46 19 24 48 46 28
-40 51 37 46 42 23 2[28 1[28 2[55 83 60 65 51 44 55 1[50
-65 69 79 51 60 28 28 69 63 46 51 64 59 51 65 3[50 1[21
-21 42 42 42 42 42 42 42 42 42 42 50 21 28 21 50 1[28
-28 23 65 2[42 31[50 50 2[{TeXBase1Encoding ReEncodeFont}79
-83.022 /Palatino-Roman rf /Fw 252[32 3[{}1 49.8132 /CMSY6
-rf /Fx 137[56 1[32 1[39 2[54 58 3[23 4[48 61 2[50 18[83
-6[76 71[{TeXBase1Encoding ReEncodeFont}11 99.6264 /Palatino-Roman
-rf /Fy 137[80 88 48 64 56 1[88 80 88 128 48 2[48 2[56
-72 1[64 88 72 12[96 88 5[143 7[88 1[104 67[{
-TeXBase1Encoding ReEncodeFont}21 143.462 /Palatino-Bold
-rf end
-%%EndProlog
-%%BeginSetup
-%%Feature: *Resolution 600dpi
-TeXDict begin
-%%BeginPaperSize: a4
-% a4
-%%EndPaperSize
-
-%%EndSetup
-%%Page: 1 1
-1 0 bop Black Black 330 377 a Fy(T)-16 b(reatment)33
-b(of)j(Epsilon)e(Moves)h(in)g(Subset)330 543 y(Construction)330
-909 y Fx(Gertjan)26 b(van)f(Noor)n(d)1160 877 y Fw(\003)330
-997 y Fv(Rijksuniversiteit)e(Gr)o(oningen)329 1331 y
-Fu(The)29 b(paper)g(discusses)h(the)f(pr)o(oblem)g(of)h(determinising)f
-(\002nite-state)g(automata)f(containing)g(lar)o(ge)330
-1439 y(numbers)34 b(of)e Ft(\017)p Fu(-moves.)f(Experiments)h(with)f
-(\002nite-state)h(appr)o(oximations)e(of)i(natural)h(language)330
-1547 y(grammars)d(often)h(give)g(rise)h(to)e(very)h(lar)o(ge)f
-(automata)g(with)g(a)g(very)h(lar)o(ge)g(number)g(of)g
-Ft(\017)p Fu(-moves.)330 1655 y(The)21 b(paper)f(identi\002es)h(and)g
-(compar)o(es)f(a)h(number)g(of)g(subset)h(construction)f(algorithms)f
-(which)g(tr)o(eat)330 1762 y Ft(\017)p Fu(-moves.)j(Experiments)h(have)
-g(been)h(performed)f(which)g(indicate)g(that)f(the)h(algorithms)f
-(differ)i(con-)330 1870 y(siderably)19 b(in)g(practice,)f(both)g(with)h
-(r)o(espect)f(to)g(the)h(size)g(of)g(the)f(r)o(esulting)h
-(deterministic)g(automaton,)330 1978 y(and)j(with)f(r)o(espect)h(to)f
-(practical)h(ef\002ciency)m(.)f(Furthermor)o(e,)h(the)g(experiments)g
-(suggest)g(that)e(the)i(av-)330 2086 y(erage)e(number)h(of)f
-Ft(\017)p Fu(-moves)f(per)h(state)g(can)f(be)i(used)f(to)g(pr)o(edict)e
-(which)h(algorithm)f(is)j(likely)e(to)h(be)h(the)330
-2194 y(fastest)g(for)g(a)f(given)h(input)f(automaton.)330
-2393 y Fs(1)g(Introduction)330 2593 y(1.1)g(Finite-state)c(Language)j
-(Processing)330 2692 y Fv(An)29 b(important)g(pr)o(oblem)f(in)i
-(computational)f(linguistics)h(is)g(posed)e(by)h(the)g(fact)f(that)h
-(the)330 2792 y(grammars)21 b(which)i(ar)o(e)e(typically)h
-(hypothesised)h(by)f(linguists)h(ar)o(e)d(unattractive)h(fr)o(om)h(the)
-330 2892 y(point)j(of)e(view)h(of)g(computation.)g(For)g(instance,)g
-(the)g(number)g(of)g(steps)f(r)o(equir)o(ed)g(to)h(anal-)330
-2991 y(yse)18 b(a)g(sentence)g(of)g Ft(n)f Fv(wor)o(ds)h(is)h
-Ft(n)1398 2961 y Fr(3)1453 2991 y Fv(for)e(context-fr)o(ee)g(grammars.)
-g(For)h(certain)g(linguistically)330 3091 y(mor)o(e)25
-b(attractive)g(grammatical)g(formalisms)h(it)g(can)f(be)g(shown)i(that)
-f(no)g(upper)o(-bound)f(to)330 3190 y(the)31 b(number)g(of)g(steps)g(r)
-o(equir)o(ed)f(to)h(\002nd)g(an)g(analysis)g(can)f(be)h(given.)g(The)g
-(human)g(lan-)330 3290 y(guage)24 b(user)-6 b(,)25 b(however)-6
-b(,)24 b(seems)h(to)g(pr)o(ocess)f(in)i(linear)e(time;)h(humans)g
-(understand)f(longer)330 3390 y(sentences)32 b(with)g(no)f(noticeable)h
-(delay)-9 b(.)30 b(This)h(implies)h(that)g(neither)f(context-fr)o(ee)f
-(gram-)330 3489 y(mars)17 b(nor)h(mor)o(e)f(powerful)h(grammatical)f
-(formalisms)h(ar)o(e)e(likely)i(models)g(for)f(human)h(lan-)330
-3589 y(guage)23 b(pr)o(ocessing.)g(An)g(important)h(issue)g(ther)o
-(efor)o(e)d(is)j(how)g(the)f(linearity)h(of)f(pr)o(ocessing)330
-3689 y(by)e(humans)g(can)g(be)f(accounted)g(for)-6 b(.)479
-3788 y(A)26 b(potential)g(solution)h(to)f(this)h(pr)o(oblem)e(concerns)
-h(the)g(possibility)h(of)f Fu(appr)o(oximating)330 3888
-y Fv(an)17 b(underlying)h(general)e(and)h(abstract)f(grammar)h(by)g
-(techniques)h(of)f(a)g(much)g(simpler)h(sort.)330 3987
-y(The)g(idea)g(that)g(a)g(competence)g(grammar)g(might)h(be)f(appr)o
-(oximated)e(by)j(\002nite-state)f(means)330 4087 y(goes)24
-b(back)g(to)g(early)f(work)h(by)g(Chomsky)i(\(Chomsky)-9
-b(,)24 b(1963;)e(Chomsky)-9 b(,)24 b(1964\).)e(Ther)o(e)g(ar)o(e)330
-4187 y(essentially)h(thr)o(ee)e(observations)i(which)g(motivate)f(the)h
-(view)f(that)g(the)h(pr)o(ocessing)f(of)g(nat-)330 4286
-y(ural)e(language)h(is)g(\002nite-state:)p Black 571
-4469 a(1.)p Black -5 w(humans)g(have)g(a)f(\002nite)h(\(small,)g
-(limited,)g(\002xed\))e(amount)j(of)f(memory)g(available)629
-4569 y(for)f(language)h(pr)o(ocessing)p Black 571 4735
-a(2.)p Black -5 w(humans)g(have)g(pr)o(oblems)f(with)i(certain)e
-(grammatical)g(constr)o(uctions,)j(such)e(as)629 4834
-y(center)o(-embedding,)e(which)j(ar)o(e)d(impossible)j(to)f(describe)f
-(by)h(\002nite-state)f(means)629 4934 y(\(Miller)g(and)g(Chomsky)-9
-b(,)22 b(1963\))p Black 571 5100 a(3.)p Black -5 w(humans)f(pr)o(ocess)
-g(natural)f(language)g(very)h(ef)o(\002ciently)f(\(in)h(linear)f
-(time\))p Black 330 5293 1495 4 v 371 5371 a Fq(\003)d
-Fp(Alfa-informatica)h(&)e(BCN.)h(E-mail:)f(vannoor)o(d@let.r)o(ug.nl)p
-Black Black 351 5942 a(c)330 5944 y Fq(\015)g Fp(2000)i(Association)f
-(for)h(Computational)e(Linguistics)p Black eop
-%%Page: 2 2
-2 1 bop Black 330 91 a Fo(van)20 b(Noor)o(d)1145 b(Epsilon)17
-b(Moves)h(in)h(Subset)g(Constr)o(uction)p Black 330 357
-a Fs(1.2)h(Finite-state)c(Approximation)i(and)i Ft(\017)p
-Fs(-moves)330 457 y Fv(In)27 b(experimenting)f(with)h(\002nite-state)f
-(appr)o(oximation)g(techniques)i(for)e(context-fr)o(ee)e(and)330
-556 y(mor)o(e)17 b(powerful)h(grammatical)f(formalisms)h(\(such)g(as)f
-(the)h(techniques)h(pr)o(esented)d(in)j(Black)330 656
-y(\(1989\),)24 b(Per)o(eira)i(and)h(W)-6 b(right)28 b(\(1991\),)d(Rood)
-j(\(1996\),)c(Per)o(eira)i(and)h(W)-6 b(right)28 b(\(1997\),)c(Evans)
-330 756 y(\(1997\),)31 b(Neder)o(hof)h(\(1997\),)f(Neder)o(hof)i
-(\(1998\),)e(Johnson)k(\(1998\))c(\))i(we)h(have)f(found)h(that)330
-855 y(the)24 b(r)o(esulting)f(automata)g(often)h(ar)o(e)e(extr)o(emely)
-g(lar)o(ge.)g(Mor)o(eover)-6 b(,)22 b(the)i(automata)e(contain)330
-955 y(many)f Ft(\017)p Fv(-moves)g(\()p Fu(jumps)p Fv(\).)e(And)i
-(\002nally)-9 b(,)21 b(if)f(such)i(automata)e(ar)o(e)f(determinised)i
-(then)g(the)g(r)o(e-)330 1054 y(sulting)h(automata)d(ar)o(e)h(often)g
-Fu(smaller)p Fv(.)h(It)f(turns)h(out)g(that)g(a)f(straightforwar)o(d)f
-(implementa-)330 1154 y(tion)j(of)f(the)g(subset)h(constr)o(uction)h
-(determinisation)e(algorithm)h(performs)f(badly)g(for)g(such)330
-1254 y(inputs.)k(In)f(this)h(paper)e(we)h(consider)g(a)g(number)g(of)g
-(variants)g(of)g(the)g(subset-constr)o(uction)330 1353
-y(algorithm)e(which)f(dif)o(fer)e(in)i(their)g(tr)o(eatment)f(of)h
-Ft(\017)p Fv(-moves.)479 1453 y(Although)30 b(we)e(have)g(observed)g
-(that)g(\002nite-state)h(appr)o(oximation)f(techniques)h(typi-)330
-1553 y(cally)h(yield)g(automata)g(with)g(lar)o(ge)f(amounts)i(of)f
-Ft(\017)p Fv(-moves,)g(this)h(is)f(obviously)i(not)f(a)e(ne-)330
-1652 y(cessity)-9 b(.)21 b(Instead)f(of)g(trying)h(to)g(impr)o(ove)g
-(upon)g(determinisation)g(techniques)g(for)g(such)g(au-)330
-1752 y(tomata)k(it)g(might)i(be)d(mor)o(e)h(fr)o(uitful,)g(per)o(haps,)
-f(to)i(try)f(to)g(impr)o(ove)g(these)g(appr)o(oximation)330
-1851 y(techniques)g(in)g(such)g(a)e(way)h(that)h(mor)o(e)f(compact)g
-(automata)f(ar)o(e)g(pr)o(oduced.)2914 1820 y Fn(1)2973
-1851 y Fv(However)-6 b(,)330 1951 y(because)26 b(r)o(esear)o(ch)f(into)
-i(\002nite-state)g(appr)o(oximation)f(is)h(still)h(of)e(an)h
-(exploratory)f(and)h(ex-)330 2051 y(perimental)g(natur)o(e,)e(it)j(can)
-e(be)h(ar)o(gued)e(that)i(mor)o(e)g(r)o(obust)f(determinisation)i
-(algorithms)330 2150 y(do)e(still)h(have)f(a)g(r)o(ole)g(to)h(play:)e
-(it)i(can)f(be)g(expected)f(that)h(appr)o(oximation)g(techniques)h(ar)o
-(e)330 2250 y(much)f(easier)f(to)h(de\002ne)f(and)g(implement)h(if)g
-(the)f(r)o(esulting)h(automaton)g(is)g(allowed)f(to)h(be)330
-2350 y(non-deterministic)c(and)e(to)h(contain)g Ft(\017)p
-Fv(-moves.)479 2449 y(Note)f(furthermor)o(e)e(that)h(even)g(if)g(our)g
-(primary)g(motivation)h(is)g(in)g(\002nite-state)f(appr)o(ox-)330
-2549 y(imation,)24 b(the)f(pr)o(oblem)g(of)g(determinising)h
-(\002nite-state)f(automata)f(with)i Ft(\017)p Fv(-moves)f(may)g(be)330
-2648 y(r)o(elevant)d(in)h(other)g(ar)o(eas)e(of)i(language)f(r)o(esear)
-o(ch)f(as)h(well.)330 2848 y Fs(1.3)g(Subset)e(construction)i(and)f
-Ft(\017)p Fs(-moves)330 2947 y Fv(The)50 b(experiments)g(wer)o(e)f
-(performed)g(using)h(the)h Fu(FSA)f(Utilities)p Fv(.)f(The)h
-Fu(FSA)g(Utilities)330 3047 y Fv(tool-box)j(\(van)e(Noor)o(d,)h(1997;)e
-(van)h(Noor)o(d,)h(1999;)e(Ger)o(demann)h(and)h(van)g(Noor)o(d,)330
-3147 y(1999;)44 b(van)i(Noor)o(d)g(and)f(Ger)o(demann,)g(1999\))f(is)j
-(a)e(collection)i(of)f(tools)i(to)e(manipu-)330 3246
-y(late)36 b(r)o(egular)f(expr)o(essions,)h(\002nite-state)h(automata)e
-(and)i(\002nite-state)f(transducers.)f(Ma-)330 3346 y(nipulations)40
-b(include)e(determinisation,)h(minimisation,)i(composition,)f
-(complementa-)330 3445 y(tion,)g(intersection,)g(Kleene)g(closur)o(e,)f
-(etc.)g(V)-8 b(arious)40 b(visualisation)h(tools)f(ar)o(e)e(available)
-330 3545 y(to)i(br)o(owse)g(\002nite-state)g(automata.)f(The)h
-(tool-box)g(is)h(implemented)f(in)g(SICStus)g(Pr)o(o-)330
-3645 y(log,)49 b(and)g(is)g(available)f(fr)o(ee)f(of)i(char)o(ge)f
-(under)g(Gnu)i(General)e(Public)i(License)e(via)330 3744
-y(anonymous)35 b(ftp)e(at)g(ftp://ftp.let.r)o(ug.nl/pub/vannoor)o
-(d/Fsa/,)h(and)f(via)g(the)h(web)f(at)330 3844 y(http://www)-8
-b(.let.r)o(ug.nl/\230vannoor)o(d/Fsa/.)38 b(At)e(the)g(time)h(of)f(our)
-g(initial)h(experiments)330 3944 y(with)31 b(\002nite-state)f(appr)o
-(oximation,)g(an)g(old)h(version)g(of)f(the)h(tool-box)g(was)f(used,)g
-(which)330 4043 y(ran)d(into)h(memory)f(pr)o(oblems)g(for)g(some)h(of)e
-(these)i(automata.)e(For)h(this)h(r)o(eason,)e(the)h(sub-)330
-4143 y(set)i(constr)o(uction)i(algorithm)f(has)f(been)f(r)o
-(e-implemented,)g(paying)h(special)g(attention)h(to)330
-4242 y(the)25 b(tr)o(eatment)f(of)h Ft(\017)p Fv(-moves.)f(Thr)o(ee)g
-(variants)g(of)h(the)g(subset)g(constr)o(uction)i(algorithm)e(ar)o(e)
-330 4342 y(identi\002ed)c(which)g(dif)o(fer)e(in)j(the)e(way)h
-Ft(\017)p Fv(-moves)g(ar)o(e)e(tr)o(eated:)p Black 330
-4525 a Fm(per)i(graph)p Black 42 w Fv(The)d(most)h(obvious)h(and)d
-(straightforwar)o(d)h(appr)o(oach)e(is)j(sequential)g(in)g(the)f(fol-)
-629 4624 y(lowing)33 b(sense.)g(Firstly)-9 b(,)32 b(an)g(equivalent)g
-(automaton)h(without)g Ft(\017)p Fv(-moves)f(is)h(con-)629
-4724 y(str)o(ucted)16 b(for)g(the)h(input.)f(In)h(or)o(der)e(to)i(do)g
-(this,)g(the)f(transitive)g(closur)o(e)g(of)h(the)f(graph)629
-4824 y(consisting)27 b(of)e(all)g Ft(\017)p Fv(-moves)f(is)i(computed.)
-f(Secondly)-9 b(,)24 b(the)h(r)o(esulting)h(automaton)629
-4923 y(is)20 b(then)g(tr)o(eated)e(by)i(a)f(subset)h(constr)o(uction)i
-(algorithm)e(for)g Ft(\017)p Fv(-fr)o(ee)d(automata.)i(Dif-)629
-5023 y(fer)o(ent)g(variants)h(of)g Fu(per)g(graph)f Fv(can)h(be)g
-(identi\002ed,)f(depending)i(on)f(the)h(implemen-)629
-5122 y(tation)g(of)g(the)g Ft(\017)p Fv(-r)o(emoval)e(step.)p
-Black 330 5289 a Fm(per)i(state)p Black 42 w Fv(For)d(each)g
-Fu(state)g Fv(which)h(occurs)f(in)h(a)f(subset)g(pr)o(oduced)f(during)h
-(subset)h(constr)o(uc-)p Black 330 5458 1495 4 v 373
-5536 a Fp(1)e(Indeed,)e(a)i(later)g(implementation)e(by)h(Neder)o(hof)h
-(avoids)f(constr)o(uction)i(of)f(the)f(complete)g(non-determistic)423
-5611 y(automaton)g(by)g(minimising)h(sub-automata)g(befor)o(e)f(they)g
-(ar)o(e)g(embedded)e(into)j(lar)o(ger)g(sub-automata.)p
-Black Black 3288 5944 a Fv(2)p Black eop
-%%Page: 3 3
-3 2 bop Black 330 91 a Fo(van)20 b(Noor)o(d)1145 b(Epsilon)17
-b(Moves)h(in)h(Subset)g(Constr)o(uction)p Black 629 357
-a Fv(tion,)i(compute)f(the)h(states)f(which)h(ar)o(e)e(r)o(eachable)f
-(using)j Ft(\017)p Fv(-moves.)f(The)g(r)o(esults)g(of)629
-457 y(this)25 b(computation)g(can)g(be)f(memorised,)g(or)h(computed)f
-(for)h(each)e(state)i(in)f(a)g(pr)o(e-)629 556 y(pr)o(ocessing)31
-b(step.)g(This)h(is)f(the)g(appr)o(oach)f(mentioned)i(brie\003y)f(in)h
-(Johnson)g(and)629 656 y(W)-8 b(ood)21 b(\(1997\).)1111
-624 y Fn(2)p Black 330 822 a Fm(per)g(subset)p Black
-43 w Fv(For)35 b(each)e Fu(subset)j Ft(Q)e Fv(of)h(states)f(which)h
-(arises)f(during)h(subset)g(constr)o(uction,)629 922
-y(compute)19 b Ft(Q)1036 891 y Fl(0)1082 922 y Fk(\023)k
-Ft(Q)18 b Fv(which)i(extends)e Ft(Q)h Fv(with)g(all)g(states)f(which)i
-(ar)o(e)e(r)o(eachable)e(fr)o(om)629 1021 y(any)25 b(member)f(of)h
-Ft(Q)f Fv(using)i Ft(\017)p Fv(-moves.)e(Such)h(an)f(algorithm)i(is)f
-(described)f(in)h(Aho,)629 1121 y(Sethi,)20 b(and)h(Ullman)f(\(1986\).)
-479 1303 y(The)d(motivation)i(for)d(this)i(paper)e(is)h(the)g
-(experience)f(that)h(the)g(\002rst)h(appr)o(oach)d(turns)j(out)330
-1403 y(to)h(be)f(impractical)g(for)g(automata)f(with)j(very)e(lar)o(ge)
-f(numbers)i(of)f Ft(\017)p Fv(-moves.)g(An)g(integration)330
-1503 y(of)32 b(the)g(subset)f(constr)o(uction)j(algorithm)e(with)h(the)
-f(computation)g(of)g Ft(\017)p Fv(-r)o(eachable)d(states)330
-1602 y(performs)20 b(much)i(better)e(in)h(practice)f(for)g(such)i
-(automata.)479 1702 y(Section)35 b(2)f(pr)o(esents)f(a)h(short)h
-(statement)f(of)h(the)f(pr)o(oblem)g(\(how)h(to)f(determinise)g(a)330
-1802 y(given)c(\002nite-state)g(automaton\),)g(and)g(a)f(subset)i
-(constr)o(uction)h(algorithm)e(which)h(solves)330 1901
-y(this)23 b(pr)o(oblem)g(in)g(the)g(absence)f(of)h Ft(\017)p
-Fv(-moves.)f(Section)h(3)f(de\002nes)h(a)f(number)h(of)g(subset)g(con-)
-330 2001 y(str)o(uction)28 b(algorithms)g(which)f(dif)o(fer)e(with)j(r)
-o(espect)e(to)h(the)g(tr)o(eatment)f(of)g Ft(\017)p Fv(-moves.)h(Most)
-330 2100 y(aspects)21 b(of)g(the)g(algorithms)h(ar)o(e)e(not)i(new)f
-(and)g(have)g(been)g(described)f(elsewher)o(e,)g(and/or)330
-2200 y(wer)o(e)j(incorporated)g(in)h(pr)o(evious)g(implementations;)h
-(a)e(comparison)h(of)g(the)g(dif)o(fer)o(ent)e(al-)330
-2300 y(gorithms)28 b(had)e(not)h(been)f(performed)g(pr)o(eviously)-9
-b(.)26 b(W)-8 b(e)26 b(pr)o(ovide)g(a)g(comparison)h(with)g(r)o(e-)330
-2399 y(spect)e(to)h(the)g(size)f(of)g(the)h(r)o(esulting)f
-(deterministic)h(automaton)g(\(in)g(section)g(3\))e(and)h(prac-)330
-2499 y(tical)d(ef)o(\002ciency)g(\(in)h(section)h(4\).)d(Section)i(4)f
-(pr)o(ovides)g(experimental)g(r)o(esults)h(both)g(for)g(ran-)330
-2599 y(domly)30 b(generated)f(automata)g(and)g(for)g(automata)g
-(generated)f(by)i(appr)o(oximation)f(algo-)330 2698 y(rithms.)j(Our)f
-(implementations)h(of)f(the)g(various)g(algorithms)i(ar)o(e)c(also)i
-(compar)o(ed)f(with)330 2798 y(A)-6 b(T&T's)20 b(FSM)g(utilities)h
-(\(Mohri,)g(Per)o(eira,)e(and)h(Riley)-9 b(,)21 b(1998\),)d(to)j
-(establish)g(that)g(the)g(experi-)330 2897 y(mental)g(dif)o(fer)o
-(ences)d(we)j(\002nd)g(between)f(the)h(algorithms)g(ar)o(e)f(tr)o(uly)h
-(caused)f(by)g(dif)o(fer)o(ences)330 2997 y(in)h(the)g(algorithm)h
-(\(as)e(opposed)h(to)g(accidental)f(implementation)h(details\).)330
-3196 y Fs(2)f(Subset)f(Construction)330 3396 y(2.1)h(Problem)f
-(statement)330 3495 y Fv(Let)30 b(a)h(\002nite-state)f(machine)h
-Ft(M)39 b Fv(be)31 b(speci\002ed)f(by)h(a)f(tuple)h Fj(\()p
-Ft(Q;)14 b Fj(\006)p Ft(;)g(\016)o(;)g(S;)g(F)e Fj(\))30
-b Fv(wher)o(e)g Ft(Q)g Fv(is)h(a)330 3595 y(\002nite)24
-b(set)f(of)h(states,)f Fj(\006)g Fv(is)h(a)f(\002nite)h(alphabet,)e
-Ft(\016)k Fv(is)e(a)f(function)h(fr)o(om)f Ft(Q)d Fk(\002)g
-Fj(\(\006)h Fk([)f(f)p Ft(\017)p Fk(g)p Fj(\))27 b Fk(!)h
-Fj(2)3253 3565 y Fi(Q)3309 3595 y Fv(.)330 3694 y(Furthermor)o(e,)20
-b Ft(S)28 b Fk(\022)23 b Ft(Q)d Fv(is)h(a)f(set)h(of)g(start)f(states)h
-(and)f Ft(F)35 b Fk(\022)23 b Ft(Q)d Fv(is)h(a)g(set)f(of)h(\002nal)g
-(states.)3075 3663 y Fn(3)479 3794 y Fv(Let)30 b Ft(\017)p
-Fv(-move)g(be)g(the)g(r)o(elation)g Fk(f)p Fj(\()p Ft(q)1608
-3806 y Fi(i)1635 3794 y Ft(;)14 b(q)1709 3806 y Fi(j)1744
-3794 y Fj(\))p Fk(j)p Ft(q)1836 3806 y Fi(j)1912 3794
-y Fk(2)40 b Ft(\016)s Fj(\()p Ft(q)2116 3806 y Fi(i)2145
-3794 y Ft(;)14 b(\017)p Fj(\))p Fk(g)p Fv(.)29 b Ft(\017)p
-Fv(-r)o(eachable)e(is)k(the)f(r)o(e\003exive)330 3894
-y(and)21 b(transitive)g(closur)o(e)f(of)i Ft(\017)p Fv(-move.)e(Let)h
-Ft(\017)p Fv(-CLOSURE:)e Fj(2)2219 3864 y Fi(Q)2299 3894
-y Fk(!)k Fj(2)2447 3864 y Fi(Q)2524 3894 y Fv(be)e(a)g(function)h
-(which)g(is)330 3993 y(de\002ned)e(as:)896 4093 y Ft(\017)p
-Fv(-CLOSURE)n Fj(\()p Ft(Q)1444 4059 y Fl(0)1468 4093
-y Fj(\))j(=)g Fk(f)p Ft(q)s Fk(j)p Ft(q)1756 4059 y Fl(0)1802
-4093 y Fk(2)g Ft(Q)1946 4059 y Fl(0)1969 4093 y Ft(;)14
-b Fj(\()p Ft(q)2078 4059 y Fl(0)2101 4093 y Ft(;)g(q)s
-Fj(\))24 b Fk(2)f Ft(\017)p Fv(-r)o(eachable)n Fk(g)330
-4242 y Fv(Furthermor)o(e,)50 b(we)g(write)g Ft(\017)p
-Fv(-CLOSURE)1721 4204 y Fl(\000)p Fr(1)1810 4242 y Fj(\()p
-Ft(Q)1908 4212 y Fl(0)1931 4242 y Fj(\))h Fv(for)f(the)g(set)h
-Fk(f)p Ft(q)s Fk(j)p Ft(q)2633 4212 y Fl(0)2733 4242
-y Fk(2)78 b Ft(Q)2932 4212 y Fl(0)2955 4242 y Ft(;)14
-b Fj(\()p Ft(q)s(;)g(q)3141 4212 y Fl(0)3165 4242 y Fj(\))78
-b Fk(2)330 4342 y Ft(\017)p Fv(-r)o(eachable)m Fk(g)p
-Fv(.)479 4442 y(For)21 b(any)g(given)g(\002nite-state)f(automaton)h
-Ft(M)32 b Fj(=)22 b(\()p Ft(Q;)14 b Fj(\006)p Ft(;)g(\016)o(;)g(S;)g(F)
-e Fj(\))20 b Fv(ther)o(e)g(is)g(an)h(equivalent)330 4541
-y(deterministic)i(automaton)h Ft(M)1349 4511 y Fl(0)1399
-4541 y Fj(=)j(\(2)1565 4511 y Fi(Q)1621 4541 y Ft(;)14
-b Fj(\006)p Ft(;)g(\016)1795 4511 y Fl(0)1818 4541 y
-Ft(;)g Fk(f)p Ft(Q)1963 4553 y Fr(0)1999 4541 y Fk(g)p
-Ft(;)g(F)2143 4511 y Fl(0)2166 4541 y Fj(\))p Fv(.)23
-b Ft(F)2307 4511 y Fl(0)2353 4541 y Fv(is)h(the)f(set)g(of)g(all)g
-(states)g(in)g Fj(2)3274 4511 y Fi(Q)330 4641 y Fv(containing)k(a)d
-(\002nal)i(state)f(of)g Ft(M)9 b Fv(,)25 b(i.e.,)f(the)i(set)f(of)h
-(subsets)f Fk(f)p Ft(Q)2351 4653 y Fi(i)2410 4641 y Fk(2)31
-b Fj(2)2538 4611 y Fi(Q)2594 4641 y Fk(j)p Ft(q)k Fk(2)d
-Ft(Q)2842 4653 y Fi(i)2869 4641 y Ft(;)14 b(q)35 b Fk(2)d
-Ft(F)12 b Fk(g)p Fv(.)24 b Ft(M)3307 4611 y Fl(0)330
-4741 y Fv(has)e(a)g(single)h(start)f(state)g Ft(Q)1226
-4753 y Fr(0)1286 4741 y Fv(which)h(is)g(the)f(epsilon)i(closur)o(e)e
-(of)g(the)g(start)h(states)f(of)g Ft(M)9 b Fv(,)22 b(i.e.,)330
-4840 y Ft(Q)396 4852 y Fr(0)456 4840 y Fj(=)h Ft(\017)p
-Fv(-CLOSURE)n Fj(\()p Ft(S)5 b Fj(\))p Fv(.)21 b(Finally)-9
-b(,)582 5046 y Ft(\016)622 5012 y Fl(0)646 5046 y Fj(\()p
-Fk(f)p Ft(q)757 5058 y Fr(1)794 5046 y Ft(;)14 b(q)868
-5058 y Fr(2)905 5046 y Ft(;)g(:)g(:)g(:)g(;)g(q)1127
-5058 y Fi(i)1154 5046 y Fk(g)p Ft(;)g(a)p Fj(\))23 b(=)f
-Ft(\017)p Fv(-CLOSURE)o Fj(\()p Ft(\016)s Fj(\()p Ft(q)2011
-5058 y Fr(1)2049 5046 y Ft(;)14 b(a)p Fj(\))k Fk([)h
-Ft(\016)s Fj(\()p Ft(q)2363 5058 y Fr(2)2401 5046 y Ft(;)14
-b(a)p Fj(\))k Fk([)h Ft(:)14 b(:)g(:)k Fk([)h Ft(\016)s
-Fj(\()p Ft(q)2904 5058 y Fi(i)2932 5046 y Ft(;)14 b(a)p
-Fj(\)\))p Black 330 5216 1495 4 v 373 5294 a Fp(2)j(Accor)o(ding)g(to)g
-(Derick)g(W)-6 b(ood)17 b(\(p.c.\),)f(this)h(appr)o(oach)g(has)g(been)e
-(implemented)g(in)i(several)f(systems,)423 5369 y(including)h(Howar)o
-(d)g(Johnson's)g(INR)h(system.)373 5439 y(3)f(Note)g(that)e(a)i(set)f
-(of)h(start)g(states)f(is)h(r)o(equir)o(ed,)f(rather)h(than)e(a)i
-(single)g(start)g(state.)e(Many)h(operations)i(on)423
-5514 y(automata)e(can)h(be)g(de\002ned)e(somewhat)h(mor)o(e)h
-(elegantly)f(in)g(this)h(way)g(\(including)g Fh(per)f(graph)2853
-5491 y Fg(t)2899 5514 y Fp(discussed)423 5589 y(below\).)h(Obviously)-7
-b(,)16 b(for)h(deterministic)g(automata)f(this)h(set)f(should)g(be)h(a)
-f(singleton)h(set.)p Black Black 3288 5944 a Fv(3)p Black
-eop
-%%Page: 4 4
-4 3 bop Black 330 91 a Fo(van)20 b(Noor)o(d)1145 b(Epsilon)17
-b(Moves)h(in)h(Subset)g(Constr)o(uction)p Black Black
-Black Black Black Black Black 705 344 a Fs(funct)p Black
-705 357 199 4 v 20 w Ff(subset)p 1162 344 25 4 v 30 w(constr)o(uction)8
-b Fj(\(\()p Ft(Q;)14 b Fj(\006)p Ft(;)g(\016)o(;)g(S;)g(F)e
-Fj(\)\))788 443 y Ff(index)p 999 443 V 30 w(transitions\(\))e
-Fj(;)37 b Ff(T)-7 b(rans)29 b Fj(:=)23 b Fk(;)p Fj(;)36
-b Ff(Finals)30 b Fj(:=)23 b Fk(;)p Fj(;)36 b Ff(States)29
-b Fj(:=)23 b Fk(;)p Fj(;)788 543 y Ff(Start)31 b Fj(:=)22
-b Ff(epsilon)p 1373 543 V 31 w(closur)o(e)6 b Fj(\()p
-Ft(S)f Fj(\))788 643 y Ff(add)k Fj(\()p Ft(S)c(tar)r(t)p
-Fj(\))p Black 788 742 a Fs(while)p Black 788 755 217
-4 v 40 w Fv(ther)o(e)20 b(is)h(an)g(unmarked)f(subset)h
-Ft(T)34 b Fk(2)24 b Ff(States)p Black 26 w Fs(do)p Black
-2504 755 97 4 v 1025 842 a Ff(mark)10 b Fj(\()p Ft(T)i
-Fj(\))p Black 1025 941 a Fs(foreach)p Black 1025 954
-282 4 v 21 w Fj(\()p Ft(a;)i(U)9 b Fj(\))23 b Fk(2)g
-Ff(instr)o(uctions)8 b Fj(\()p Ft(T)k Fj(\))p Black 21
-w Fs(do)p Black 2226 954 97 4 v 1108 1041 a Ft(U)32 b
-Fj(:=)23 b Ff(epsilon)p 1579 1041 25 4 v 31 w(closur)o(e)6
-b Fj(\()p Ft(U)j Fj(\))1108 1141 y Ff(T)-7 b(rans)6 b
-Fj([)p Ft(T)h(;)14 b(a)p Fj(])23 b(:=)f Fk(f)p Ft(U)9
-b Fk(g)1108 1240 y Ff(add)g Fj(\()p Ft(U)g Fj(\))p Black
-1025 1340 a Fs(od)p Black 1025 1353 97 4 v Black 788
-1440 a(od)p Black 788 1453 V Black 788 1539 a(return)p
-Black 788 1552 236 4 v 20 w Fj(\()p Ff(States)d Ft(;)14
-b Fj(\006)p Ft(;)g Ff(T)-7 b(rans)5 b Ft(;)14 b Fk(f)p
-Ff(Start)7 b Fk(g)p Ft(;)14 b Ff(Finals)7 b Fj(\))p Black
-705 1639 a Fs(end)p Black 705 1652 143 4 v Black 705
-1838 a(proc)p Black 705 1851 167 4 v 21 w Ff(add)i Fj(\()p
-Ft(U)g Fj(\))584 b Fv(Reachable-state-set)19 b(Maintenance)p
-Black 788 1938 a Fs(if)p Black 788 1951 60 4 v 21 w Ft(U)41
-b(=)-51 b Fk(2)23 b Ff(States)p Black 869 2037 a Fs(then)p
-Black 869 2050 171 4 v 40 w Fv(add)d Ft(U)29 b Fv(unmarked)20
-b(to)i Ff(States)p Black 1060 2137 a Fs(if)p Black 1060
-2150 60 4 v 21 w Ft(U)27 b Fk(\\)19 b Ft(F)p Black 32
-w Fs(then)p Black 1384 2150 171 4 v 20 w Ff(Finals)30
-b Fj(:=)23 b Ff(Finals)i Fk([)19 b(f)p Ft(U)9 b Fk(g)p
-Black 19 w Fs(\002)p Black 2423 2150 51 4 v Black 788
-2237 a(\002)p Black 788 2250 V Black 705 2336 a(end)p
-Black 705 2349 143 4 v Black 705 2535 a(funct)p Black
-705 2548 199 4 v 20 w Ff(instr)o(uctions)f Fj(\()p Ft(P)k
-Fj(\))548 b Fv(Instr)o(uction)22 b(Computation)p Black
-788 2635 a Fs(return)p Black 788 2648 236 4 v 20 w Ff(mer)o(ge)6
-b Fj(\()1313 2573 y Fe(S)1382 2660 y Fi(p)p Fl(2)p Fi(P)1530
-2635 y Ff(transitions)i Fj(\()p Ft(p)p Fj(\)\))p Black
-705 2741 a Fs(end)p Black 705 2754 143 4 v Black 705
-2940 a(funct)p Black 705 2953 199 4 v 20 w Ff(epsilon)p
-1195 2940 25 4 v 31 w(closur)o(e)e Fj(\()p Ft(U)j Fj(\))532
-b Fv(variant)20 b(1:)g(No)h Ft(\017)p Fv(-moves)p Black
-788 3040 a Fs(return)p Black 788 3053 236 4 v 20 w Ft(U)p
-Black 705 3140 a Fs(end)p Black 705 3153 143 4 v 330
-3313 a Fd(Figure)d(1)330 3396 y Fo(Subset-constr)o(uction)i(algorithm.)
-p Black 479 3699 a Fv(An)27 b(algorithm)h(which)g(computes)g
-Ft(M)1738 3669 y Fl(0)1788 3699 y Fv(for)f(a)f(given)i
-Ft(M)35 b Fv(will)28 b(only)g(need)f(to)h(take)e(into)330
-3799 y(account)c(states)f(in)h Fj(2)1001 3769 y Fi(Q)1079
-3799 y Fv(which)g(ar)o(e)e(r)o(eachable)g(fr)o(om)h(the)h(start)f
-(state)g Ft(Q)2611 3811 y Fr(0)2648 3799 y Fv(.)h(This)g(is)g(the)g(r)o
-(eason)330 3899 y(that)27 b(for)f(many)h(input)h(automata)e(the)h
-(algorithm)h(does)e(not)i(need)e(to)i(tr)o(eat)d(all)i(subsets)g(of)330
-3998 y(states)33 b(\(but)g(note)g(that)g(ther)o(e)f(ar)o(e)g(automata)g
-(for)h(which)h(all)f(subsets)g(ar)o(e)f(r)o(elevant,)f(and)330
-4098 y(hence)21 b(exponential)g(behaviour)f(cannot)h(be)g(avoided)f(in)
-h(general\).)479 4198 y(Consider)28 b(the)g(subset)h(constr)o(uction)g
-(algorithm)g(in)f(\002gur)o(e)f(1.)h(The)f(algorithm)i(main-)330
-4297 y(tains)23 b(a)e(set)i(of)f(subsets)h Fu(States)p
-Fv(.)f(Each)g(subset)g(can)g(be)g(either)g(marked)g(or)h(unmarked)e
-(\(to)i(in-)330 4397 y(dicate)e(whether)g(the)h(subset)g(has)f(been)g
-(tr)o(eated)f(by)i(the)f(algorithm\);)h(the)f(set)h(of)f(unmarked)330
-4497 y(subsets)28 b(is)f(sometimes)i(r)o(eferr)o(ed)24
-b(to)k(as)f(the)g(agenda.)g(The)g(algorithm)h(takes)f(such)h(an)f(un-)
-330 4596 y(marked)21 b(subset)h Ft(T)32 b Fv(and)21 b(computes)h(all)g
-(transitions)g(leaving)g Ft(T)12 b Fv(.)20 b(This)i(computation)h(is)e
-(per)o(-)330 4696 y(formed)d(by)h(the)f(function)i Fu(instructions)f
-Fv(and)f(is)h(called)e Fu(instruction)i(computation)e
-Fv(by)i(Johnson)330 4795 y(and)h(W)-8 b(ood)22 b(\(1997\).)479
-4895 y(The)j(function)g Fu(index)p 1165 4895 25 4 v 29
-w(transitions)g Fv(constr)o(ucts)g(the)g(function)g Fu(transitions)p
-Fv(:)f Ft(Q)30 b Fk(!)f Fj(\006)21 b Fk(\002)g Fj(2)3274
-4865 y Fi(Q)330 4995 y Fv(which)i(r)o(eturns)e(for)g(a)h(given)g(state)
-f Ft(p)g Fv(the)h(set)g(of)g(pairs)f Fj(\()p Ft(s;)14
-b(T)e Fj(\))21 b Fv(r)o(epr)o(esenting)g(the)h(transitions)330
-5094 y(leaving)f Ft(p)p Fv(.)g(Furthermor)o(e,)g(the)g(function)h
-Fu(mer)o(ge)f Fv(takes)g(such)h(a)f(set)g(of)h(pairs)e(and)h(mer)o(ges)
-g(all)330 5194 y(pairs)d(with)i(the)e(same)h(\002rst)g(element)g(\(by)f
-(taking)h(the)g(union)h(of)e(the)h(corr)o(esponding)g(second)330
-5294 y(elements\).)i(For)g(example:)p Black Black 330
-5538 a Ff(mer)o(ge)6 b Fj(\()p Fk(f)p Fj(\()p Ft(a;)14
-b Fk(f)p Fj(1)p Ft(;)g Fj(2)p Ft(;)g Fj(4)p Fk(g)p Fj(\))p
-Ft(;)g Fj(\()p Ft(b;)g Fk(f)p Fj(2)p Ft(;)g Fj(4)p Fk(g)p
-Fj(\))p Ft(;)g Fj(\()p Ft(a;)g Fk(f)p Fj(3)p Ft(;)g Fj(4)p
-Fk(g)o Fj(\))p Ft(;)g Fj(\()p Ft(b;)g Fk(f)p Fj(5)o Ft(;)g
-Fj(6)p Fk(g)o Fj(\))p Fk(g)p Fj(\))j(=)538 5637 y Fk(f)p
-Fj(\()p Ft(a;)d Fk(f)p Fj(1)p Ft(;)g Fj(2)p Ft(;)g Fj(3)p
-Ft(;)g Fj(4)p Fk(g)p Fj(\))p Ft(;)g Fj(\()p Ft(b;)g Fk(f)p
-Fj(2)p Ft(;)g Fj(4)p Ft(;)g Fj(5)p Ft(;)g Fj(6)o Fk(g)p
-Fj(\))p Fk(g)p Black 3288 5944 a Fv(4)p Black eop
-%%Page: 5 5
-5 4 bop Black 330 91 a Fo(van)20 b(Noor)o(d)1145 b(Epsilon)17
-b(Moves)h(in)h(Subset)g(Constr)o(uction)p Black 479 357
-a Fv(The)24 b(pr)o(ocedur)o(e)e Fu(add)g Fv(is)i(r)o(esponsible)f(for)h
-(`r)o(eachable-state-set)c(maintenance',)k(by)f(en-)330
-457 y(suring)h(that)f(tar)o(get)g(subsets)g(ar)o(e)f(added)g(to)i(the)f
-(set)h(of)f(subsets)h(if)f(these)g(subsets)h(wer)o(e)e(not)330
-556 y(encounter)o(ed)d(befor)o(e.)g(Mor)o(eover)-6 b(,)18
-b(if)i(such)h(a)f(new)g(subset)g(contains)h(a)f(\002nal)g(state,)g
-(then)g(this)330 656 y(subset)h(is)g(added)e(to)i(the)g(set)g(of)g
-(\002nal)g(states.)330 855 y Fs(3)f(V)-9 b(ariants)19
-b(for)i Ft(\017)p Fs(-Moves)330 1054 y Fv(The)31 b(algorithm)i(pr)o
-(esented)d(in)i(the)f(pr)o(evious)h(section)g(does)f(not)h(tr)o(eat)e
-Ft(\017)p Fv(-moves.)i(In)f(this)330 1154 y(section,)21
-b(possible)h(extensions)f(of)g(the)g(algorithm)h(ar)o(e)d(identi\002ed)
-i(to)g(tr)o(eat)e Ft(\017)p Fv(-moves.)330 1353 y Fs(3.1)h(Per)g(graph)
-330 1453 y Fv(In)h(the)f Fu(per)g(graph)f Fv(variant)h(two)h(steps)f
-(can)g(be)g(identi\002ed.)g(In)g(the)h(\002rst)f(step,)g
-Fu(efr)o(ee)p Fv(,)h(an)f(equiv-)330 1553 y(alent)26
-b Ft(\017)p Fv(-fr)o(ee)f(automaton)h(is)h(constr)o(ucted.)g(In)g(the)f
-(second)h(step)f(this)h Ft(\017)p Fv(-fr)o(ee)e(automaton)i(is)330
-1652 y(determinised)g(using)h(the)g(subset)f(constr)o(uction)i
-(algorithm.)f(The)f(advantage)f(of)h(this)h(ap-)330 1752
-y(pr)o(oach)i(is)h(that)g(the)g(subset)g(constr)o(uction)i(algorithm)f
-(can)e(r)o(emain)g(simple)i(because)e(the)330 1851 y(input)21
-b(automaton)h(is)f Ft(\017)p Fv(-fr)o(ee.)479 1951 y(An)43
-b(algorithm)h(for)f Fu(efr)o(ee)h Fv(is)g(described)e(for)h(instance)g
-(in)h(Hopcr)o(oft)e(and)h(Ullman)330 2051 y(\(1979\)[page)29
-b(26-27].)h(The)i(main)h(ingr)o(edient)g(of)f Fu(efr)o(ee)i
-Fv(is)f(the)g(constr)o(uction)h(of)f(the)f(func-)330
-2150 y(tion)c Ft(\017)p Fv(-CLOSURE,)d(which)j(can)f(be)g(computed)g
-(by)g(using)h(a)f(standar)o(d)e(transitive)i(closur)o(e)330
-2250 y(algorithm)22 b(for)f(dir)o(ected)f(graphs:)g(this)i(algorithm)g
-(is)g(applied)e(to)i(the)f(dir)o(ected)f(graph)h(con-)330
-2350 y(sisting)27 b(of)e(all)h Ft(\017)p Fv(-moves)f(of)h
-Ft(M)9 b Fv(.)25 b(Such)g(an)h(algorithm)g(can)g(be)f(found)h(in)g
-(several)e(textbooks)330 2449 y(\(see,)c(for)g(instance,)h(Cormen,)g
-(Leiserson,)g(and)f(Rivest)h(\(1990\)\).)479 2549 y(For)31
-b(a)f(given)g(\002nite-state)g(automaton)h Ft(M)49 b
-Fj(=)40 b(\()p Ft(Q;)14 b Fj(\006)p Ft(;)g(\016)o(;)g(S;)g(F)e
-Fj(\))29 b Fu(efr)o(ee)i Fv(computes)g Ft(M)3202 2519
-y Fl(0)3265 2549 y Fj(=)330 2648 y(\()p Ft(Q;)14 b Fj(\006)p
-Ft(;)g(\016)602 2618 y Fl(0)625 2648 y Ft(;)g(S)718 2618
-y Fl(0)741 2648 y Ft(;)g(F)843 2618 y Fl(0)866 2648 y
-Fj(\))p Fv(,)46 b(wher)o(e)g Ft(S)1296 2618 y Fl(0)1389
-2648 y Fj(=)69 b Ft(\017)p Fv(-CLOSURE)o Fj(\()p Ft(S)5
-b Fj(\))p Fv(,)46 b Ft(F)2226 2618 y Fl(0)2319 2648 y
-Fj(=)69 b Ft(\017)p Fv(-CLOSURE)2904 2610 y Fl(\000)p
-Fr(1)2993 2648 y Fj(\()p Ft(F)12 b Fj(\))p Fv(,)46 b(and)330
-2748 y Ft(\016)370 2718 y Fl(0)393 2748 y Fj(\()p Ft(p;)14
-b(a)p Fj(\))42 b(=)f Fk(f)p Ft(q)s Fk(j)p Ft(q)873 2718
-y Fl(0)938 2748 y Fk(2)h Ft(\016)s Fj(\()p Ft(p)1149
-2718 y Fl(0)1172 2748 y Ft(;)14 b(a)p Fj(\))p Ft(;)g(p)1364
-2718 y Fl(0)1429 2748 y Fk(2)42 b Ft(\017)p Fv(-CLOSURE)1977
-2710 y Fl(\000)p Fr(1)2066 2748 y Fj(\()p Ft(p)p Fj(\))p
-Ft(;)14 b(q)45 b Fk(2)d Ft(\017)p Fv(-CLOSURE)n Fj(\()p
-Ft(q)2910 2718 y Fl(0)2934 2748 y Fj(\))p Fk(g)p Fv(.)30
-b(Instead)330 2848 y(of)20 b(using)h Ft(\017)p Fv(-CLOSURE)e(on)i(both)
-g(the)f(sour)o(ce)g(and)g(tar)o(get)f(side)h(of)g(a)g(transition,)g
-Fu(efr)o(ee)h Fv(can)f(be)330 2947 y(optimised)h(in)h(two)f(dif)o(fer)o
-(ent)e(ways)i(by)f(using)i Ft(\017)p Fv(-CLOSURE)d(only)j(on)f(one)h
-(side:)p Black 571 3130 a Fk(\017)p Black 16 w Fu(efr)o(ee)779
-3100 y Fi(t)809 3130 y Fu(:)e Ft(M)940 3100 y Fl(0)986
-3130 y Fj(=)j(\()p Ft(Q;)14 b Fj(\006)p Ft(;)g(\016)1346
-3100 y Fl(0)1369 3130 y Ft(;)g(S)1462 3100 y Fl(0)1485
-3130 y Ft(;)g(F)e Fj(\))p Fv(,)20 b(wher)o(e)h Ft(S)1966
-3100 y Fl(0)2012 3130 y Fj(=)h Ft(\017)p Fv(-CLOSURE)o
-Fj(\()p Ft(S)5 b Fj(\))p Fv(,)21 b(and)629 3230 y Ft(\016)669
-3199 y Fl(0)692 3230 y Fj(\()p Ft(p;)14 b(a)p Fj(\))23
-b(=)g Fk(f)p Ft(q)s Fk(j)p Ft(q)1135 3199 y Fl(0)1181
-3230 y Fk(2)g Ft(\016)s Fj(\()p Ft(p;)14 b(a)p Fj(\))p
-Ft(;)g(q)27 b Fk(2)c Ft(\017)p Fv(-CLOSURE)o Fj(\()p
-Ft(q)2188 3199 y Fl(0)2211 3230 y Fj(\))p Fk(g)p Fv(.)p
-Black 571 3396 a Fk(\017)p Black 16 w Fu(efr)o(ee)779
-3365 y Fi(s)815 3396 y Fu(:)e Ft(M)947 3365 y Fl(0)993
-3396 y Fj(=)h(\()p Ft(Q;)14 b Fj(\006)p Ft(;)g(\016)1352
-3365 y Fl(0)1375 3396 y Ft(;)g(S;)g(F)1565 3365 y Fl(0)1588
-3396 y Fj(\))p Fv(,)21 b(wher)o(e)f Ft(F)1976 3365 y
-Fl(0)2023 3396 y Fj(=)i Ft(\017)p Fv(-CLOSURE)2561 3357
-y Fl(\000)p Fr(1)2650 3396 y Fj(\()p Ft(F)12 b Fj(\))p
-Fv(,)21 b(and)629 3495 y Ft(\016)669 3465 y Fl(0)692
-3495 y Fj(\()p Ft(p;)14 b(a)p Fj(\))23 b(=)g Fk(f)p Ft(q)s
-Fk(j)p Ft(q)j Fk(2)d Ft(\016)s Fj(\()p Ft(p)1350 3465
-y Fl(0)1374 3495 y Ft(;)14 b(a)p Fj(\))p Ft(;)g(p)1566
-3465 y Fl(0)1612 3495 y Fk(2)23 b Ft(\017)p Fv(-CLOSURE)2141
-3457 y Fl(\000)p Fr(1)2230 3495 y Fj(\()p Ft(p)p Fj(\))p
-Fk(g)p Fv(.)479 3678 y(Although)d(both)e(variants)g(appear)f(very)g
-(similar)-6 b(,)18 b(ther)o(e)g(ar)o(e)e(some)j(dif)o(fer)o(ences.)d
-(Firstly)-9 b(,)330 3778 y Fu(efr)o(ee)480 3747 y Fi(t)533
-3778 y Fv(might)24 b(intr)o(oduce)e(states)h(which)g(ar)o(e)f(not)h
-Fu(co-accessible)p Fv(:)g(states)g(fr)o(om)f(which)i(no)f(path)330
-3877 y(exists)g(to)g(a)f(\002nal)h(state;)f(in)h(contrast,)g
-Fu(efr)o(ee)1700 3847 y Fi(s)1759 3877 y Fv(might)g(intr)o(oduce)g
-(states)f(which)i(ar)o(e)d(not)i Fu(acces-)330 3977 y(sible)p
-Fv(:)e(states)g(fr)o(om)e(which)j(no)f(path)f(exists)h(fr)o(om)f(the)g
-(start)g(state.)g(A)g(straightforwar)o(d)f(mod-)330 4076
-y(i\002cation)27 b(of)g(both)g(algorithms)g(is)g(possible)g(to)g(ensur)
-o(e)f(that)g(these)h(states)f(ar)o(e)f(not)j(pr)o(esent)330
-4176 y(in)i(the)g(output.)f(Thus)h Fu(efr)o(ee)1240 4146
-y Fi(t;c)1349 4176 y Fv(ensur)o(es)f(that)h(all)f(states)g(in)h(the)g
-(r)o(esulting)f(automaton)h(ar)o(e)330 4276 y(co-accessible;)24
-b Fu(efr)o(ee)995 4246 y Fi(s;a)1111 4276 y Fv(ensur)o(es)g(that)h(all)
-g(states)f(in)h(the)g(r)o(esulting)g(automaton)g(ar)o(e)e
-Fu(accessi-)330 4375 y(ble)p Fv(.)k(As)f(a)f(consequence,)i(the)f(size)
-g(of)g(the)g(determinised)g(machine)g(is)h(in)g(general)e(smaller)330
-4475 y(if)j Fu(efr)o(ee)560 4445 y Fi(t;c)667 4475 y
-Fv(is)g(employed,)g(because)f(states)h(which)h(wer)o(e)e(not)i
-(co-accessible)e(\(in)h(the)g(input\))330 4575 y(ar)o(e)c(r)o(emoved)h
-(\(this)h(is)g(ther)o(efor)o(e)e(an)h(additional)g(bene\002t)h(of)f
-Fu(efr)o(ee)2493 4544 y Fi(t;c)2573 4575 y Fv(;)g(the)h(fact)e(that)i
-Fu(efr)o(ee)3238 4544 y Fi(s;a)330 4674 y Fv(r)o(emoves)31
-b(accessible)f(states)h(has)g(no)g(ef)o(fect)f(on)h(the)g(size)g(of)g
-(the)g(determinised)g(machine)330 4774 y(because)20 b(the)h(subset)g
-(constr)o(uction)h(algorithm)g(alr)o(eady)d(ensur)o(es)h(accessibility)
-h(anyway\).)479 4873 y(Secondly)-9 b(,)37 b(it)g(turns)g(out)g(that)g
-(applying)g Fu(efr)o(ee)2038 4843 y Fi(t)2105 4873 y
-Fv(in)g(combination)i(with)e(the)g(subset-)330 4973 y(constr)o(uction)
-32 b(algorithm)g(generally)e(pr)o(oduces)f(smaller)i(automata)f(than)h
-Fu(efr)o(ee)2979 4943 y Fi(s)3045 4973 y Fv(\(even)f(if)330
-5073 y(we)21 b(ignor)o(e)g(the)g(bene\002t)g(of)g(ensuring)g
-(co-accessibility\).)g(An)f(example)h(is)g(pr)o(esented)f(in)h(\002g-)
-330 5172 y(ur)o(e)f(2.)g(The)h(dif)o(fer)o(ences)d(can)j(be)f(quite)h
-(signi\002cant.)h(This)f(is)g(illustrated)g(in)g(\002gur)o(e)f(3.)479
-5272 y(Below)g(we)f(will)h(write)f Fu(per)h(graph)1550
-5242 y Fi(X)1631 5272 y Fv(to)f(indicate)g(the)h(non-integrated)f
-(algorithm)h(based)330 5372 y(on)h Fu(efr)o(ee)594 5341
-y Fi(X)658 5372 y Fv(.)p Black 3288 5944 a(5)p Black
-eop
-%%Page: 6 6
-6 5 bop Black 330 91 a Fo(van)20 b(Noor)o(d)1145 b(Epsilon)17
-b(Moves)h(in)h(Subset)g(Constr)o(uction)p Black Black
-Black Black 1101 592 a
- tx@Dict begin tx@NodeDict begin {5.0 2 div 6.8299 0.15997 add 2 div
-2 copy 0.15997 sub 4 2 roll Pyth 3.0 add 0.8 add} false /N@0 11 {InitCnode
-} NewNode end end
- 1101 592 a @beginspecial @setspecial
- tx@Dict begin STP newpath 0.8 SLW 0  setgray  5.0 2 div 6.8299 0.15997
-add 2 div 2 copy 0.15997 sub 4 2 roll Pyth 3.0 add CLW 2 div add 0
-360 arc closepath gsave 0.8 SLW 0  setgray 0 setlinecap stroke  grestore
-end
-
-
-@endspecial Fv(0)1121 565 y
- tx@Dict begin tx@NodeDict begin {-28.44543 0.0 } false /N@start0 10
-{InitPnode } NewNode end end
- 1121 565 a 1121 565 a
- tx@Dict begin gsave STV newpath 0.8 SLW 0  setgray  /ArrowA { moveto
-} def /ArrowB { BeginArrow 1.  1.  scale false 0.4 1.4 1.5 2. Arrow
- EndArrow  } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 0.0
-0 0 /N@start0 /N@0 InitNC { yB yA sub xB xA sub Atan dup 0.  add /AngleA
-ED 0.  sub 180 add /AngleB ED 0.67  0.67  NCCurve  } if end gsave 0.8
-SLW 0  setgray 0 setlinecap stroke  grestore  grestore end
- 1121
-565 a 2281 593 a
- tx@Dict begin tx@NodeDict begin {5.0 2 div 6.97992 0.05994 add 2 div
-2 copy 0.05994 sub 4 2 roll Pyth 3.0 add 2.6 add} false /N@1 11 {InitCnode
-} NewNode end end
- 2281 593 a @beginspecial @setspecial
- tx@Dict begin STP newpath 2.6 SLW 0  setgray  5.0 2 div 6.97992 0.05994
-add 2 div 2 copy 0.05994 sub 4 2 roll Pyth 3.0 add CLW 2 div add 0
-360 arc closepath gsave 2.6 SLW 0  setgray 0 setlinecap stroke  grestore
-gsave 1.0 SLW 1  setgray stroke grestore end
-
-
-@endspecial Fv(1)1691 593 y
- tx@Dict begin tx@NodeDict begin {5.0 2 div 6.8299 0.05994 add 2 div
-2 copy 0.05994 sub 4 2 roll Pyth 3.0 add 0.8 add} false /N@2 11 {InitCnode
-} NewNode end end
- 1691 593 a @beginspecial
-@setspecial
- tx@Dict begin STP newpath 0.8 SLW 0  setgray  5.0 2 div 6.8299 0.05994
-add 2 div 2 copy 0.05994 sub 4 2 roll Pyth 3.0 add CLW 2 div add 0
-360 arc closepath gsave 0.8 SLW 0  setgray 0 setlinecap stroke  grestore
-end
- 
-@endspecial Fv(2)1121 565 y
- tx@Dict begin gsave STV newpath 0.8 SLW 0  setgray  /ArrowA { moveto
-} def /ArrowB { BeginArrow 1.  1.  scale false 0.4 1.4 1.5 2. Arrow
- EndArrow  } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 0.0
-0 0 /N@0 /N@2 InitNC { yB yA sub xB xA sub Atan dup 15.0  add /AngleA
-ED 15.0  sub 180 add /AngleB ED 0.67  0.67  NCCurve  } if end gsave
-0.8 SLW 0  setgray 0 setlinecap stroke  grestore  grestore end
- 1121 565 a 1121
-565 a
- tx@Dict begin tx@NodeDict begin /t .5 def LPut end PutBegin  end
- 1121 565 a 1121 565 a
- tx@Dict begin { 5.0 tx@Dict /NCLW known { NCLW add } if 11.55904 4.71497
-0.15997 NAngle 90 add  Uput exch pop add a PtoC h1 add exch w1 add
-exch } PutCoor PutBegin  end
- 1121 565 a 1073 583 a
- tx@Dict begin tx@NodeDict begin {4.71497 0.15997 11.55904 5.77951
-2.2775 } false /N@x 16 {InitRnode } NewNode end end
- 1073
-583 a Ft(\017)i Fv(a)1121 565 y
- tx@Dict begin PutEnd  end
- 1121 565 a 1121 565 a
- tx@Dict begin PutEnd  end
-
-1121 565 a 1121 565 a
- tx@Dict begin gsave STV newpath 0.8 SLW 0  setgray  /ArrowA { moveto
-} def /ArrowB { BeginArrow 1.  1.  scale false 0.4 1.4 1.5 2. Arrow
- EndArrow  } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 0.0
-0 0 /N@1 /N@2 InitNC { yB yA sub xB xA sub Atan dup 15.0  add /AngleA
-ED 15.0  sub 180 add /AngleB ED 0.67  0.67  NCCurve  } if end gsave
-0.8 SLW 0  setgray 0 setlinecap stroke  grestore  grestore end
- 1121 565 a 1121 565 a
- tx@Dict begin tx@NodeDict begin /t .5 def LPut end PutBegin  end
- 1121 565
-a 1121 565 a
- tx@Dict begin { 5.0 tx@Dict /NCLW known { NCLW add } if 4.05904 4.30554
-0.0 NAngle 90 add  Uput exch pop add a PtoC h1 add exch w1 add exch
-} PutCoor PutBegin  end
- 1121 565 a 1104 582 a
- tx@Dict begin tx@NodeDict begin {4.30554 0.0 4.05904 2.02951 2.15277
-} false /N@x 16 {InitRnode } NewNode end end
- 1104 582 a Ft(\017)1121
-565 y
- tx@Dict begin PutEnd  end
- 1121 565 a 1121 565 a
- tx@Dict begin PutEnd  end
- 1121 565 a 1121 565 a
- tx@Dict begin gsave STV newpath 0.8 SLW 0  setgray  /ArrowA { moveto
-} def /ArrowB { BeginArrow 1.  1.  scale false 0.4 1.4 1.5 2. Arrow
- EndArrow  } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 0.0
-0 0 /N@2 /N@1 InitNC { yB yA sub xB xA sub Atan dup 15.0  add /AngleA
-ED 15.0  sub 180 add /AngleB ED 0.67  0.67  NCCurve  } if end gsave
-0.8 SLW 0  setgray 0 setlinecap stroke  grestore  grestore end
- 1121
-565 a 1121 565 a
- tx@Dict begin tx@NodeDict begin /t .5 def LPut end PutBegin  end
- 1121 565 a 1121 565 a
- tx@Dict begin { 5.0 tx@Dict /NCLW known { NCLW add } if 5.0 4.71497
-0.15997 NAngle 90 add  Uput exch pop add a PtoC h1 add exch w1 add
-exch } PutCoor PutBegin  end
- 1121 565 a 1100
-583 a
- tx@Dict begin tx@NodeDict begin {4.71497 0.15997 5.0 2.5 2.2775 }
-false /N@x 16 {InitRnode } NewNode end end
- 1100 583 a Fv(a)1121 565 y
- tx@Dict begin PutEnd  end
- 1121 565 a 1121 565
-a
- tx@Dict begin PutEnd  end
- 1121 565 a 1653 860 a Fv(\(1\))869 1073 y
- tx@Dict begin tx@NodeDict begin {5.0 2 div 6.8299 0.15997 add 2 div
-2 copy 0.15997 sub 4 2 roll Pyth 3.0 add 0.8 add} false /N@0 11 {InitCnode
-} NewNode end end
- 869 1073
-a @beginspecial @setspecial
- tx@Dict begin STP newpath 0.8 SLW 0  setgray  5.0 2 div 6.8299 0.15997
-add 2 div 2 copy 0.15997 sub 4 2 roll Pyth 3.0 add CLW 2 div add 0
-360 arc closepath gsave 0.8 SLW 0  setgray 0 setlinecap stroke  grestore
-end
- 
-@endspecial Fv(0)890 1748
-y
- tx@Dict begin tx@NodeDict begin {-28.44543 84.62517 } false /N@start0
-10 {InitPnode } NewNode end end
- 890 1748 a 890 1748 a
- tx@Dict begin gsave STV newpath 0.8 SLW 0  setgray  /ArrowA { moveto
-} def /ArrowB { BeginArrow 1.  1.  scale false 0.4 1.4 1.5 2. Arrow
- EndArrow  } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 0.0
-0 0 /N@start0 /N@0 InitNC { yB yA sub xB xA sub Atan dup 0.  add /AngleA
-ED 0.  sub 180 add /AngleB ED 0.67  0.67  NCCurve  } if end gsave 0.8
-SLW 0  setgray 0 setlinecap stroke  grestore  grestore end
- 890 1748 a 1312 1777 a
- tx@Dict begin tx@NodeDict begin {5.0 2 div 6.97992 0.05994 add 2 div
-2 copy 0.05994 sub 4 2 roll Pyth 3.0 add 2.6 add} false /N@1 11 {InitCnode
-} NewNode end end
- 1312 1777
-a @beginspecial @setspecial
- tx@Dict begin STP newpath 2.6 SLW 0  setgray  5.0 2 div 6.97992 0.05994
-add 2 div 2 copy 0.05994 sub 4 2 roll Pyth 3.0 add CLW 2 div add 0
-360 arc closepath gsave 2.6 SLW 0  setgray 0 setlinecap stroke  grestore
-gsave 1.0 SLW 1  setgray stroke grestore end
- 
-@endspecial Fv(1)1312 1251
-y
- tx@Dict begin tx@NodeDict begin {5.0 2 div 6.8299 0.05994 add 2 div
-2 copy 0.05994 sub 4 2 roll Pyth 3.0 add 0.8 add} false /N@2 11 {InitCnode
-} NewNode end end
- 1312 1251 a @beginspecial @setspecial
- tx@Dict begin STP newpath 0.8 SLW 0  setgray  5.0 2 div 6.8299 0.05994
-add 2 div 2 copy 0.05994 sub 4 2 roll Pyth 3.0 add CLW 2 div add 0
-360 arc closepath gsave 0.8 SLW 0  setgray 0 setlinecap stroke  grestore
-end
- 
-@endspecial
-Fv(2)890 1748 y
- tx@Dict begin tx@NodeDict begin {24.88976 63.29109 } false /N@start2
-10 {InitPnode } NewNode end end
- 890 1748 a 890 1748 a
- tx@Dict begin gsave STV newpath 0.8 SLW 0  setgray  /ArrowA { moveto
-} def /ArrowB { BeginArrow 1.  1.  scale false 0.4 1.4 1.5 2. Arrow
- EndArrow  } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 0.0
-0 0 /N@start2 /N@2 InitNC { yB yA sub xB xA sub Atan dup 0.  add /AngleA
-ED 0.  sub 180 add /AngleB ED 0.67  0.67  NCCurve  } if end gsave 0.8
-SLW 0  setgray 0 setlinecap stroke  grestore  grestore end
- 890 1748 a 890
-1748 a
- tx@Dict begin gsave STV newpath 0.8 SLW 0  setgray  /ArrowA { moveto
-} def /ArrowB { BeginArrow 1.  1.  scale false 0.4 1.4 1.5 2. Arrow
- EndArrow  } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 0.0
-0 0 /N@0 /N@2 InitNC { yB yA sub xB xA sub Atan dup 15.0  add /AngleA
-ED 15.0  sub 180 add /AngleB ED 0.67  0.67  NCCurve  } if end gsave
-0.8 SLW 0  setgray 0 setlinecap stroke  grestore  grestore end
- 890 1748 a 890 1748 a
- tx@Dict begin tx@NodeDict begin /t .5 def LPut end PutBegin  end
- 890 1748 a 890 1748 a
- tx@Dict begin { 5.0 tx@Dict /NCLW known { NCLW add } if 5.0 4.71497
-0.15997 NAngle 90 add  Uput exch pop add a PtoC h1 add exch w1 add
-exch } PutCoor PutBegin  end
- 890
-1748 a 869 1767 a
- tx@Dict begin tx@NodeDict begin {4.71497 0.15997 5.0 2.5 2.2775 }
-false /N@x 16 {InitRnode } NewNode end end
- 869 1767 a Fv(a)890 1748 y
- tx@Dict begin PutEnd  end
- 890 1748
-a 890 1748 a
- tx@Dict begin PutEnd  end
- 890 1748 a 890 1748 a
- tx@Dict begin gsave STV newpath 0.8 SLW 0  setgray  /ArrowA { moveto
-} def /ArrowB { BeginArrow 1.  1.  scale false 0.4 1.4 1.5 2. Arrow
- EndArrow  } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 0.0
-0 0 /N@2 /N@1 InitNC { yB yA sub xB xA sub Atan dup 15.0  add /AngleA
-ED 15.0  sub 180 add /AngleB ED 0.67  0.67  NCCurve  } if end gsave
-0.8 SLW 0  setgray 0 setlinecap stroke  grestore  grestore end
- 890 1748 a 890 1748
-a
- tx@Dict begin tx@NodeDict begin /t .5 def LPut end PutBegin  end
- 890 1748 a 890 1748 a
- tx@Dict begin { 5.0 tx@Dict /NCLW known { NCLW add } if 5.0 4.71497
-0.15997 NAngle 90 add  Uput exch pop add a PtoC h1 add exch w1 add
-exch } PutCoor PutBegin  end
- 890 1748 a 869 1767 a
- tx@Dict begin tx@NodeDict begin {4.71497 0.15997 5.0 2.5 2.2775 }
-false /N@x 16 {InitRnode } NewNode end end
- 869 1767
-a Fv(a)890 1748 y
- tx@Dict begin PutEnd  end
- 890 1748 a 890 1748 a
- tx@Dict begin PutEnd  end
- 890 1748 a 890
-1748 a
- tx@Dict begin gsave STV newpath 0.8 SLW 0  setgray  /ArrowA { BeginArrow
-1.  1.  scale false 0.4 1.4 1.5 2. Arrow  EndArrow  moveto } def /ArrowB
-{ } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 0.0 0 0 /N@2
-/N@2 InitNC { /AngleA -90. def /r 14.22636 def NCCircle x y r angleA
-{ ArrowA CP } { add } ArcArrow angleB arc end } if end gsave 0.8 SLW
-0  setgray 0 setlinecap stroke  grestore  grestore end
- 890 1748 a 890 1748 a
- tx@Dict begin tx@NodeDict begin /t 0.5 def tx@NodeDict /HPutPos known
-{ HPutPos } { CP /Y ED /X ED /NAngle 0 def /NCLW 0 def } ifelse /Sin
-NAngle sin def /Cos NAngle cos def /s 5.0 NCLW add def /l 2.5 def /r
-2.5 def /h 1.43202 def /d 3.44292 def /flag false def HPutAdjust LPutCoor
-end PutBegin  end
- 890 1748 a 869 1775 a
- tx@Dict begin tx@NodeDict begin {4.71497 0.15997 5.0 2.5 2.2775 }
-false /N@x 16 {InitRnode } NewNode end end
- 869
-1775 a Fv(a)890 1748 y
- tx@Dict begin PutEnd  end
- 890 1748 a 1185 1925 a Fv(\(2\))2041
-1539 y
- tx@Dict begin tx@NodeDict begin {5.0 2 div 6.8299 0.15997 add 2 div
-2 copy 0.15997 sub 4 2 roll Pyth 3.0 add 0.8 add} false /N@0 11 {InitCnode
-} NewNode end end
- 2041 1539 a @beginspecial @setspecial
- tx@Dict begin STP newpath 0.8 SLW 0  setgray  5.0 2 div 6.8299 0.15997
-add 2 div 2 copy 0.15997 sub 4 2 roll Pyth 3.0 add CLW 2 div add 0
-360 arc closepath gsave 0.8 SLW 0  setgray 0 setlinecap stroke  grestore
-end
- 
-@endspecial
-Fv(0)2062 1748 y
- tx@Dict begin tx@NodeDict begin {-22.76672 28.4584 } false /N@start0
-10 {InitPnode } NewNode end end
- 2062 1748 a 2062 1748 a
- tx@Dict begin gsave STV newpath 0.8 SLW 0  setgray  /ArrowA { moveto
-} def /ArrowB { BeginArrow 1.  1.  scale false 0.4 1.4 1.5 2. Arrow
- EndArrow  } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 0.0
-0 0 /N@start0 /N@0 InitNC { yB yA sub xB xA sub Atan dup 0.  add /AngleA
-ED 0.  sub 180 add /AngleB ED 0.67  0.67  NCCurve  } if end gsave 0.8
-SLW 0  setgray 0 setlinecap stroke  grestore  grestore end
- 2062 1748 a
-2514 1304 a
- tx@Dict begin tx@NodeDict begin {5.0 2 div 6.97992 0.05994 add 2 div
-2 copy 0.05994 sub 4 2 roll Pyth 3.0 add 2.6 add} false /N@1 11 {InitCnode
-} NewNode end end
- 2514 1304 a @beginspecial @setspecial
- tx@Dict begin STP newpath 2.6 SLW 0  setgray  5.0 2 div 6.97992 0.05994
-add 2 div 2 copy 0.05994 sub 4 2 roll Pyth 3.0 add CLW 2 div add 0
-360 arc closepath gsave 2.6 SLW 0  setgray 0 setlinecap stroke  grestore
-gsave 1.0 SLW 1  setgray stroke grestore end
- 
-@endspecial
-Fv(1)2514 1776 y
- tx@Dict begin tx@NodeDict begin {5.0 2 div 6.8299 0.05994 add 2 div
-2 copy 0.05994 sub 4 2 roll Pyth 3.0 add 0.8 add} false /N@2 11 {InitCnode
-} NewNode end end
- 2514 1776 a @beginspecial @setspecial
- tx@Dict begin STP newpath 0.8 SLW 0  setgray  5.0 2 div 6.8299 0.05994
-add 2 div 2 copy 0.05994 sub 4 2 roll Pyth 3.0 add CLW 2 div add 0
-360 arc closepath gsave 0.8 SLW 0  setgray 0 setlinecap stroke  grestore
-end
-
-
-@endspecial Fv(2)2062 1748 y
- tx@Dict begin gsave STV newpath 0.8 SLW 0  setgray  /ArrowA { moveto
-} def /ArrowB { BeginArrow 1.  1.  scale false 0.4 1.4 1.5 2. Arrow
- EndArrow  } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 0.0
-0 0 /N@0 /N@1 InitNC { yB yA sub xB xA sub Atan dup 20.0  add /AngleA
-ED 20.0  sub 180 add /AngleB ED 0.67  0.67  NCCurve  } if end gsave
-0.8 SLW 0  setgray 0 setlinecap stroke  grestore  grestore end
- 2062 1748 a 2062 1748 a
- tx@Dict begin tx@NodeDict begin /t .5 def LPut end PutBegin  end
-
-2062 1748 a 2062 1748 a
- tx@Dict begin { 5.0 tx@Dict /NCLW known { NCLW add } if 5.0 4.71497
-0.15997 NAngle 90 add  Uput exch pop add a PtoC h1 add exch w1 add
-exch } PutCoor PutBegin  end
- 2062 1748 a 2041 1767 a
- tx@Dict begin tx@NodeDict begin {4.71497 0.15997 5.0 2.5 2.2775 }
-false /N@x 16 {InitRnode } NewNode end end
- 2041
-1767 a Fv(a)2062 1748 y
- tx@Dict begin PutEnd  end
- 2062 1748 a 2062 1748 a
- tx@Dict begin PutEnd  end
- 2062
-1748 a 2062 1748 a
- tx@Dict begin gsave STV newpath 0.8 SLW 0  setgray  /ArrowA { moveto
-} def /ArrowB { BeginArrow 1.  1.  scale false 0.4 1.4 1.5 2. Arrow
- EndArrow  } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 0.0
-0 0 /N@0 /N@2 InitNC { yB yA sub xB xA sub Atan dup 20.0  add /AngleA
-ED 20.0  sub 180 add /AngleB ED 0.67  0.67  NCCurve  } if end gsave
-0.8 SLW 0  setgray 0 setlinecap stroke  grestore  grestore end
- 2062 1748 a 2062 1748 a
- tx@Dict begin tx@NodeDict begin /t .5 def LPut end PutBegin  end
- 2062 1748
-a 2062 1748 a
- tx@Dict begin { 5.0 tx@Dict /NCLW known { NCLW add } if 5.0 4.71497
-0.15997 NAngle 90 add  Uput exch pop add a PtoC h1 add exch w1 add
-exch } PutCoor PutBegin  end
- 2062 1748 a 2041 1767 a
- tx@Dict begin tx@NodeDict begin {4.71497 0.15997 5.0 2.5 2.2775 }
-false /N@x 16 {InitRnode } NewNode end end
- 2041 1767 a Fv(a)2062
-1748 y
- tx@Dict begin PutEnd  end
- 2062 1748 a 2062 1748 a
- tx@Dict begin PutEnd  end
- 2062 1748 a 2062 1748
-a
- tx@Dict begin gsave STV newpath 0.8 SLW 0  setgray  /ArrowA { BeginArrow
-1.  1.  scale false 0.4 1.4 1.5 2. Arrow  EndArrow  moveto } def /ArrowB
-{ } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 0.0 0 0 /N@1
-/N@1 InitNC { /AngleA -90. def /r 14.22636 def NCCircle x y r angleA
-{ ArrowA CP } { add } ArcArrow angleB arc end } if end gsave 0.8 SLW
-0  setgray 0 setlinecap stroke  grestore  grestore end
- 2062 1748 a 2062 1748 a
- tx@Dict begin tx@NodeDict begin /t 0.5 def tx@NodeDict /HPutPos known
-{ HPutPos } { CP /Y ED /X ED /NAngle 0 def /NCLW 0 def } ifelse /Sin
-NAngle sin def /Cos NAngle cos def /s 5.0 NCLW add def /l 2.5 def /r
-2.5 def /h 1.43202 def /d 3.44292 def /flag false def HPutAdjust LPutCoor
-end PutBegin  end
- 2062 1748 a 2041 1775 a
- tx@Dict begin tx@NodeDict begin {4.71497 0.15997 5.0 2.5 2.2775 }
-false /N@x 16 {InitRnode } NewNode end end
- 2041
-1775 a Fv(a)2062 1748 y
- tx@Dict begin PutEnd  end
- 2062 1748 a 2062 1748 a
- tx@Dict begin gsave STV newpath 0.8 SLW 0  setgray  /ArrowA { moveto
-} def /ArrowB { BeginArrow 1.  1.  scale false 0.4 1.4 1.5 2. Arrow
- EndArrow  } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 0.0
-0 0 /N@2 /N@1 InitNC { yB yA sub xB xA sub Atan dup 20.0  add /AngleA
-ED 20.0  sub 180 add /AngleB ED 0.67  0.67  NCCurve  } if end gsave
-0.8 SLW 0  setgray 0 setlinecap stroke  grestore  grestore end
- 2062
-1748 a 2062 1748 a
- tx@Dict begin tx@NodeDict begin /t .5 def LPut end PutBegin  end
- 2062 1748 a 2062 1748 a
- tx@Dict begin { 5.0 tx@Dict /NCLW known { NCLW add } if 5.0 4.71497
-0.15997 NAngle 90 add  Uput exch pop add a PtoC h1 add exch w1 add
-exch } PutCoor PutBegin  end
- 2062 1748
-a 2041 1767 a
- tx@Dict begin tx@NodeDict begin {4.71497 0.15997 5.0 2.5 2.2775 }
-false /N@x 16 {InitRnode } NewNode end end
- 2041 1767 a Fv(a)2062 1748 y
- tx@Dict begin PutEnd  end
- 2062 1748
-a 2062 1748 a
- tx@Dict begin PutEnd  end
- 2062 1748 a 2298 1890 a Fv(\(3\))653 2209
-y
- tx@Dict begin tx@NodeDict begin {5.0 2 div 6.8299 0.15997 add 2 div
-2 copy 0.15997 sub 4 2 roll Pyth 3.0 add 0.8 add} false /N@0 11 {InitCnode
-} NewNode end end
- 653 2209 a @beginspecial @setspecial
- tx@Dict begin STP newpath 0.8 SLW 0  setgray  5.0 2 div 6.8299 0.15997
-add 2 div 2 copy 0.15997 sub 4 2 roll Pyth 3.0 add CLW 2 div add 0
-360 arc closepath gsave 0.8 SLW 0  setgray 0 setlinecap stroke  grestore
-end
- 
-@endspecial Fv(0)674
-2182 y
- tx@Dict begin tx@NodeDict begin {-22.76672 0.0 } false /N@start0 10
-{InitPnode } NewNode end end
- 674 2182 a 674 2182 a
- tx@Dict begin gsave STV newpath 0.8 SLW 0  setgray  /ArrowA { moveto
-} def /ArrowB { BeginArrow 1.  1.  scale false 0.4 1.4 1.5 2. Arrow
- EndArrow  } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 0.0
-0 0 /N@start0 /N@0 InitNC { yB yA sub xB xA sub Atan dup 0.  add /AngleA
-ED 0.  sub 180 add /AngleB ED 0.67  0.67  NCCurve  } if end gsave 0.8
-SLW 0  setgray 0 setlinecap stroke  grestore  grestore end
- 674 2182 a 1126 2210 a
- tx@Dict begin tx@NodeDict begin {5.0 2 div 6.97992 0.05994 add 2 div
-2 copy 0.05994 sub 4 2 roll Pyth 3.0 add 2.6 add} false /N@1 11 {InitCnode
-} NewNode end end
- 1126
-2210 a @beginspecial @setspecial
- tx@Dict begin STP newpath 2.6 SLW 0  setgray  5.0 2 div 6.97992 0.05994
-add 2 div 2 copy 0.05994 sub 4 2 roll Pyth 3.0 add CLW 2 div add 0
-360 arc closepath gsave 2.6 SLW 0  setgray 0 setlinecap stroke  grestore
-gsave 1.0 SLW 1  setgray stroke grestore end
- 
-@endspecial Fv(1)674
-2182 y
- tx@Dict begin gsave STV newpath 0.8 SLW 0  setgray  /ArrowA { moveto
-} def /ArrowB { BeginArrow 1.  1.  scale false 0.4 1.4 1.5 2. Arrow
- EndArrow  } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 0.0
-0 0 /N@0 /N@1 InitNC { yB yA sub xB xA sub Atan dup 20.0  add /AngleA
-ED 20.0  sub 180 add /AngleB ED 0.67  0.67  NCCurve  } if end gsave
-0.8 SLW 0  setgray 0 setlinecap stroke  grestore  grestore end
- 674 2182 a 674 2182 a
- tx@Dict begin tx@NodeDict begin /t .5 def LPut end PutBegin  end
- 674 2182 a 674 2182 a
- tx@Dict begin { 5.0 tx@Dict /NCLW known { NCLW add } if 5.0 4.71497
-0.15997 NAngle 90 add  Uput exch pop add a PtoC h1 add exch w1 add
-exch } PutCoor PutBegin  end
- 674
-2182 a 653 2200 a
- tx@Dict begin tx@NodeDict begin {4.71497 0.15997 5.0 2.5 2.2775 }
-false /N@x 16 {InitRnode } NewNode end end
- 653 2200 a Fv(a)674 2182 y
- tx@Dict begin PutEnd  end
- 674 2182
-a 674 2182 a
- tx@Dict begin PutEnd  end
- 674 2182 a 674 2182 a
- tx@Dict begin gsave STV newpath 0.8 SLW 0  setgray  /ArrowA { BeginArrow
-1.  1.  scale false 0.4 1.4 1.5 2. Arrow  EndArrow  moveto } def /ArrowB
-{ } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 0.0 0 0 /N@1
-/N@1 InitNC { /AngleA -90. def /r 14.22636 def NCCircle x y r angleA
-{ ArrowA CP } { add } ArcArrow angleB arc end } if end gsave 0.8 SLW
-0  setgray 0 setlinecap stroke  grestore  grestore end
- 674 2182 a 674 2182
-a
- tx@Dict begin tx@NodeDict begin /t 0.5 def tx@NodeDict /HPutPos known
-{ HPutPos } { CP /Y ED /X ED /NAngle 0 def /NCLW 0 def } ifelse /Sin
-NAngle sin def /Cos NAngle cos def /s 5.0 NCLW add def /l 2.5 def /r
-2.5 def /h 1.43202 def /d 3.44292 def /flag false def HPutAdjust LPutCoor
-end PutBegin  end
- 674 2182 a 653 2209 a
- tx@Dict begin tx@NodeDict begin {4.71497 0.15997 5.0 2.5 2.2775 }
-false /N@x 16 {InitRnode } NewNode end end
- 653 2209 a Fv(a)674 2182 y
- tx@Dict begin PutEnd  end
- 674
-2182 a 910 2323 a Fv(\(4\))1855 2209 y
- tx@Dict begin tx@NodeDict begin {5.0 2 div 6.8299 0.15997 add 2 div
-2 copy 0.15997 sub 4 2 roll Pyth 3.0 add 0.8 add} false /N@0 11 {InitCnode
-} NewNode end end
- 1855 2209 a @beginspecial
-@setspecial
- tx@Dict begin STP newpath 0.8 SLW 0  setgray  5.0 2 div 6.8299 0.15997
-add 2 div 2 copy 0.15997 sub 4 2 roll Pyth 3.0 add CLW 2 div add 0
-360 arc closepath gsave 0.8 SLW 0  setgray 0 setlinecap stroke  grestore
-end
- 
-@endspecial Fv(0)1876 2182 y
- tx@Dict begin tx@NodeDict begin {-22.76672 0.0 } false /N@start0 10
-{InitPnode } NewNode end end
- 1876 2182 a
-1876 2182 a
- tx@Dict begin gsave STV newpath 0.8 SLW 0  setgray  /ArrowA { moveto
-} def /ArrowB { BeginArrow 1.  1.  scale false 0.4 1.4 1.5 2. Arrow
- EndArrow  } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 0.0
-0 0 /N@start0 /N@0 InitNC { yB yA sub xB xA sub Atan dup 0.  add /AngleA
-ED 0.  sub 180 add /AngleB ED 0.67  0.67  NCCurve  } if end gsave 0.8
-SLW 0  setgray 0 setlinecap stroke  grestore  grestore end
- 1876 2182 a 2328 2210 a
- tx@Dict begin tx@NodeDict begin {5.0 2 div 6.97992 0.05994 add 2 div
-2 copy 0.05994 sub 4 2 roll Pyth 3.0 add 2.6 add} false /N@1 11 {InitCnode
-} NewNode end end
- 2328 2210 a @beginspecial
-@setspecial
- tx@Dict begin STP newpath 2.6 SLW 0  setgray  5.0 2 div 6.97992 0.05994
-add 2 div 2 copy 0.05994 sub 4 2 roll Pyth 3.0 add CLW 2 div add 0
-360 arc closepath gsave 2.6 SLW 0  setgray 0 setlinecap stroke  grestore
-gsave 1.0 SLW 1  setgray stroke grestore end
- 
-@endspecial Fv(1)2800 2210 y
- tx@Dict begin tx@NodeDict begin {5.0 2 div 6.8299 0.05994 add 2 div
-2 copy 0.05994 sub 4 2 roll Pyth 3.0 add 2.6 add} false /N@2 11 {InitCnode
-} NewNode end end
- 2800 2210 a
-@beginspecial @setspecial
- tx@Dict begin STP newpath 2.6 SLW 0  setgray  5.0 2 div 6.8299 0.05994
-add 2 div 2 copy 0.05994 sub 4 2 roll Pyth 3.0 add CLW 2 div add 0
-360 arc closepath gsave 2.6 SLW 0  setgray 0 setlinecap stroke  grestore
-gsave 1.0 SLW 1  setgray stroke grestore end
- 
-@endspecial Fv(2)1876 2182
-y
- tx@Dict begin gsave STV newpath 0.8 SLW 0  setgray  /ArrowA { moveto
-} def /ArrowB { BeginArrow 1.  1.  scale false 0.4 1.4 1.5 2. Arrow
- EndArrow  } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 0.0
-0 0 /N@0 /N@1 InitNC { yB yA sub xB xA sub Atan dup 20.0  add /AngleA
-ED 20.0  sub 180 add /AngleB ED 0.67  0.67  NCCurve  } if end gsave
-0.8 SLW 0  setgray 0 setlinecap stroke  grestore  grestore end
- 1876 2182 a 1876 2182 a
- tx@Dict begin tx@NodeDict begin /t .5 def LPut end PutBegin  end
- 1876 2182 a 1876 2182 a
- tx@Dict begin { 5.0 tx@Dict /NCLW known { NCLW add } if 5.0 4.71497
-0.15997 NAngle 90 add  Uput exch pop add a PtoC h1 add exch w1 add
-exch } PutCoor PutBegin  end
- 1876
-2182 a 1855 2200 a
- tx@Dict begin tx@NodeDict begin {4.71497 0.15997 5.0 2.5 2.2775 }
-false /N@x 16 {InitRnode } NewNode end end
- 1855 2200 a Fv(a)1876 2182 y
- tx@Dict begin PutEnd  end
- 1876
-2182 a 1876 2182 a
- tx@Dict begin PutEnd  end
- 1876 2182 a 1876 2182 a
- tx@Dict begin gsave STV newpath 0.8 SLW 0  setgray  /ArrowA { moveto
-} def /ArrowB { BeginArrow 1.  1.  scale false 0.4 1.4 1.5 2. Arrow
- EndArrow  } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 0.0
-0 0 /N@1 /N@2 InitNC { yB yA sub xB xA sub Atan dup 20.0  add /AngleA
-ED 20.0  sub 180 add /AngleB ED 0.67  0.67  NCCurve  } if end gsave
-0.8 SLW 0  setgray 0 setlinecap stroke  grestore  grestore end
- 1876 2182
-a 1876 2182 a
- tx@Dict begin tx@NodeDict begin /t .5 def LPut end PutBegin  end
- 1876 2182 a 1876 2182 a
- tx@Dict begin { 5.0 tx@Dict /NCLW known { NCLW add } if 5.0 4.71497
-0.15997 NAngle 90 add  Uput exch pop add a PtoC h1 add exch w1 add
-exch } PutCoor PutBegin  end
- 1876 2182 a 1855
-2200 a
- tx@Dict begin tx@NodeDict begin {4.71497 0.15997 5.0 2.5 2.2775 }
-false /N@x 16 {InitRnode } NewNode end end
- 1855 2200 a Fv(a)1876 2182 y
- tx@Dict begin PutEnd  end
- 1876 2182 a 1876
-2182 a
- tx@Dict begin PutEnd  end
- 1876 2182 a 1876 2182 a
- tx@Dict begin gsave STV newpath 0.8 SLW 0  setgray  /ArrowA { BeginArrow
-1.  1.  scale false 0.4 1.4 1.5 2. Arrow  EndArrow  moveto } def /ArrowB
-{ } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 0.0 0 0 /N@2
-/N@2 InitNC { /AngleA -90. def /r 14.22636 def NCCircle x y r angleA
-{ ArrowA CP } { add } ArcArrow angleB arc end } if end gsave 0.8 SLW
-0  setgray 0 setlinecap stroke  grestore  grestore end
- 1876 2182 a 1876 2182
-a
- tx@Dict begin tx@NodeDict begin /t 0.5 def tx@NodeDict /HPutPos known
-{ HPutPos } { CP /Y ED /X ED /NAngle 0 def /NCLW 0 def } ifelse /Sin
-NAngle sin def /Cos NAngle cos def /s 5.0 NCLW add def /l 2.5 def /r
-2.5 def /h 1.43202 def /d 3.44292 def /flag false def HPutAdjust LPutCoor
-end PutBegin  end
- 1876 2182 a 1855 2209 a
- tx@Dict begin tx@NodeDict begin {4.71497 0.15997 5.0 2.5 2.2775 }
-false /N@x 16 {InitRnode } NewNode end end
- 1855 2209 a Fv(a)1876 2182
-y
- tx@Dict begin PutEnd  end
- 1876 2182 a 2348 2371 a Fv(\(5\))330 2584 y Fd(Figure)d(2)330
-2667 y Fo(Illustration)h(of)f(the)h(dif)o(fer)o(ence)e(in)i(size)f
-(between)i(two)f(variants)g(of)g Fc(efr)o(ee)p Fo(.)f(\(1\))h(is)f(the)
-h(input)330 2759 y(automaton.)h(The)f(r)o(esult)e(of)i
-Fc(efr)o(ee)1297 2727 y Fg(t)1343 2759 y Fo(is)f(given)g(in)h(\(2\);)g
-(\(3\))g(is)f(the)h(r)o(esult)e(of)i Fc(efr)o(ee)2553
-2727 y Fg(s)2586 2759 y Fo(.)f(\(4\))h(and)g(\(5\))g(ar)o(e)f(the)330
-2850 y(r)o(esult)f(of)i(applying)f(the)h(subset)g(constr)o(uction)g(to)
-g(the)g(r)o(esult)f(of)g Fc(efr)o(ee)2348 2819 y Fg(t)2395
-2850 y Fo(and)h Fc(efr)o(ee)2676 2819 y Fg(s)2709 2850
-y Fo(,)f(r)o(espectively)-8 b(.)p Black Black 330 3047
-a
- 23681433 16577003 3289088 3289088 26970521 19866091 startTexFig
- 330 3047 a
-%%BeginDocument: csizes.ps
-/gnudict 40 dict def
-gnudict begin
-/Color false def
-/Solid true def
-/gnulinewidth 5.000 def
-/vshift -60 def
-/dl {10 mul} def
-/hpt 31.5 def
-/vpt 31.5 def
-/M {moveto} bind def
-/L {lineto} bind def
-/R {rmoveto} bind def
-/V {rlineto} bind def
-/vpt2 vpt 2 mul def
-/hpt2 hpt 2 mul def
-/Lshow { currentpoint stroke M
-  0 vshift R show } def
-/Rshow { currentpoint stroke M
-  dup stringwidth pop neg vshift R show } def
-/Cshow { currentpoint stroke M
-  dup stringwidth pop -2 div vshift R show } def
-/DL { Color {setrgbcolor Solid {pop []} if 0 setdash }
- {pop pop pop Solid {pop []} if 0 setdash} ifelse } def
-/BL { stroke gnulinewidth 2 mul setlinewidth } def
-/AL { stroke gnulinewidth 2 div setlinewidth } def
-/PL { stroke gnulinewidth setlinewidth } def
-/LTb { BL [] 0 0 0 DL } def
-/LTa { AL [1 dl 2 dl] 0 setdash 0 0 0 setrgbcolor } def
-/LT0 { PL [] 0 1 0 DL } def
-/LT1 { PL [4 dl 2 dl] 0 0 1 DL } def
-/LT2 { PL [2 dl 3 dl] 1 0 0 DL } def
-/LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def
-/LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def
-/LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def
-/LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def
-/LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def
-/LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def
-/P { stroke [] 0 setdash
-  currentlinewidth 2 div sub M
-  0 currentlinewidth V stroke } def
-/D { stroke [] 0 setdash 2 copy vpt add M
-  hpt neg vpt neg V hpt vpt neg V
-  hpt vpt V hpt neg vpt V closepath stroke
-  P } def
-/A { stroke [] 0 setdash vpt sub M 0 vpt2 V
-  currentpoint stroke M
-  hpt neg vpt neg R hpt2 0 V stroke
-  } def
-/B { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M
-  0 vpt2 neg V hpt2 0 V 0 vpt2 V
-  hpt2 neg 0 V closepath stroke
-  P } def
-/C { stroke [] 0 setdash exch hpt sub exch vpt add M
-  hpt2 vpt2 neg V currentpoint stroke M
-  hpt2 neg 0 R hpt2 vpt2 V stroke } def
-/T { stroke [] 0 setdash 2 copy vpt 1.12 mul add M
-  hpt neg vpt -1.62 mul V
-  hpt 2 mul 0 V
-  hpt neg vpt 1.62 mul V closepath stroke
-  P  } def
-/S { 2 copy A C} def
-end
-gnudict begin
-gsave
-50 50 translate
-0.050 0.050 scale
-0 setgray
-/Palatino-Roman findfont 180 scalefont setfont
-newpath
-LTa
-1080 451 M
-5841 0 V
--5841 0 R
-0 4498 V
-LTb
-1080 451 M
-63 0 V
-5778 0 R
--63 0 V
-972 451 M
-(0) Rshow
-1080 901 M
-63 0 V
-5778 0 R
--63 0 V
-972 901 M
-(2000) Rshow
-1080 1351 M
-63 0 V
-5778 0 R
--63 0 V
--5886 0 R
-(4000) Rshow
-1080 1800 M
-63 0 V
-5778 0 R
--63 0 V
--5886 0 R
-(6000) Rshow
-1080 2250 M
-63 0 V
-5778 0 R
--63 0 V
--5886 0 R
-(8000) Rshow
-1080 2700 M
-63 0 V
-5778 0 R
--63 0 V
--5886 0 R
-(10000) Rshow
-1080 3150 M
-63 0 V
-5778 0 R
--63 0 V
--5886 0 R
-(12000) Rshow
-1080 3600 M
-63 0 V
-5778 0 R
--63 0 V
--5886 0 R
-(14000) Rshow
-1080 4049 M
-63 0 V
-5778 0 R
--63 0 V
--5886 0 R
-(16000) Rshow
-1080 4499 M
-63 0 V
-5778 0 R
--63 0 V
--5886 0 R
-(18000) Rshow
-1080 4949 M
-63 0 V
-5778 0 R
--63 0 V
--5886 0 R
-(20000) Rshow
-1080 451 M
-0 63 V
-0 4435 R
-0 -63 V
-0 -4615 R
-(0) Cshow
-1664 451 M
-0 63 V
-0 4435 R
-0 -63 V
-0 -4615 R
-(0.2) Cshow
-2248 451 M
-0 63 V
-0 4435 R
-0 -63 V
-0 -4615 R
-(0.4) Cshow
-2832 451 M
-0 63 V
-0 4435 R
-0 -63 V
-0 -4615 R
-(0.6) Cshow
-3416 451 M
-0 63 V
-0 4435 R
-0 -63 V
-0 -4615 R
-(0.8) Cshow
-4001 451 M
-0 63 V
-0 4435 R
-0 -63 V
-0 -4615 R
-(1) Cshow
-4585 451 M
-0 63 V
-0 4435 R
-0 -63 V
-0 -4615 R
-(1.2) Cshow
-5169 451 M
-0 63 V
-0 4435 R
-0 -63 V
-0 -4615 R
-(1.4) Cshow
-5753 451 M
-0 63 V
-0 4435 R
-0 -63 V
-0 -4615 R
-(1.6) Cshow
-6337 451 M
-0 63 V
-0 4435 R
-0 -63 V
-0 -4615 R
-(1.8) Cshow
-6921 451 M
-0 63 V
-0 4435 R
-0 -63 V
-0 -4615 R
-(2) Cshow
-1080 451 M
-5841 0 V
-0 4498 V
--5841 0 V
-0 -4498 V
-180 2700 M
-currentpoint gsave translate 90 rotate 0 0 M
-(Number of States) Cshow
-grestore
-4000 91 M
-(Deterministic Jump Density \(mean\)) Cshow
-LT0
-6318 4706 M
-(efree-source) Rshow
-6426 4706 M
-324 0 V
-1372 880 M
-292 26 V
-1956 574 L
-292 1055 V
-292 1381 V
-292 1873 V
-3124 2334 L
-292 792 V
-3708 1439 L
-293 1469 V
-4293 1550 L
-4585 714 L
-292 645 V
-5169 541 L
-292 20 V
-292 -48 V
-292 -31 V
-292 3 V
-292 11 V
-292 -19 V
-6534 4706 D
-1372 880 D
-1664 906 D
-1956 574 D
-2248 1629 D
-2540 3010 D
-2832 4883 D
-3124 2334 D
-3416 3126 D
-3708 1439 D
-4001 2908 D
-4293 1550 D
-4585 714 D
-4877 1359 D
-5169 541 D
-5461 561 D
-5753 513 D
-6045 482 D
-6337 485 D
-6629 496 D
-6921 477 D
-LT1
-6318 4526 M
-(efree-target) Rshow
-6426 4526 M
-324 0 V
-1372 877 M
-292 25 V
-1956 571 L
-292 1012 V
-292 1218 V
-292 1409 V
-3124 2002 L
-292 428 V
-3708 1114 L
-293 830 V
-4293 999 L
-4585 571 L
-292 254 V
-5169 483 L
-292 3 V
-292 -17 V
-292 -9 V
-292 0 V
-292 1 V
-292 -3 V
-6534 4526 A
-1372 877 A
-1664 902 A
-1956 571 A
-2248 1583 A
-2540 2801 A
-2832 4210 A
-3124 2002 A
-3416 2430 A
-3708 1114 A
-4001 1944 A
-4293 999 A
-4585 571 A
-4877 825 A
-5169 483 A
-5461 486 A
-5753 469 A
-6045 460 A
-6337 460 A
-6629 461 A
-6921 458 A
-stroke
-grestore
-end
-showpage
-
-%%EndDocument
-
- endTexFig
- 330 5230 a Fd(Figure)18 b(3)330 5313 y Fo(Dif)o(fer)o(ence)f(in)i
-(sizes)f(of)g(deterministic)g(automata)i(constr)o(ucted)f(with)h
-(either)e Fc(efr)o(ee)2740 5281 y Fg(s)2792 5313 y Fo(or)g
-Fc(efr)o(ee)3017 5281 y Fg(t)3044 5313 y Fo(,)h(for)330
-5396 y(randomly)f(generated)g(input)h(automata)h(consisting)f(of)f(100)
-i(states,)e(15)i(symbols,)d(and)i(various)330 5479 y(numbers)g(of)f
-(transitions)h(and)g(jumps)g(\(cf.)f(section)h(4\).)f(Note)h(that)h
-(all)f(states)g(in)g(the)g(input)g(ar)o(e)330 5562 y(co-accessible;)f
-(the)h(dif)o(fer)o(ence)e(in)i(size)f(is)g(due)g(solely)f(to)i(the)g
-(ef)o(fect)f(illustrated)g(in)h(\002gur)o(e)e(2.)p Black
-Black 3288 5944 a Fv(6)p Black eop
-%%Page: 7 7
-7 6 bop Black 330 91 a Fo(van)20 b(Noor)o(d)1145 b(Epsilon)17
-b(Moves)h(in)h(Subset)g(Constr)o(uction)p Black Black
-Black Black Black Black Black 933 344 a Fs(funct)p Black
-933 357 199 4 v 20 w Ff(closur)o(e)7 b Fj(\()p Ft(T)12
-b Fj(\))1016 443 y Ft(D)26 b Fj(:=)c Fk(;)p Black 1016
-543 a Fs(foreach)p Black 1016 556 282 4 v 21 w Ft(t)h
-Fk(2)g Ft(T)p Black 32 w Fs(do)p Black 1531 556 97 4
-v 41 w Fv(add)d Ft(t)h Fv(unmarked)f(to)h Ft(D)p Black
-23 w Fs(od)p Black 2472 556 V Black 1016 643 a(while)p
-Black 1016 656 217 4 v 41 w Fv(ther)o(e)f(is)h(an)f(unmarked)h(state)f
-Ft(t)j Fk(2)h Ft(D)p Black 22 w Fs(do)p Black 2490 656
-97 4 v 1254 742 a Ff(mark)10 b Fj(\()p Ft(t)p Fj(\))p
-Black 1254 842 a Fs(foreach)p Black 1254 855 282 4 v
-20 w Ft(q)26 b Fk(2)d Ft(\016)s Fj(\()p Ft(t;)14 b(\017)p
-Fj(\))p Black 21 w Fs(do)p Black 1923 855 97 4 v Black
-1337 941 a(if)p Black 1337 954 60 4 v 21 w Ft(q)35 b(=)-51
-b Fk(2)23 b Ft(D)p Black 23 w Fs(then)p Black 1651 954
-171 4 v 40 w Fv(add)d Ft(q)k Fv(unmarked)c(to)h Ft(D)p
-Black 23 w Fs(\002)p Black 2676 954 51 4 v Black 1254
-1041 a(od)p Black 1254 1054 97 4 v Black 1016 1141 a(od)p
-Black 1016 1154 V Black 1016 1240 a(return)p Black 1016
-1253 236 4 v 20 w Ft(D)p Black 933 1340 a Fs(end)p Black
-933 1353 143 4 v 330 1514 a Fd(Figure)d(4)330 1597 y
-Fo(Epsilon-closur)o(e)e(Algorithm)p Black 330 1900 a
-Fs(3.2)k(Per)g(subset)f(and)h(per)g(state)330 2000 y
-Fv(Next)i(we)f(discuss)i(two)f(variants)f(\()p Fu(per)h(subset)h
-Fv(and)e Fu(per)h(state)p Fv(\))g(in)g(which)h(the)f(tr)o(eatment)f(of)
-h Ft(\017)p Fv(-)330 2099 y(moves)17 b(is)g(integrated)g(with)g(the)g
-(subset)g(constr)o(uction)h(algorithm.)g(W)-8 b(e)17
-b(will)g(show)h(later)e(that)330 2199 y(such)27 b(an)g(integrated)f
-(appr)o(oach)f(is)i(in)g(practice)f(often)g(mor)o(e)h(ef)o(\002cient)f
-(than)h(the)g Fu(per)f(graph)330 2298 y Fv(appr)o(oach)i(if)h(ther)o(e)
-g(ar)o(e)f(many)i Ft(\017)p Fv(-moves.)f(The)g Fu(per)h(subset)h
-Fv(and)e Fu(per)g(state)g Fv(appr)o(oaches)f(ar)o(e)330
-2398 y(also)c(mor)o(e)g(suitable)g(for)f(a)h Fu(lazy)f
-Fv(implementation)i(of)f(the)g(subset)h(constr)o(uction)g(algorithm)330
-2498 y(\(in)d(such)g(a)f(lazy)g(implementation)i(subsets)f(ar)o(e)f
-(only)h(computed)g(with)h(r)o(espect)d(to)i(a)g(given)330
-2597 y(input)f(string\).)479 2697 y(The)i Fu(per)f(subset)i
-Fv(and)e(the)g Fu(per)h(state)f Fv(algorithms)i(use)e(a)g(simpli\002ed)
-h(variant)f(of)g(the)h(tran-)330 2797 y(sitive)g(closur)o(e)g
-(algorithm)h(for)f(graphs.)g(Instead)f(of)i(computing)g(the)f
-(transitive)g(closur)o(e)g(of)330 2896 y(a)i(given)i(graph,)e(this)i
-(algorithm)f(only)h(computes)g(the)f(closur)o(e)f(for)h(a)f(given)i
-(set)f(of)f(states.)330 2996 y(Such)c(an)f(algorithm)i(is)f(given)g(in)
-g(\002gur)o(e)f(4.)479 3095 y(In)i(both)g(of)f(the)g(two)h(integrated)f
-(appr)o(oaches,)e(the)i(subset)h(constr)o(uction)h(algorithm)f(is)330
-3195 y(initialised)k(with)g(an)f(agenda)f(containing)i(a)f(single)h
-(subset)f(which)h(is)g(the)f Ft(\017)p Fv(-CLOSURE)f(of)330
-3295 y(the)h(set)f(of)g(start-states)g(of)g(the)h(input;)g(furthermor)o
-(e,)e(the)i(way)f(in)h(which)g(new)g(transitions)330
-3394 y(ar)o(e)j(computed)i(also)g(takes)f(the)h(ef)o(fect)e(of)i
-Ft(\017)p Fv(-moves)f(into)i(account.)e(Both)h(dif)o(fer)o(ences)d(ar)o
-(e)330 3494 y(accounted)20 b(for)h(by)g(an)f(alternative)g
-(de\002nition)i(of)f(the)f Fu(epsilon)p 2339 3494 25
-4 v 31 w(closur)o(e)h Fv(function.)479 3594 y(The)c(appr)o(oach)d(in)j
-(which)g(the)f(transitive)g(closur)o(e)g(is)h(computed)f(for)g(one)h
-(state)e(at)h(a)g(time)330 3693 y(is)25 b(de\002ned)e(by)h(the)h
-(following)g(de\002nition)h(of)e(the)g Fu(epsilon)p 2210
-3693 V 30 w(closur)o(e)h Fv(function.)g(Note)f(that)g(we)330
-3793 y(make)c(sur)o(e)g(that)h(the)g(transitive)f(closur)o(e)h
-(computation)g(is)g(only)h(performed)d(once)i(for)g(each)330
-3892 y(input)f(state,)e(by)i(memorising)g(the)g Fu(closur)o(e)f
-Fv(function;)h(the)g(full)f(computation)h(is)g(memorised)330
-3992 y(as)g(well.)626 3960 y Fn(4)p Black Black Black
-330 4258 a Fs(funct)p Black 330 4271 199 4 v 20 w Ff(epsilon)p
-820 4258 25 4 v 31 w(closur)o(e)6 b Fj(\()p Ft(U)j Fj(\))1405
-b Fv(variant)20 b(2:)g(per)g(state)p Black 413 4357 a
-Fs(return)p Black 413 4370 236 4 v 20 w Ff(memo)7 b Fj(\()939
-4295 y Fe(S)1009 4382 y Fi(u)p Fl(2)p Fi(U)1162 4357
-y Ff(memo)g Fj(\()p Ff(closur)o(e)g Fj(\()p Fk(f)p Ft(u)p
-Fk(g)p Fj(\)\)\))p Black 330 4457 a Fs(end)p Black 330
-4470 143 4 v 479 4623 a Fv(In)23 b(the)g(case)f(of)h(the)g
-Fu(per)g(subset)h Fv(appr)o(oach,)d(the)i(closur)o(e)f(algorithm)i(is)f
-(applied)e(to)j(each)330 4723 y(subset.)f(W)-8 b(e)24
-b(also)f(memorise)h(the)g(closur)o(e)f(function,)h(in)g(or)o(der)e(to)i
-(ensur)o(e)e(that)i(the)f(closur)o(e)330 4822 y(computation)j(is)f
-(performed)f(only)h(once)g(for)g(each)f(subset.)h(This)g(can)g(be)f
-(useful)h(since)g(the)330 4922 y(same)d(subset)h(can)f(be)g(generated)g
-(many)g(times)h(during)g(subset)g(constr)o(uction.)h(The)e(de\002ni-)
-330 5022 y(tion)g(simply)f(is:)p Black Black Black 330
-5287 a Fs(funct)p Black 330 5300 199 4 v 20 w Ff(epsilon)p
-820 5287 25 4 v 31 w(closur)o(e)6 b Fj(\()p Ft(U)j Fj(\))1343
-b Fv(variant)20 b(3:)g(per)g(subset)p Black 330 5457
-1495 4 v 373 5535 a Fp(4)d(This)f(is)i(an)e(impr)o(ovement)f(over)h
-(the)g(algorithm)h(given)f(in)g(a)h(pr)o(eliminary)g(version)g(of)g
-(this)f(paper)h(\(van)423 5610 y(Noor)o(d,)g(1998\).)p
-Black Black 3288 5944 a Fv(7)p Black eop
-%%Page: 8 8
-8 7 bop Black 330 91 a Fo(van)20 b(Noor)o(d)1145 b(Epsilon)17
-b(Moves)h(in)h(Subset)g(Constr)o(uction)p Black Black
-413 357 a Fs(return)p Black 413 370 236 4 v 20 w Ff(memo)7
-b Fj(\()p Ff(closur)o(e)g Fj(\()p Ft(U)i Fj(\)\))p Black
-330 457 a Fs(end)p Black 330 470 143 4 v 479 606 a Fv(The)17
-b(motivation)h(for)f(the)g Fu(per)g(state)f Fv(variant)g(is)h(the)g
-(insight)i(that)d(in)i(this)f(case)f(the)h(closur)o(e)330
-706 y(algorithm)31 b(is)g(called)e(at)h(most)i Fk(j)p
-Ft(Q)p Fk(j)e Fv(times.)h(In)f(contrast,)g(in)h(the)g
-Fu(per)f(subset)i Fv(appr)o(oach)d(the)330 806 y(transitive)c(closur)o
-(e)f(algorithm)i(may)f(need)f(to)i(be)e(called)g Fj(2)2258
-776 y Fl(j)p Fi(Q)p Fl(j)2379 806 y Fv(times.)h(On)g(the)g(other)g
-(hand,)330 905 y(in)19 b(the)f Fu(per)g(state)g Fv(appr)o(oach)f(some)h
-(over)o(head)f(must)i(be)f(accepted)e(for)i(computing)i(the)e(union)330
-1005 y(of)27 b(the)g(r)o(esults)f(for)h(each)f(state.)g(Mor)o(eover)-6
-b(,)26 b(in)h(practice)f(the)h(number)g(of)f(subsets)i(is)f(often)330
-1105 y(much)c(smaller)f(than)h Fj(2)1084 1074 y Fl(j)p
-Fi(Q)p Fl(j)1179 1105 y Fv(.)g(In)f(some)h(cases,)f(the)h(number)f(of)h
-(r)o(eachable)d(subsets)j(is)g(smaller)330 1204 y(than)e(the)g(number)g
-(of)g(states)f(encounter)o(ed)g(in)h(those)h(subsets.)330
-1403 y Fs(3.3)e(Implementation)330 1503 y Fv(In)f(or)o(der)f(to)i
-(implement)g(the)f(algorithms)h(ef)o(\002ciently)f(in)h(Pr)o(olog,)f
-(it)g(is)h(important)f(to)h(use)f(ef-)330 1603 y(\002cient)g(data-str)o
-(uctur)o(es.)e(In)i(particular)-6 b(,)17 b(we)i(use)g(an)g
-(implementation)h(of)e(\(non-updatable\))330 1702 y(arrays)h(based)g
-(on)i(the)f(N+K)h(tr)o(ees)e(of)h(O'Keefe)g(\(1990,)e(pp.142-145\))e
-(with)21 b(N=95)e(and)h(K=32.)330 1802 y(On)f(top)f(of)g(this)g
-(datastr)o(uctur)o(e,)e(a)i(hash)g(array)f(is)h(implemented)g(using)h
-(the)f(SICStus)g(library)330 1902 y(pr)o(edicate)23 b
-Fb(term)p 901 1902 25 4 v 29 w(hash/4)g Fv(which)j(constr)o(ucts)f(a)f
-(key)h(for)f(a)g(given)h(term.)f(In)h(such)g(hashes,)330
-2001 y(a)h(value)f(in)i(the)g(underlying)f(array)f(is)i(a)f(partial)f
-(list)i(of)f(key-value)g(pairs;)f(thus)i(collisions)330
-2101 y(ar)o(e)22 b(r)o(esolved)h(by)h(chaining.)g(This)g(pr)o(ovides)f
-(ef)o(\002cient)g(access)g(in)i(practice,)d(although)j(such)330
-2200 y(arrays)17 b(ar)o(e)f(quite)j(memory-intensive:)f(car)o(e)e(must)
-j(be)e(taken)h(to)g(ensur)o(e)g(that)f(the)h(determin-)330
-2300 y(istic)f(algorithms)h(indeed)e(ar)o(e)f(implemented)i(without)h
-(intr)o(oducing)f(choice-points)h(during)330 2400 y(r)o(untime.)330
-2599 y Fs(4)i(Experiments)330 2798 y Fv(T)-7 b(wo)22
-b(sets)f(of)h(experiments)f(have)g(been)h(performed.)e(In)i(the)g
-(\002rst)f(set)h(of)g(experiments,)f(ran-)330 2898 y(dom)33
-b(automata)e(ar)o(e)g(generated)g(accor)o(ding)h(to)g(a)g(number)g(of)h
-(criteria)e(based)g(on)i(Leslie)330 2997 y(\(1995\).)13
-b(In)j(the)g(second)g(set)g(of)f(experiments,)h(r)o(esults)f(ar)o(e)g
-(pr)o(ovided)f(for)i(a)f(number)h(of)g(\(much)330 3097
-y(lar)o(ger\))i(automata)h(that)h(surfaced)f(during)h(actual)f
-(development)g(work)i(on)f(\002nite-state)g(ap-)330 3197
-y(pr)o(oximation)h(techniques.)1241 3165 y Fn(5)330 3396
-y Fu(Random)34 b(automata.)d Fv(Firstly)-9 b(,)35 b(we)g(r)o(eport)g
-(on)g(a)g(number)g(of)g(experiments)g(for)g(randomly)330
-3496 y(generated)30 b(automata.)g(Following)j(Leslie)d(\(1995\),)e(the)
-j Fu(absolute)h(transition)f(density)f Fv(of)h(an)330
-3595 y(automaton)g(is)f(de\002ned)g(as)f(the)i(number)f(of)g
-(transitions)h(divided)e(by)h(the)g(squar)o(e)g(of)g(the)330
-3695 y(number)25 b(of)f(states)h(multiplied)g(by)g(the)f(number)h(of)g
-(symbols)h(\(i.e.)d(the)i(number)g(of)f(transi-)330 3794
-y(tions)19 b(divided)e(by)i(the)f(maximum)g(number)h(of)f(`possible')h
-(transitions,)g(or)-6 b(,)17 b(in)i(other)f(wor)o(ds,)330
-3894 y(the)k(pr)o(obability)f(that)h(a)f(possible)i(transition)f(in)h
-(fact)e(exists\).)g Fu(Deterministic)h(transition)f(den-)330
-3994 y(sity)f Fv(is)h(the)g(number)g(of)g(transitions)h(divided)e(by)h
-(the)g(number)f(of)h(states)g(multiplied)g(by)g(the)330
-4093 y(number)26 b(of)g(symbols)h(\(i.e.)e(the)i(ratio)e(of)h(the)h
-(number)f(of)g(transitions)h(and)e(the)i(maximum)330
-4193 y(number)21 b(of)g(`possible')g(transitions)h(in)f(a)g
-(deterministic)g(machine\).)479 4293 y(In)28 b(both)g(of)f(these)g
-(de\002nitions,)h(the)f(number)h(of)f(transitions)h(should)g(be)f
-(understood)330 4392 y(as)f(the)g(the)h(number)f(of)h(non-duplicate)f
-(transitions)h(which)g(do)g(not)g(lead)e(to)i(a)f(sink)h(state.)330
-4492 y(A)c(sink)h(state)f(is)h(a)f(state)g(fr)o(om)g(which)h(ther)o(e)f
-(exists)g(no)i(sequence)e(of)h(transitions)g(to)g(a)f(\002nal)330
-4591 y(state.)g(In)g(the)h(randomly)f(generated)g(automata,)f(states)h
-(ar)o(e)f(accessible)h(and)g(co-accessible)330 4691 y(by)e(constr)o
-(uction;)h(sink)g(states)e(and)h(associated)f(transitions)h(ar)o(e)f
-(not)h(r)o(epr)o(esented.)479 4791 y(Leslie)g(\(1995\))e(shows)k(that)e
-Fu(deterministic)g(transition)g(density)g Fv(is)g(a)g(r)o(eliable)f
-(measur)o(e)g(for)330 4890 y(the)k(dif)o(\002culty)g(of)g(subset)h
-(constr)o(uction.)g(Exponential)g(blow-up)f(can)g(be)g(expected)f(for)h
-(in-)330 4990 y(put)34 b(automata)e(with)j(deterministic)f(transition)g
-(density)g(of)f(ar)o(ound)g(2.)2753 4958 y Fn(6)2820
-4990 y Fv(He)h(concludes)330 5090 y(\(page)20 b(66\):)p
-Black Black 629 5252 a([.)12 b(.)g(.)g(])27 b(randomly)g(generated)f
-(automata)g(exhibit)i(the)f(maximum)g(execu-)p Black
-330 5413 1495 4 v 373 5491 a Fp(5)17 b(All)g(the)f(automata)g(used)g
-(in)h(the)f(experiments)g(ar)o(e)g(fr)o(eely)h(available)g(fr)o(om)423
-5566 y(http://www)-6 b(.let.r)o(ug.nl/\230vannoor)o(d/Fsa/.)373
-5637 y(6)17 b(Leslie)g(uses)f(the)g(terms)g Fh(absolute)i(density)f
-Fp(and)f Fh(deterministic)h(density)p Fp(.)p Black Black
-3288 5944 a Fv(8)p Black eop
-%%Page: 9 9
-9 8 bop Black 330 91 a Fo(van)20 b(Noor)o(d)1145 b(Epsilon)17
-b(Moves)h(in)h(Subset)g(Constr)o(uction)p Black Black
-330 1687 a
- 23681433 16577003 3289088 3289088 26970521 19866091 startTexFig
- 330 1687 a
-%%BeginDocument: dts25n.ps
-/gnudict 40 dict def
-gnudict begin
-/Color false def
-/Solid true def
-/gnulinewidth 5.000 def
-/vshift -60 def
-/dl {10 mul} def
-/hpt 31.5 def
-/vpt 31.5 def
-/M {moveto} bind def
-/L {lineto} bind def
-/R {rmoveto} bind def
-/V {rlineto} bind def
-/vpt2 vpt 2 mul def
-/hpt2 hpt 2 mul def
-/Lshow { currentpoint stroke M
-  0 vshift R show } def
-/Rshow { currentpoint stroke M
-  dup stringwidth pop neg vshift R show } def
-/Cshow { currentpoint stroke M
-  dup stringwidth pop -2 div vshift R show } def
-/DL { Color {setrgbcolor Solid {pop []} if 0 setdash }
- {pop pop pop Solid {pop []} if 0 setdash} ifelse } def
-/BL { stroke gnulinewidth 2 mul setlinewidth } def
-/AL { stroke gnulinewidth 2 div setlinewidth } def
-/PL { stroke gnulinewidth setlinewidth } def
-/LTb { BL [] 0 0 0 DL } def
-/LTa { AL [1 dl 2 dl] 0 setdash 0 0 0 setrgbcolor } def
-/LT0 { PL [] 0 1 0 DL } def
-/LT1 { PL [4 dl 2 dl] 0 0 1 DL } def
-/LT2 { PL [2 dl 3 dl] 1 0 0 DL } def
-/LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def
-/LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def
-/LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def
-/LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def
-/LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def
-/LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def
-/P { stroke [] 0 setdash
-  currentlinewidth 2 div sub M
-  0 currentlinewidth V stroke } def
-/D { stroke [] 0 setdash 2 copy vpt add M
-  hpt neg vpt neg V hpt vpt neg V
-  hpt vpt V hpt neg vpt V closepath stroke
-  P } def
-/A { stroke [] 0 setdash vpt sub M 0 vpt2 V
-  currentpoint stroke M
-  hpt neg vpt neg R hpt2 0 V stroke
-  } def
-/B { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M
-  0 vpt2 neg V hpt2 0 V 0 vpt2 V
-  hpt2 neg 0 V closepath stroke
-  P } def
-/C { stroke [] 0 setdash exch hpt sub exch vpt add M
-  hpt2 vpt2 neg V currentpoint stroke M
-  hpt2 neg 0 R hpt2 vpt2 V stroke } def
-/T { stroke [] 0 setdash 2 copy vpt 1.12 mul add M
-  hpt neg vpt -1.62 mul V
-  hpt 2 mul 0 V
-  hpt neg vpt 1.62 mul V closepath stroke
-  P  } def
-/S { 2 copy A C} def
-end
-gnudict begin
-gsave
-50 50 translate
-0.050 0.050 scale
-0 setgray
-/Palatino-Roman findfont 180 scalefont setfont
-newpath
-LTa
-LTb
-1080 451 M
-63 0 V
-5778 0 R
--63 0 V
-972 451 M
-(1) Rshow
-1080 677 M
-31 0 V
-5810 0 R
--31 0 V
-1080 975 M
-31 0 V
-5810 0 R
--31 0 V
-1080 1128 M
-31 0 V
-5810 0 R
--31 0 V
--5810 73 R
-63 0 V
-5778 0 R
--63 0 V
--5886 0 R
-(10) Rshow
-1080 1426 M
-31 0 V
-5810 0 R
--31 0 V
-1080 1725 M
-31 0 V
-5810 0 R
--31 0 V
-1080 1878 M
-31 0 V
-5810 0 R
--31 0 V
--5810 72 R
-63 0 V
-5778 0 R
--63 0 V
--5886 0 R
-(100) Rshow
-1080 2176 M
-31 0 V
-5810 0 R
--31 0 V
-1080 2474 M
-31 0 V
-5810 0 R
--31 0 V
-1080 2627 M
-31 0 V
-5810 0 R
--31 0 V
--5810 73 R
-63 0 V
-5778 0 R
--63 0 V
--5886 0 R
-(1000) Rshow
-1080 2926 M
-31 0 V
-5810 0 R
--31 0 V
-1080 3224 M
-31 0 V
-5810 0 R
--31 0 V
-1080 3377 M
-31 0 V
-5810 0 R
--31 0 V
--5810 73 R
-63 0 V
-5778 0 R
--63 0 V
--5886 0 R
-(10000) Rshow
-1080 3675 M
-31 0 V
-5810 0 R
--31 0 V
-1080 3974 M
-31 0 V
-5810 0 R
--31 0 V
-1080 4127 M
-31 0 V
-5810 0 R
--31 0 V
--5810 72 R
-63 0 V
-5778 0 R
--63 0 V
--5886 0 R
-(100000) Rshow
-1080 4425 M
-31 0 V
-5810 0 R
--31 0 V
-1080 4723 M
-31 0 V
-5810 0 R
--31 0 V
-1080 4876 M
-31 0 V
-5810 0 R
--31 0 V
--5810 73 R
-63 0 V
-5778 0 R
--63 0 V
--5886 0 R
-(1e+06) Rshow
-1479 451 M
-0 31 V
-0 4467 R
-0 -31 V
-2042 451 M
-0 31 V
-0 4467 R
-0 -31 V
-2441 451 M
-0 31 V
-0 4467 R
-0 -31 V
-2751 451 M
-0 31 V
-0 4467 R
-0 -31 V
-3004 451 M
-0 31 V
-0 4467 R
-0 -31 V
-3217 451 M
-0 31 V
-0 4467 R
-0 -31 V
-3403 451 M
-0 31 V
-0 4467 R
-0 -31 V
-3566 451 M
-0 31 V
-0 4467 R
-0 -31 V
-3712 451 M
-0 63 V
-0 4435 R
-0 -63 V
-0 -4615 R
-(1) Cshow
-4674 451 M
-0 31 V
-0 4467 R
-0 -31 V
-5237 451 M
-0 31 V
-0 4467 R
-0 -31 V
-5636 451 M
-0 31 V
-0 4467 R
-0 -31 V
-5945 451 M
-0 31 V
-0 4467 R
-0 -31 V
-6198 451 M
-0 31 V
-0 4467 R
-0 -31 V
-6412 451 M
-0 31 V
-0 4467 R
-0 -31 V
-6598 451 M
-0 31 V
-0 4467 R
-0 -31 V
-6761 451 M
-0 31 V
-0 4467 R
-0 -31 V
-6907 451 M
-0 63 V
-0 4435 R
-0 -63 V
-0 -4615 R
-(10) Cshow
-1080 451 M
-5841 0 V
-0 4498 V
--5841 0 V
-0 -4498 V
-180 2700 M
-currentpoint gsave translate 90 rotate 0 0 M
-(CPU-time \(msec\) / Number of States \(input+output\)) Cshow
-grestore
-4000 91 M
-(Deterministic Density) Cshow
-LT0
-6318 4706 M
-(fsa) Rshow
-6534 4706 D
-1479 1070 D
-2042 1558 D
-2441 1950 D
-2751 2617 D
-3004 2859 D
-3217 3229 D
-3403 3308 D
-3566 3601 D
-3712 3914 D
-3845 4026 D
-3965 4198 D
-4076 4274 D
-4179 4434 D
-4364 4541 D
-5369 4438 D
-5636 3841 D
-5945 3431 D
-6412 2687 D
-6907 2481 D
-LT1
-6318 4526 M
-(fsm) Rshow
-6534 4526 A
-1479 1070 A
-2042 1426 A
-2441 1558 A
-2751 2151 A
-3004 2418 A
-3217 2849 A
-3403 2950 A
-3566 3316 A
-3712 3676 A
-3845 3813 A
-3965 3982 A
-4076 4049 A
-4179 4262 A
-4364 4332 A
-5369 4329 A
-5636 3756 A
-5945 3371 A
-6412 2693 A
-6907 2499 A
-LT2
-6318 4346 M
-(states) Rshow
-6534 4346 B
-1479 1624 B
-2042 2067 B
-2441 2350 B
-2751 2865 B
-3004 3043 B
-3217 3348 B
-3403 3412 B
-3566 3624 B
-3712 3893 B
-3845 3981 B
-3965 4106 B
-4076 4154 B
-4179 4314 B
-4364 4359 B
-5369 4018 B
-5636 3372 B
-5945 2909 B
-6412 2125 B
-6907 1905 B
-stroke
-grestore
-end
-showpage
-
-%%EndDocument
-
- endTexFig
- 330 3871 a Fd(Figure)f(5)330 3954 y Fo(Deterministic)g(transition)h
-(density)f(versus)g(CPU-time)g(in)h(msec.)f(The)h(input)g(automata)h
-(have)g(25)330 4037 y(states,)f(15)g(symbols,)e(and)i(no)g
-Fa(\017)p Fo(-moves.)f Fc(fsa)h Fo(r)o(epr)o(esents)d(the)k(CPU-time)e
-(r)o(equir)o(ed)e(by)j(our)f(FSA6)330 4120 y(implementation;)h
-Fc(fsm)g Fo(r)o(epr)o(esents)d(the)j(CPU-time)g(r)o(equir)o(ed)d(by)i
-(A)-6 b(T&T's)19 b(FSM)f(library;)f Fc(states)330 4203
-y Fo(r)o(epr)o(esents)g(the)i(sum)f(of)h(the)g(number)g(of)f(states)h
-(of)f(the)i(input)f(and)g(output)g(automata.)p Black
-Black 3288 5944 a Fv(9)p Black eop
-%%Page: 10 10
-10 9 bop Black 330 91 a Fo(van)20 b(Noor)o(d)1145 b(Epsilon)17
-b(Moves)h(in)h(Subset)g(Constr)o(uction)p Black 629 357
-a Fv(tion)k(time,)f(and)g(the)h(maximum)g(number)f(of)h(states,)e(at)h
-(an)h(appr)o(oximate)629 457 y(deterministic)c(density)g(of)f(2.)g
-(Most)h(of)f(the)h(ar)o(ea)d(under)i(the)h(curve)f(occurs)629
-556 y(within)k(0.5)e(and)h(2.5)f(deterministic)i(density\227this)g(is)g
-(the)f(ar)o(ea)f(in)h(which)629 656 y(subset)g(constr)o(uction)h(is)f
-(expensive.)629 789 y Fs(Conjecture.)d Fv(For)i(a)g(given)h(NF)-6
-b(A,)19 b(we)h(can)g(compute)h(the)f(expected)f(num-)629
-888 y(bers)g(of)g(states)g(and)g(transitions)i(in)f(the)f(corr)o
-(esponding)g(DF)-6 b(A,)19 b(pr)o(oduced)629 988 y(by)g(subset)g
-(constr)o(uction,)h(fr)o(om)f(the)g(deterministic)g(density)g(of)g(the)
-g(NF)-6 b(A.)629 1088 y(In)18 b(addition,)g(this)h(functional)f(r)o
-(elationship)g(gives)h(rise)f(to)g(a)g(Poisson-like)629
-1187 y(curve)i(with)i(its)f(peak)f(appr)o(oximately)f(at)i(a)f
-(deterministic)h(density)g(of)g(2.)479 1370 y(A)h(number)h(of)f
-(automata)f(wer)o(e)g(generated)g(randomly)-9 b(,)22
-b(accor)o(ding)g(to)g(the)h(number)f(of)330 1469 y(states,)32
-b(symbols,)g(and)g(transition)h(density)-9 b(.)32 b(For)g(the)g
-(\002rst)g(experiment,)g(automata)f(wer)o(e)330 1569
-y(generated)i(consisting)j(of)e(15)f(symbols,)i(25)e(states,)g(and)h
-(various)g(densities)g(\(and)f(no)i Ft(\017)p Fv(-)330
-1669 y(moves\).)22 b(The)f(r)o(esults)g(ar)o(e)g(summarised)g(in)h
-(\002gur)o(e)g(5.)e(CPU-time)i(was)f(measur)o(ed)f(on)j(a)e(HP)330
-1768 y(9000/785)c(machine)j(r)o(unning)h(HP-UX)f(10.20.)d(Note)j(that)g
-(our)g(timings)h(do)f(not)g(include)g(the)330 1868 y(start-up)g(of)h
-(the)g(Pr)o(olog)g(engine,)g(nor)g(the)g(time)g(r)o(equir)o(ed)e(for)i
-(garbage)e(collection.)479 1968 y(In)26 b(or)o(der)d(to)j(establish)f
-(that)f(the)h(dif)o(fer)o(ences)e(we)i(obtain)g(later)f(ar)o(e)g
-(genuinely)h(due)g(to)330 2067 y(dif)o(fer)o(ences)30
-b(in)k(the)e(underlying)i(algorithm,)f(and)f(not)i(due)e(to)h
-(`accidental')f(implemen-)330 2167 y(tation)h(details,)g(we)g(have)f
-(compar)o(ed)g(our)h(implementation)h(with)g(the)f(determiniser)g(of)
-330 2267 y(A)-6 b(T&T's)30 b(FSM)f(utilities)i(\(Mohri,)f(Per)o(eira,)f
-(and)h(Riley)-9 b(,)31 b(1998\).)d(For)i(automata)g(without)i
-Ft(\017)p Fv(-)330 2366 y(moves)19 b(we)f(establish)g(that)g(FSM)f
-(normally)i(is)f(faster:)f(for)h(automata)f(with)i(very)e(small)i
-(tran-)330 2466 y(sition)24 b(densities)g(FSM)f(is)g(up)g(to)h(four)f
-(times)h(as)f(fast,)f(for)h(automata)g(with)h(lar)o(ger)e(densities)330
-2565 y(the)f(r)o(esults)f(ar)o(e)g(similar)-6 b(.)479
-2665 y(A)27 b(new)g(concept)g(called)g Fu(absolute)g(jump)f(density)h
-Fv(is)g(intr)o(oduced)g(to)g(specify)g(the)g(num-)330
-2765 y(ber)h(of)g Ft(\017)p Fv(-moves.)g(It)g(is)h(de\002ned)e(as)h
-(the)h(number)f(of)g Ft(\017)p Fv(-moves)g(divided)g(by)g(the)g(squar)o
-(e)g(of)330 2864 y(the)c(number)h(of)f(states)g(\(i.e.,)f(the)h(pr)o
-(obability)g(that)g(an)g Ft(\017)p Fv(-move)g(exists)g(for)g(a)g(given)
-g(pair)g(of)330 2964 y(states\).)i(Furthermor)o(e,)h
-Fu(deterministic)g(jump)g(density)f Fv(is)i(the)f(number)h(of)f
-Ft(\017)p Fv(-moves)g(divided)330 3064 y(by)d(the)g(number)g(of)g
-(states)g(\(i.e.,)f(the)h(average)e(number)i(of)g Ft(\017)p
-Fv(-moves)g(which)h(leave)e(a)h(given)330 3163 y(state\).)j(In)i(or)o
-(der)e(to)i(measur)o(e)e(the)i(dif)o(fer)o(ences)d(between)i(the)g(thr)
-o(ee)g(implementations,)h(a)330 3263 y(number)g(of)f(automata)g(has)h
-(been)f(generated)f(consisting)k(of)d(15)g(states)g(and)g(15)g
-(symbols,)330 3362 y(using)33 b(various)f(transition)h(densities)g
-(between)f(0.01)e(and)i(0.3)f(\(for)g(lar)o(ger)g(densities)i(the)330
-3462 y(automata)d(tend)g(to)h(collapse)f(to)h(an)f(automaton)h(for)g
-Fj(\006)2184 3432 y Fl(\003)2222 3462 y Fv(\).)e(For)i(each)f(of)h
-(these)f(transition)330 3562 y(densities,)19 b(deterministic)h(jump)g
-(densities)g(wer)o(e)e(chosen)i(in)g(the)f(range)g(0)g(to)h(2.5)e
-(\(again,)g(for)330 3661 y(lar)o(ger)f(values)g(the)h(automata)f(tend)h
-(to)g(collapse\).)f(In)h(\002gur)o(es)g(6)f(to)36 b(9)17
-b(the)h(outcomes)h(of)f(these)330 3761 y(experiments)j(ar)o(e)g
-(summarised)g(by)h(listing)h(the)f(average)e(amount)i(of)f(CPU-time)g
-(r)o(equir)o(ed)330 3861 y(per)k(deterministic)g(jump)h(density)f
-(\(for)g(each)f(of)h(the)g(algorithms\),)h(using)g(automata)e(with)330
-3960 y(15,)16 b(20,)h(25)g(and)g(100)f(states)h(r)o(espectively)-9
-b(.)17 b(Thus,)g(every)h(dot)f(r)o(epr)o(esents)g(the)g(average)f(for)i
-(de-)330 4060 y(terminising)k(a)d(number)i(of)f(dif)o(fer)o(ent)e
-(input)j(automata)f(with)h(various)f(absolute)g(transition)330
-4159 y(densities)h(and)f(the)h(same)g(deterministic)g(jump)g(density)-9
-b(.)479 4259 y(The)18 b(striking)g(aspect)e(of)i(these)f(experiments)g
-(is)g(that)h(the)f(integrated)g Fu(per)g(subset)h Fv(and)f
-Fu(per)330 4359 y(state)h Fv(variants)f(ar)o(e)g(much)i(mor)o(e)f(ef)o
-(\002cient)f(for)h(lar)o(ger)f(deterministic)h(jump)h(density)-9
-b(.)18 b(The)g Fu(per)330 4458 y(graph)525 4428 y Fi(t)579
-4458 y Fv(is)27 b(typically)g(the)g(fastest)f(algorithm)h(of)f(the)h
-(non-integrated)g(versions.)g(However)-6 b(,)330 4558
-y(in)26 b(these)g(experiments)g(all)g(states)f(in)i(the)e(input)i(ar)o
-(e)d(co-accessible)h(by)h(constr)o(uction;)h(and)330
-4658 y(mor)o(eover)-6 b(,)26 b(all)g(states)h(in)g(the)g(input)g(ar)o
-(e)f(\002nal)h(states.)f(Ther)o(efor)o(e,)f(the)i(advantages)e(of)i
-(the)330 4757 y Fu(per)21 b(graph)652 4727 y Fi(t;c)750
-4757 y Fv(algorithm)g(could)g(not)h(be)e(observed)g(her)o(e.)479
-4857 y(The)30 b(turning)g(point)h(is)e(ar)o(ound)g(a)g(deterministic)h
-(jump)g(density)g(of)f(ar)o(ound)g(0.8:)f(for)330 4956
-y(smaller)f(densities)g(the)f Fu(per)h(graph)1448 4926
-y Fi(t)1503 4956 y Fv(is)g(typically)g(slightly)h(faster;)d(for)h(lar)o
-(ger)g(densities)h(the)330 5056 y Fu(per)19 b(state)g
-Fv(algorithm)g(is)g(much)h(faster)-6 b(.)17 b(For)j(densities)f(beyond)
-g(1.5,)e(the)i Fu(per)g(subset)h Fv(algorithm)330 5156
-y(tends)25 b(to)g(perform)g(better)f(than)h(the)g Fu(per)g(state)f
-Fv(algorithm.)i(Inter)o(estingly)-9 b(,)24 b(this)i(generalisa-)330
-5255 y(tion)i(is)g(supported)f(by)h(the)g(experiments)f(on)h(automata)f
-(which)h(wer)o(e)f(generated)f(by)i(ap-)330 5355 y(pr)o(oximation)k
-(techniques)g(\(although)h(the)e(r)o(esults)h(for)f(randomly)h
-(generated)f(automata)330 5455 y(ar)o(e)19 b(mor)o(e)i(consistent)h
-(than)f(the)g(r)o(esults)f(for)h(`r)o(eal')e(examples\).)p
-Black 3247 5944 a(10)p Black eop
-%%Page: 11 11
-11 10 bop Black 330 91 a Fo(van)20 b(Noor)o(d)1145 b(Epsilon)17
-b(Moves)h(in)h(Subset)g(Constr)o(uction)p Black Black
-330 413 a
- 23681433 16577003 3289088 3289088 26970521 19866091 startTexFig
- 330 413 a
-%%BeginDocument: 15n.ps
-/gnudict 40 dict def
-gnudict begin
-/Color false def
-/Solid true def
-/gnulinewidth 5.000 def
-/vshift -60 def
-/dl {10 mul} def
-/hpt 31.5 def
-/vpt 31.5 def
-/M {moveto} bind def
-/L {lineto} bind def
-/R {rmoveto} bind def
-/V {rlineto} bind def
-/vpt2 vpt 2 mul def
-/hpt2 hpt 2 mul def
-/Lshow { currentpoint stroke M
-  0 vshift R show } def
-/Rshow { currentpoint stroke M
-  dup stringwidth pop neg vshift R show } def
-/Cshow { currentpoint stroke M
-  dup stringwidth pop -2 div vshift R show } def
-/DL { Color {setrgbcolor Solid {pop []} if 0 setdash }
- {pop pop pop Solid {pop []} if 0 setdash} ifelse } def
-/BL { stroke gnulinewidth 2 mul setlinewidth } def
-/AL { stroke gnulinewidth 2 div setlinewidth } def
-/PL { stroke gnulinewidth setlinewidth } def
-/LTb { BL [] 0 0 0 DL } def
-/LTa { AL [1 dl 2 dl] 0 setdash 0 0 0 setrgbcolor } def
-/LT0 { PL [] 0 1 0 DL } def
-/LT1 { PL [4 dl 2 dl] 0 0 1 DL } def
-/LT2 { PL [2 dl 3 dl] 1 0 0 DL } def
-/LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def
-/LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def
-/LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def
-/LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def
-/LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def
-/LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def
-/P { stroke [] 0 setdash
-  currentlinewidth 2 div sub M
-  0 currentlinewidth V stroke } def
-/D { stroke [] 0 setdash 2 copy vpt add M
-  hpt neg vpt neg V hpt vpt neg V
-  hpt vpt V hpt neg vpt V closepath stroke
-  P } def
-/A { stroke [] 0 setdash vpt sub M 0 vpt2 V
-  currentpoint stroke M
-  hpt neg vpt neg R hpt2 0 V stroke
-  } def
-/B { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M
-  0 vpt2 neg V hpt2 0 V 0 vpt2 V
-  hpt2 neg 0 V closepath stroke
-  P } def
-/C { stroke [] 0 setdash exch hpt sub exch vpt add M
-  hpt2 vpt2 neg V currentpoint stroke M
-  hpt2 neg 0 R hpt2 vpt2 V stroke } def
-/T { stroke [] 0 setdash 2 copy vpt 1.12 mul add M
-  hpt neg vpt -1.62 mul V
-  hpt 2 mul 0 V
-  hpt neg vpt 1.62 mul V closepath stroke
-  P  } def
-/S { 2 copy A C} def
-end
-gnudict begin
-gsave
-50 50 translate
-0.050 0.050 scale
-0 setgray
-/Palatino-Roman findfont 180 scalefont setfont
-newpath
-LTa
-1080 451 M
-0 4498 V
-LTb
-1080 451 M
-63 0 V
-5778 0 R
--63 0 V
-972 451 M
-(10) Rshow
-1080 902 M
-31 0 V
-5810 0 R
--31 0 V
-1080 1166 M
-31 0 V
-5810 0 R
--31 0 V
-1080 1354 M
-31 0 V
-5810 0 R
--31 0 V
-1080 1499 M
-31 0 V
-5810 0 R
--31 0 V
-1080 1618 M
-31 0 V
-5810 0 R
--31 0 V
-1080 1718 M
-31 0 V
-5810 0 R
--31 0 V
--5810 87 R
-31 0 V
-5810 0 R
--31 0 V
--5810 77 R
-31 0 V
-5810 0 R
--31 0 V
--5810 68 R
-63 0 V
-5778 0 R
--63 0 V
--5886 0 R
-(100) Rshow
-1080 2402 M
-31 0 V
-5810 0 R
--31 0 V
-1080 2666 M
-31 0 V
-5810 0 R
--31 0 V
-1080 2853 M
-31 0 V
-5810 0 R
--31 0 V
-1080 2998 M
-31 0 V
-5810 0 R
--31 0 V
-1080 3117 M
-31 0 V
-5810 0 R
--31 0 V
-1080 3217 M
-31 0 V
-5810 0 R
--31 0 V
--5810 87 R
-31 0 V
-5810 0 R
--31 0 V
--5810 77 R
-31 0 V
-5810 0 R
--31 0 V
--5810 69 R
-63 0 V
-5778 0 R
--63 0 V
--5886 0 R
-(1000) Rshow
-1080 3901 M
-31 0 V
-5810 0 R
--31 0 V
-1080 4165 M
-31 0 V
-5810 0 R
--31 0 V
-1080 4352 M
-31 0 V
-5810 0 R
--31 0 V
-1080 4498 M
-31 0 V
-5810 0 R
--31 0 V
-1080 4616 M
-31 0 V
-5810 0 R
--31 0 V
-1080 4717 M
-31 0 V
-5810 0 R
--31 0 V
--5810 87 R
-31 0 V
-5810 0 R
--31 0 V
--5810 76 R
-31 0 V
-5810 0 R
--31 0 V
--5810 69 R
-63 0 V
-5778 0 R
--63 0 V
--5886 0 R
-(10000) Rshow
-1080 451 M
-0 63 V
-0 4435 R
-0 -63 V
-0 -4615 R
-(0) Cshow
-2087 451 M
-0 63 V
-0 4435 R
-0 -63 V
-0 -4615 R
-(0.5) Cshow
-3094 451 M
-0 63 V
-0 4435 R
-0 -63 V
-0 -4615 R
-(1) Cshow
-4101 451 M
-0 63 V
-0 4435 R
-0 -63 V
-0 -4615 R
-(1.5) Cshow
-5108 451 M
-0 63 V
-0 4435 R
-0 -63 V
-0 -4615 R
-(2) Cshow
-6115 451 M
-0 63 V
-0 4435 R
-0 -63 V
-0 -4615 R
-(2.5) Cshow
-1080 451 M
-5841 0 V
-0 4498 V
--5841 0 V
-0 -4498 V
-180 2700 M
-currentpoint gsave translate 90 rotate 0 0 M
-(Mean CPU-time \(msec\)) Cshow
-grestore
-4000 91 M
-(#Jumps/#States) Cshow
-LT0
-6318 4706 M
-(per_graph\(t\)) Rshow
-6426 4706 M
-324 0 V
-1483 4047 M
-403 -642 V
-402 -251 V
-403 -554 V
-403 -290 V
-403 -369 V
-403 -96 V
-403 -279 V
-402 -212 V
-403 0 V
-403 171 V
-403 -26 V
-403 -333 V
-403 300 V
-6534 4706 D
-1483 4047 D
-1886 3405 D
-2288 3154 D
-2691 2600 D
-3094 2310 D
-3497 1941 D
-3900 1845 D
-4303 1566 D
-4705 1354 D
-5108 1354 D
-5511 1525 D
-5914 1499 D
-6317 1166 D
-6720 1466 D
-LT1
-6318 4526 M
-(per_graph\(s\)) Rshow
-6426 4526 M
-324 0 V
-1483 4241 M
-403 -505 V
-402 -144 V
-403 -432 V
-403 -243 V
-403 -368 V
-403 -33 V
-403 -372 V
-402 -151 V
-403 -215 V
-403 246 V
-403 117 V
-403 73 V
-403 -248 V
-6534 4526 A
-1483 4241 A
-1886 3736 A
-2288 3592 A
-2691 3160 A
-3094 2917 A
-3497 2549 A
-3900 2516 A
-4303 2144 A
-4705 1993 A
-5108 1778 A
-5511 2024 A
-5914 2141 A
-6317 2214 A
-6720 1966 A
-LT2
-6318 4346 M
-(per_graph\(s,a\)) Rshow
-6426 4346 M
-324 0 V
-1483 4237 M
-403 -497 V
-402 -145 V
-403 -421 V
-403 -224 V
-403 -307 V
-403 -13 V
-403 -218 V
-402 -97 V
-403 -194 V
-403 388 V
-403 -82 V
-403 6 V
-403 67 V
-6534 4346 B
-1483 4237 B
-1886 3740 B
-2288 3595 B
-2691 3174 B
-3094 2950 B
-3497 2643 B
-3900 2630 B
-4303 2412 B
-4705 2315 B
-5108 2121 B
-5511 2509 B
-5914 2427 B
-6317 2433 B
-6720 2500 B
-LT3
-6318 4166 M
-(per_graph\(t,c\)) Rshow
-6426 4166 M
-324 0 V
-1483 4048 M
-403 -635 V
-402 -246 V
-403 -518 V
-403 -233 V
-403 -295 V
-403 -40 V
-403 -111 V
-402 -88 V
-403 -134 V
-403 252 V
-403 12 V
-403 -130 V
-403 145 V
-6534 4166 C
-1483 4048 C
-1886 3413 C
-2288 3167 C
-2691 2649 C
-3094 2416 C
-3497 2121 C
-3900 2081 C
-4303 1970 C
-4705 1882 C
-5108 1748 C
-5511 2000 C
-5914 2012 C
-6317 1882 C
-6720 2027 C
-LT4
-6318 3986 M
-(per_subset) Rshow
-6426 3986 M
-324 0 V
-1483 4169 M
-403 -659 V
-402 -271 V
-403 -577 V
-403 -330 V
-403 -424 V
-403 -142 V
-403 -507 V
-4705 955 L
-403 -53 V
-5511 757 L
-403 264 V
-403 145 V
-6720 715 L
-6534 3986 T
-1483 4169 T
-1886 3510 T
-2288 3239 T
-2691 2662 T
-3094 2332 T
-3497 1908 T
-3900 1766 T
-4303 1259 T
-4705 955 T
-5108 902 T
-5511 757 T
-5914 1021 T
-6317 1166 T
-6720 715 T
-LT5
-6318 3806 M
-(per_state) Rshow
-6426 3806 M
-324 0 V
-1483 4157 M
-403 -663 V
-402 -279 V
-403 -596 V
-403 -311 V
-403 -451 V
-403 -135 V
-403 -508 V
-4705 845 L
-403 157 V
-5511 670 L
-403 294 V
-403 -62 V
-6720 715 L
-6534 3806 S
-1483 4157 S
-1886 3494 S
-2288 3215 S
-2691 2619 S
-3094 2308 S
-3497 1857 S
-3900 1722 S
-4303 1214 S
-4705 845 S
-5108 1002 S
-5511 670 S
-5914 964 S
-6317 902 S
-6720 715 S
-LT6
-6318 3626 M
-(fsm) Rshow
-6426 3626 M
-324 0 V
-1483 3879 M
-403 -448 V
-402 -101 V
-403 -387 V
-403 -188 V
-403 -320 V
-403 -7 V
-403 -448 V
-402 -135 V
-403 -127 V
-403 54 V
-403 252 V
-403 232 V
-403 -612 V
-stroke
-grestore
-end
-showpage
-
-%%EndDocument
-
- endTexFig
- 330 2596 a Fd(Figure)f(6)330 2679 y Fo(A)-7 b(verage)18
-b(amount)i(of)e(CPU-time)h(versus)f(jump)h(density)f(for)f(each)j(of)e
-(the)i(algorithms,)d(and)i(FSM.)330 2762 y(Input)h(automata)g(have)g
-(15)f(states.)f(Absolute)h(transition)g(densities:)f(0.01-0.3.)p
-Black Black 330 3128 a
- 23681433 16577003 3289088 3289088 26970521 19866091 startTexFig
- 330 3128 a
-%%BeginDocument: 20n.ps
-/gnudict 40 dict def
-gnudict begin
-/Color false def
-/Solid true def
-/gnulinewidth 5.000 def
-/vshift -60 def
-/dl {10 mul} def
-/hpt 31.5 def
-/vpt 31.5 def
-/M {moveto} bind def
-/L {lineto} bind def
-/R {rmoveto} bind def
-/V {rlineto} bind def
-/vpt2 vpt 2 mul def
-/hpt2 hpt 2 mul def
-/Lshow { currentpoint stroke M
-  0 vshift R show } def
-/Rshow { currentpoint stroke M
-  dup stringwidth pop neg vshift R show } def
-/Cshow { currentpoint stroke M
-  dup stringwidth pop -2 div vshift R show } def
-/DL { Color {setrgbcolor Solid {pop []} if 0 setdash }
- {pop pop pop Solid {pop []} if 0 setdash} ifelse } def
-/BL { stroke gnulinewidth 2 mul setlinewidth } def
-/AL { stroke gnulinewidth 2 div setlinewidth } def
-/PL { stroke gnulinewidth setlinewidth } def
-/LTb { BL [] 0 0 0 DL } def
-/LTa { AL [1 dl 2 dl] 0 setdash 0 0 0 setrgbcolor } def
-/LT0 { PL [] 0 1 0 DL } def
-/LT1 { PL [4 dl 2 dl] 0 0 1 DL } def
-/LT2 { PL [2 dl 3 dl] 1 0 0 DL } def
-/LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def
-/LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def
-/LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def
-/LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def
-/LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def
-/LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def
-/P { stroke [] 0 setdash
-  currentlinewidth 2 div sub M
-  0 currentlinewidth V stroke } def
-/D { stroke [] 0 setdash 2 copy vpt add M
-  hpt neg vpt neg V hpt vpt neg V
-  hpt vpt V hpt neg vpt V closepath stroke
-  P } def
-/A { stroke [] 0 setdash vpt sub M 0 vpt2 V
-  currentpoint stroke M
-  hpt neg vpt neg R hpt2 0 V stroke
-  } def
-/B { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M
-  0 vpt2 neg V hpt2 0 V 0 vpt2 V
-  hpt2 neg 0 V closepath stroke
-  P } def
-/C { stroke [] 0 setdash exch hpt sub exch vpt add M
-  hpt2 vpt2 neg V currentpoint stroke M
-  hpt2 neg 0 R hpt2 vpt2 V stroke } def
-/T { stroke [] 0 setdash 2 copy vpt 1.12 mul add M
-  hpt neg vpt -1.62 mul V
-  hpt 2 mul 0 V
-  hpt neg vpt 1.62 mul V closepath stroke
-  P  } def
-/S { 2 copy A C} def
-end
-gnudict begin
-gsave
-50 50 translate
-0.050 0.050 scale
-0 setgray
-/Palatino-Roman findfont 180 scalefont setfont
-newpath
-LTa
-1080 451 M
-0 4498 V
-LTb
-1080 451 M
-63 0 V
-5778 0 R
--63 0 V
-972 451 M
-(10) Rshow
-1080 902 M
-31 0 V
-5810 0 R
--31 0 V
-1080 1166 M
-31 0 V
-5810 0 R
--31 0 V
-1080 1354 M
-31 0 V
-5810 0 R
--31 0 V
-1080 1499 M
-31 0 V
-5810 0 R
--31 0 V
-1080 1618 M
-31 0 V
-5810 0 R
--31 0 V
-1080 1718 M
-31 0 V
-5810 0 R
--31 0 V
--5810 87 R
-31 0 V
-5810 0 R
--31 0 V
--5810 77 R
-31 0 V
-5810 0 R
--31 0 V
--5810 68 R
-63 0 V
-5778 0 R
--63 0 V
--5886 0 R
-(100) Rshow
-1080 2402 M
-31 0 V
-5810 0 R
--31 0 V
-1080 2666 M
-31 0 V
-5810 0 R
--31 0 V
-1080 2853 M
-31 0 V
-5810 0 R
--31 0 V
-1080 2998 M
-31 0 V
-5810 0 R
--31 0 V
-1080 3117 M
-31 0 V
-5810 0 R
--31 0 V
-1080 3217 M
-31 0 V
-5810 0 R
--31 0 V
--5810 87 R
-31 0 V
-5810 0 R
--31 0 V
--5810 77 R
-31 0 V
-5810 0 R
--31 0 V
--5810 69 R
-63 0 V
-5778 0 R
--63 0 V
--5886 0 R
-(1000) Rshow
-1080 3901 M
-31 0 V
-5810 0 R
--31 0 V
-1080 4165 M
-31 0 V
-5810 0 R
--31 0 V
-1080 4352 M
-31 0 V
-5810 0 R
--31 0 V
-1080 4498 M
-31 0 V
-5810 0 R
--31 0 V
-1080 4616 M
-31 0 V
-5810 0 R
--31 0 V
-1080 4717 M
-31 0 V
-5810 0 R
--31 0 V
--5810 87 R
-31 0 V
-5810 0 R
--31 0 V
--5810 76 R
-31 0 V
-5810 0 R
--31 0 V
--5810 69 R
-63 0 V
-5778 0 R
--63 0 V
--5886 0 R
-(10000) Rshow
-1080 451 M
-0 63 V
-0 4435 R
-0 -63 V
-0 -4615 R
-(0) Cshow
-2087 451 M
-0 63 V
-0 4435 R
-0 -63 V
-0 -4615 R
-(0.5) Cshow
-3094 451 M
-0 63 V
-0 4435 R
-0 -63 V
-0 -4615 R
-(1) Cshow
-4101 451 M
-0 63 V
-0 4435 R
-0 -63 V
-0 -4615 R
-(1.5) Cshow
-5108 451 M
-0 63 V
-0 4435 R
-0 -63 V
-0 -4615 R
-(2) Cshow
-6115 451 M
-0 63 V
-0 4435 R
-0 -63 V
-0 -4615 R
-(2.5) Cshow
-1080 451 M
-5841 0 V
-0 4498 V
--5841 0 V
-0 -4498 V
-180 2700 M
-currentpoint gsave translate 90 rotate 0 0 M
-(Mean CPU-time \(msec\)) Cshow
-grestore
-4000 91 M
-(#Jumps/#States) Cshow
-LT0
-6318 4706 M
-(per_graph\(t\)) Rshow
-6426 4706 M
-324 0 V
-1483 4654 M
-403 -225 V
-402 -601 V
-403 -329 V
-403 -698 V
-403 -215 V
-403 -314 V
-403 -197 V
-402 -197 V
-403 143 V
-403 -104 V
-403 -169 V
-403 -78 V
-403 187 V
-6534 4706 D
-1483 4654 D
-1886 4429 D
-2288 3828 D
-2691 3499 D
-3094 2801 D
-3497 2586 D
-3900 2272 D
-4303 2075 D
-4705 1878 D
-5108 2021 D
-5511 1917 D
-5914 1748 D
-6317 1670 D
-6720 1857 D
-LT1
-6318 4526 M
-(per_graph\(s\)) Rshow
-6426 4526 M
-324 0 V
-1483 4822 M
-403 -82 V
-402 -466 V
-403 -276 V
-403 -652 V
-403 -215 V
-403 -273 V
-403 -207 V
-402 -155 V
-403 161 V
-403 -123 V
-403 13 V
-403 -162 V
-403 171 V
-6534 4526 A
-1483 4822 A
-1886 4740 A
-2288 4274 A
-2691 3998 A
-3094 3346 A
-3497 3131 A
-3900 2858 A
-4303 2651 A
-4705 2496 A
-5108 2657 A
-5511 2534 A
-5914 2547 A
-6317 2385 A
-6720 2556 A
-LT2
-6318 4346 M
-(per_graph\(s,a\)) Rshow
-6426 4346 M
-324 0 V
-1483 4817 M
-403 -77 V
-402 -463 V
-403 -278 V
-403 -594 V
-403 -212 V
-403 -197 V
-403 -115 V
-402 46 V
-403 61 V
-403 37 V
-403 -14 V
-403 -438 V
-403 493 V
-6534 4346 B
-1483 4817 B
-1886 4740 B
-2288 4277 B
-2691 3999 B
-3094 3405 B
-3497 3193 B
-3900 2996 B
-4303 2881 B
-4705 2927 B
-5108 2988 B
-5511 3025 B
-5914 3011 B
-6317 2573 B
-6720 3066 B
-LT3
-6318 4166 M
-(per_graph\(t,c\)) Rshow
-6426 4166 M
-324 0 V
-1483 4661 M
-403 -221 V
-402 -595 V
-403 -329 V
-403 -604 V
-403 -168 V
-403 -230 V
-403 -53 V
-402 -28 V
-403 55 V
-403 10 V
-403 4 V
-403 -288 V
-403 283 V
-6534 4166 C
-1483 4661 C
-1886 4440 C
-2288 3845 C
-2691 3516 C
-3094 2912 C
-3497 2744 C
-3900 2514 C
-4303 2461 C
-4705 2433 C
-5108 2488 C
-5511 2498 C
-5914 2502 C
-6317 2214 C
-6720 2497 C
-LT4
-6318 3986 M
-(per_subset) Rshow
-6426 3986 M
-324 0 V
-1483 4760 M
-403 -273 V
-402 -627 V
-403 -339 V
-403 -737 V
-403 -294 V
-403 -358 V
-403 -280 V
-402 -397 V
-403 249 V
-403 -274 V
-403 -340 V
-403 76 V
-403 -76 V
-6534 3986 T
-1483 4760 T
-1886 4487 T
-2288 3860 T
-2691 3521 T
-3094 2784 T
-3497 2490 T
-3900 2132 T
-4303 1852 T
-4705 1455 T
-5108 1704 T
-5511 1430 T
-5914 1090 T
-6317 1166 T
-6720 1090 T
-LT5
-6318 3806 M
-(per_state) Rshow
-6426 3806 M
-324 0 V
-1483 4756 M
-403 -275 V
-402 -652 V
-403 -347 V
-403 -752 V
-403 -246 V
-403 -377 V
-403 -268 V
-402 -340 V
-403 171 V
-403 -254 V
-403 -326 V
-403 177 V
-403 58 V
-6534 3806 S
-1483 4756 S
-1886 4481 S
-2288 3829 S
-2691 3482 S
-3094 2730 S
-3497 2484 S
-3900 2107 S
-4303 1839 S
-4705 1499 S
-5108 1670 S
-5511 1416 S
-5914 1090 S
-6317 1267 S
-6720 1325 S
-LT6
-6318 3626 M
-(fsm) Rshow
-6426 3626 M
-324 0 V
-1483 4510 M
-403 21 V
-402 -411 V
-403 -282 V
-403 -577 V
-403 -156 V
-403 -236 V
-403 -269 V
-402 -188 V
-403 206 V
-403 -213 V
-403 -37 V
-403 0 V
-403 -29 V
-stroke
-grestore
-end
-showpage
-
-%%EndDocument
-
- endTexFig
- 330 5311 a Fd(Figure)g(7)330 5394 y Fo(A)-7 b(verage)18
-b(amount)i(of)e(CPU-time)h(versus)f(jump)h(density)f(for)f(each)j(of)e
-(the)i(algorithms,)d(and)i(FSM.)330 5477 y(Input)h(automata)g(have)g
-(20)f(states.)f(Absolute)h(transition)g(densities:)f(0.01-0.3.)p
-Black Black 3252 5944 a Fv(1)-5 b(1)p Black eop
-%%Page: 12 12
-12 11 bop Black 330 91 a Fo(van)20 b(Noor)o(d)1145 b(Epsilon)17
-b(Moves)h(in)h(Subset)g(Constr)o(uction)p Black Black
-330 413 a
- 23681433 16577003 3289088 3289088 26970521 19866091 startTexFig
- 330 413 a
-%%BeginDocument: 25n.ps
-/gnudict 40 dict def
-gnudict begin
-/Color false def
-/Solid true def
-/gnulinewidth 5.000 def
-/vshift -60 def
-/dl {10 mul} def
-/hpt 31.5 def
-/vpt 31.5 def
-/M {moveto} bind def
-/L {lineto} bind def
-/R {rmoveto} bind def
-/V {rlineto} bind def
-/vpt2 vpt 2 mul def
-/hpt2 hpt 2 mul def
-/Lshow { currentpoint stroke M
-  0 vshift R show } def
-/Rshow { currentpoint stroke M
-  dup stringwidth pop neg vshift R show } def
-/Cshow { currentpoint stroke M
-  dup stringwidth pop -2 div vshift R show } def
-/DL { Color {setrgbcolor Solid {pop []} if 0 setdash }
- {pop pop pop Solid {pop []} if 0 setdash} ifelse } def
-/BL { stroke gnulinewidth 2 mul setlinewidth } def
-/AL { stroke gnulinewidth 2 div setlinewidth } def
-/PL { stroke gnulinewidth setlinewidth } def
-/LTb { BL [] 0 0 0 DL } def
-/LTa { AL [1 dl 2 dl] 0 setdash 0 0 0 setrgbcolor } def
-/LT0 { PL [] 0 1 0 DL } def
-/LT1 { PL [4 dl 2 dl] 0 0 1 DL } def
-/LT2 { PL [2 dl 3 dl] 1 0 0 DL } def
-/LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def
-/LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def
-/LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def
-/LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def
-/LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def
-/LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def
-/P { stroke [] 0 setdash
-  currentlinewidth 2 div sub M
-  0 currentlinewidth V stroke } def
-/D { stroke [] 0 setdash 2 copy vpt add M
-  hpt neg vpt neg V hpt vpt neg V
-  hpt vpt V hpt neg vpt V closepath stroke
-  P } def
-/A { stroke [] 0 setdash vpt sub M 0 vpt2 V
-  currentpoint stroke M
-  hpt neg vpt neg R hpt2 0 V stroke
-  } def
-/B { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M
-  0 vpt2 neg V hpt2 0 V 0 vpt2 V
-  hpt2 neg 0 V closepath stroke
-  P } def
-/C { stroke [] 0 setdash exch hpt sub exch vpt add M
-  hpt2 vpt2 neg V currentpoint stroke M
-  hpt2 neg 0 R hpt2 vpt2 V stroke } def
-/T { stroke [] 0 setdash 2 copy vpt 1.12 mul add M
-  hpt neg vpt -1.62 mul V
-  hpt 2 mul 0 V
-  hpt neg vpt 1.62 mul V closepath stroke
-  P  } def
-/S { 2 copy A C} def
-end
-gnudict begin
-gsave
-50 50 translate
-0.050 0.050 scale
-0 setgray
-/Palatino-Roman findfont 180 scalefont setfont
-newpath
-LTa
-1080 451 M
-0 4498 V
-LTb
-1080 451 M
-63 0 V
-5778 0 R
--63 0 V
-972 451 M
-(10) Rshow
-1080 790 M
-31 0 V
-5810 0 R
--31 0 V
-1080 988 M
-31 0 V
-5810 0 R
--31 0 V
-1080 1128 M
-31 0 V
-5810 0 R
--31 0 V
-1080 1237 M
-31 0 V
-5810 0 R
--31 0 V
--5810 89 R
-31 0 V
-5810 0 R
--31 0 V
--5810 75 R
-31 0 V
-5810 0 R
--31 0 V
--5810 66 R
-31 0 V
-5810 0 R
--31 0 V
--5810 57 R
-31 0 V
-5810 0 R
--31 0 V
--5810 52 R
-63 0 V
-5778 0 R
--63 0 V
--5886 0 R
-(100) Rshow
-1080 1914 M
-31 0 V
-5810 0 R
--31 0 V
-1080 2112 M
-31 0 V
-5810 0 R
--31 0 V
-1080 2253 M
-31 0 V
-5810 0 R
--31 0 V
-1080 2361 M
-31 0 V
-5810 0 R
--31 0 V
--5810 90 R
-31 0 V
-5810 0 R
--31 0 V
--5810 75 R
-31 0 V
-5810 0 R
--31 0 V
--5810 65 R
-31 0 V
-5810 0 R
--31 0 V
--5810 58 R
-31 0 V
-5810 0 R
--31 0 V
--5810 51 R
-63 0 V
-5778 0 R
--63 0 V
--5886 0 R
-(1000) Rshow
-1080 3039 M
-31 0 V
-5810 0 R
--31 0 V
-1080 3237 M
-31 0 V
-5810 0 R
--31 0 V
-1080 3377 M
-31 0 V
-5810 0 R
--31 0 V
-1080 3486 M
-31 0 V
-5810 0 R
--31 0 V
--5810 89 R
-31 0 V
-5810 0 R
--31 0 V
--5810 75 R
-31 0 V
-5810 0 R
--31 0 V
--5810 66 R
-31 0 V
-5810 0 R
--31 0 V
--5810 57 R
-31 0 V
-5810 0 R
--31 0 V
--5810 52 R
-63 0 V
-5778 0 R
--63 0 V
--5886 0 R
-(10000) Rshow
-1080 4163 M
-31 0 V
-5810 0 R
--31 0 V
-1080 4361 M
-31 0 V
-5810 0 R
--31 0 V
-1080 4502 M
-31 0 V
-5810 0 R
--31 0 V
-1080 4610 M
-31 0 V
-5810 0 R
--31 0 V
--5810 90 R
-31 0 V
-5810 0 R
--31 0 V
--5810 75 R
-31 0 V
-5810 0 R
--31 0 V
--5810 65 R
-31 0 V
-5810 0 R
--31 0 V
--5810 58 R
-31 0 V
-5810 0 R
--31 0 V
--5810 51 R
-63 0 V
-5778 0 R
--63 0 V
--5886 0 R
-(100000) Rshow
-1080 451 M
-0 63 V
-0 4435 R
-0 -63 V
-0 -4615 R
-(0) Cshow
-2087 451 M
-0 63 V
-0 4435 R
-0 -63 V
-0 -4615 R
-(0.5) Cshow
-3094 451 M
-0 63 V
-0 4435 R
-0 -63 V
-0 -4615 R
-(1) Cshow
-4101 451 M
-0 63 V
-0 4435 R
-0 -63 V
-0 -4615 R
-(1.5) Cshow
-5108 451 M
-0 63 V
-0 4435 R
-0 -63 V
-0 -4615 R
-(2) Cshow
-6115 451 M
-0 63 V
-0 4435 R
-0 -63 V
-0 -4615 R
-(2.5) Cshow
-1080 451 M
-5841 0 V
-0 4498 V
--5841 0 V
-0 -4498 V
-180 2700 M
-currentpoint gsave translate 90 rotate 0 0 M
-(Mean CPU-time \(msec\)) Cshow
-grestore
-4000 91 M
-(#Jumps/#States) Cshow
-LT0
-6318 4706 M
-(per_graph\(t\)) Rshow
-6426 4706 M
-324 0 V
-1483 4180 M
-403 -175 V
-402 -587 V
-403 -454 V
-403 -359 V
-403 -363 V
-403 -319 V
-403 -68 V
-402 -108 V
-403 -59 V
-403 -32 V
-403 17 V
-403 9 V
-403 77 V
-6534 4706 D
-1483 4180 D
-1886 4005 D
-2288 3418 D
-2691 2964 D
-3094 2605 D
-3497 2242 D
-3900 1923 D
-4303 1855 D
-4705 1747 D
-5108 1688 D
-5511 1656 D
-5914 1673 D
-6317 1682 D
-6720 1759 D
-LT1
-6318 4526 M
-(per_graph\(s\)) Rshow
-6426 4526 M
-324 0 V
-1483 4351 M
-403 -94 V
-402 -526 V
-403 -351 V
-403 -345 V
-403 -346 V
-403 -376 V
-403 -29 V
-402 -24 V
-403 -50 V
-403 -27 V
-403 31 V
-403 -1 V
-403 73 V
-6534 4526 A
-1483 4351 A
-1886 4257 A
-2288 3731 A
-2691 3380 A
-3094 3035 A
-3497 2689 A
-3900 2313 A
-4303 2284 A
-4705 2260 A
-5108 2210 A
-5511 2183 A
-5914 2214 A
-6317 2213 A
-6720 2286 A
-LT2
-6318 4346 M
-(per_graph\(s,a\)) Rshow
-6426 4346 M
-324 0 V
--5267 6 R
-403 -95 V
-402 -523 V
-403 -347 V
-403 -333 V
-403 -307 V
-403 -269 V
-403 35 V
-402 14 V
-403 34 V
-403 -13 V
-403 57 V
-403 13 V
-403 115 V
-6534 4346 B
-1483 4352 B
-1886 4257 B
-2288 3734 B
-2691 3387 B
-3094 3054 B
-3497 2747 B
-3900 2478 B
-4303 2513 B
-4705 2527 B
-5108 2561 B
-5511 2548 B
-5914 2605 B
-6317 2618 B
-6720 2733 B
-LT3
-6318 4166 M
-(per_graph\(t,c\)) Rshow
-6426 4166 M
-324 0 V
--5267 14 R
-403 -175 V
-402 -580 V
-403 -436 V
-403 -335 V
-403 -287 V
-403 -199 V
-403 4 V
-402 -37 V
-403 2 V
-403 -15 V
-403 29 V
-403 -21 V
-403 108 V
-6534 4166 C
-1483 4180 C
-1886 4005 C
-2288 3425 C
-2691 2989 C
-3094 2654 C
-3497 2367 C
-3900 2168 C
-4303 2172 C
-4705 2135 C
-5108 2137 C
-5511 2122 C
-5914 2151 C
-6317 2130 C
-6720 2238 C
-LT4
-6318 3986 M
-(per_subset) Rshow
-6426 3986 M
-324 0 V
-1483 4211 M
-403 -166 V
-402 -612 V
-403 -477 V
-403 -402 V
-403 -406 V
-403 -417 V
-403 -90 V
-402 -210 V
-403 -137 V
-403 -135 V
-403 23 V
-403 -37 V
-403 63 V
-6534 3986 T
-1483 4211 T
-1886 4045 T
-2288 3433 T
-2691 2956 T
-3094 2554 T
-3497 2148 T
-3900 1731 T
-4303 1641 T
-4705 1431 T
-5108 1294 T
-5511 1159 T
-5914 1182 T
-6317 1145 T
-6720 1208 T
-LT5
-6318 3806 M
-(per_state) Rshow
-6426 3806 M
-324 0 V
-1483 4208 M
-403 -175 V
-402 -614 V
-403 -486 V
-403 -401 V
-403 -398 V
-403 -408 V
-403 -90 V
-402 -166 V
-403 -119 V
-403 -105 V
-403 22 V
-403 22 V
-403 12 V
-6534 3806 S
-1483 4208 S
-1886 4033 S
-2288 3419 S
-2691 2933 S
-3094 2532 S
-3497 2134 S
-3900 1726 S
-4303 1636 S
-4705 1470 S
-5108 1351 S
-5511 1246 S
-5914 1268 S
-6317 1290 S
-6720 1302 S
-LT6
-6318 3626 M
-(fsm) Rshow
-6426 3626 M
-324 0 V
-1483 4200 M
-403 -116 V
-402 -501 V
-403 -296 V
-403 -307 V
-403 -301 V
-403 -366 V
-403 -4 V
-402 -34 V
-403 -163 V
-403 -59 V
-403 46 V
-403 -87 V
-403 22 V
-stroke
-grestore
-end
-showpage
-
-%%EndDocument
-
- endTexFig
- 330 2596 a Fd(Figure)f(8)330 2679 y Fo(A)-7 b(verage)17
-b(amount)i(of)f(CPU-time)g(versus)f(deterministic)g(jump)h(density)f
-(for)g(each)i(of)f(the)g(algorithms,)330 2762 y(and)h(FSM.)f(Input)i
-(automata)g(have)g(25)f(states.)f(Absolute)h(transition)g(densities:)f
-(0.01-0.3.)p Black Black 330 3128 a
- 23681433 16577003 3289088 3289088 26970521 19866091 startTexFig
- 330 3128 a
-%%BeginDocument: 100n.ps
-/gnudict 40 dict def
-gnudict begin
-/Color false def
-/Solid true def
-/gnulinewidth 5.000 def
-/vshift -60 def
-/dl {10 mul} def
-/hpt 31.5 def
-/vpt 31.5 def
-/M {moveto} bind def
-/L {lineto} bind def
-/R {rmoveto} bind def
-/V {rlineto} bind def
-/vpt2 vpt 2 mul def
-/hpt2 hpt 2 mul def
-/Lshow { currentpoint stroke M
-  0 vshift R show } def
-/Rshow { currentpoint stroke M
-  dup stringwidth pop neg vshift R show } def
-/Cshow { currentpoint stroke M
-  dup stringwidth pop -2 div vshift R show } def
-/DL { Color {setrgbcolor Solid {pop []} if 0 setdash }
- {pop pop pop Solid {pop []} if 0 setdash} ifelse } def
-/BL { stroke gnulinewidth 2 mul setlinewidth } def
-/AL { stroke gnulinewidth 2 div setlinewidth } def
-/PL { stroke gnulinewidth setlinewidth } def
-/LTb { BL [] 0 0 0 DL } def
-/LTa { AL [1 dl 2 dl] 0 setdash 0 0 0 setrgbcolor } def
-/LT0 { PL [] 0 1 0 DL } def
-/LT1 { PL [4 dl 2 dl] 0 0 1 DL } def
-/LT2 { PL [2 dl 3 dl] 1 0 0 DL } def
-/LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def
-/LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def
-/LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def
-/LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def
-/LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def
-/LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def
-/P { stroke [] 0 setdash
-  currentlinewidth 2 div sub M
-  0 currentlinewidth V stroke } def
-/D { stroke [] 0 setdash 2 copy vpt add M
-  hpt neg vpt neg V hpt vpt neg V
-  hpt vpt V hpt neg vpt V closepath stroke
-  P } def
-/A { stroke [] 0 setdash vpt sub M 0 vpt2 V
-  currentpoint stroke M
-  hpt neg vpt neg R hpt2 0 V stroke
-  } def
-/B { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M
-  0 vpt2 neg V hpt2 0 V 0 vpt2 V
-  hpt2 neg 0 V closepath stroke
-  P } def
-/C { stroke [] 0 setdash exch hpt sub exch vpt add M
-  hpt2 vpt2 neg V currentpoint stroke M
-  hpt2 neg 0 R hpt2 vpt2 V stroke } def
-/T { stroke [] 0 setdash 2 copy vpt 1.12 mul add M
-  hpt neg vpt -1.62 mul V
-  hpt 2 mul 0 V
-  hpt neg vpt 1.62 mul V closepath stroke
-  P  } def
-/S { 2 copy A C} def
-end
-gnudict begin
-gsave
-50 50 translate
-0.050 0.050 scale
-0 setgray
-/Palatino-Roman findfont 180 scalefont setfont
-newpath
-LTa
-1080 451 M
-0 4498 V
-LTb
-1080 451 M
-63 0 V
-5778 0 R
--63 0 V
-972 451 M
-(100) Rshow
-1080 902 M
-31 0 V
-5810 0 R
--31 0 V
-1080 1166 M
-31 0 V
-5810 0 R
--31 0 V
-1080 1354 M
-31 0 V
-5810 0 R
--31 0 V
-1080 1499 M
-31 0 V
-5810 0 R
--31 0 V
-1080 1618 M
-31 0 V
-5810 0 R
--31 0 V
-1080 1718 M
-31 0 V
-5810 0 R
--31 0 V
--5810 87 R
-31 0 V
-5810 0 R
--31 0 V
--5810 77 R
-31 0 V
-5810 0 R
--31 0 V
--5810 68 R
-63 0 V
-5778 0 R
--63 0 V
--5886 0 R
-(1000) Rshow
-1080 2402 M
-31 0 V
-5810 0 R
--31 0 V
-1080 2666 M
-31 0 V
-5810 0 R
--31 0 V
-1080 2853 M
-31 0 V
-5810 0 R
--31 0 V
-1080 2998 M
-31 0 V
-5810 0 R
--31 0 V
-1080 3117 M
-31 0 V
-5810 0 R
--31 0 V
-1080 3217 M
-31 0 V
-5810 0 R
--31 0 V
--5810 87 R
-31 0 V
-5810 0 R
--31 0 V
--5810 77 R
-31 0 V
-5810 0 R
--31 0 V
--5810 69 R
-63 0 V
-5778 0 R
--63 0 V
--5886 0 R
-(10000) Rshow
-1080 3901 M
-31 0 V
-5810 0 R
--31 0 V
-1080 4165 M
-31 0 V
-5810 0 R
--31 0 V
-1080 4352 M
-31 0 V
-5810 0 R
--31 0 V
-1080 4498 M
-31 0 V
-5810 0 R
--31 0 V
-1080 4616 M
-31 0 V
-5810 0 R
--31 0 V
-1080 4717 M
-31 0 V
-5810 0 R
--31 0 V
--5810 87 R
-31 0 V
-5810 0 R
--31 0 V
--5810 76 R
-31 0 V
-5810 0 R
--31 0 V
--5810 69 R
-63 0 V
-5778 0 R
--63 0 V
--5886 0 R
-(100000) Rshow
-1080 451 M
-0 63 V
-0 4435 R
-0 -63 V
-0 -4615 R
-(0) Cshow
-2087 451 M
-0 63 V
-0 4435 R
-0 -63 V
-0 -4615 R
-(0.5) Cshow
-3094 451 M
-0 63 V
-0 4435 R
-0 -63 V
-0 -4615 R
-(1) Cshow
-4101 451 M
-0 63 V
-0 4435 R
-0 -63 V
-0 -4615 R
-(1.5) Cshow
-5108 451 M
-0 63 V
-0 4435 R
-0 -63 V
-0 -4615 R
-(2) Cshow
-6115 451 M
-0 63 V
-0 4435 R
-0 -63 V
-0 -4615 R
-(2.5) Cshow
-1080 451 M
-5841 0 V
-0 4498 V
--5841 0 V
-0 -4498 V
-180 2700 M
-currentpoint gsave translate 90 rotate 0 0 M
-(Mean CPU-time \(msec\)) Cshow
-grestore
-4000 91 M
-(#Jumps/#States) Cshow
-LT0
-6318 4706 M
-(per_graph\(t\)) Rshow
-6426 4706 M
-324 0 V
-1483 1826 M
-403 888 V
-402 958 V
-403 -82 V
-403 80 V
-403 -400 V
-403 -466 V
-403 -663 V
-402 -104 V
-403 -65 V
-403 -45 V
-403 -110 V
-403 80 V
-403 -28 V
-201 -18 V
-6534 4706 D
-1483 1826 D
-1886 2714 D
-2288 3672 D
-2691 3590 D
-3094 3670 D
-3497 3270 D
-3900 2804 D
-4303 2141 D
-4705 2037 D
-5108 1972 D
-5511 1927 D
-5914 1817 D
-6317 1897 D
-6720 1869 D
-LT1
-6318 4526 M
-(per_graph\(s\)) Rshow
-6426 4526 M
-324 0 V
-1483 1801 M
-403 837 V
-402 891 V
-403 -130 V
-403 49 V
-403 -324 V
-403 -390 V
-403 -509 V
-402 0 V
-403 15 V
-403 -85 V
-403 -121 V
-403 125 V
-403 20 V
-201 -49 V
-6534 4526 A
-1483 1801 A
-1886 2638 A
-2288 3529 A
-2691 3399 A
-3094 3448 A
-3497 3124 A
-3900 2734 A
-4303 2225 A
-4705 2225 A
-5108 2240 A
-5511 2155 A
-5914 2034 A
-6317 2159 A
-6720 2179 A
-LT2
-6318 4346 M
-(per_graph\(s,a\)) Rshow
-6426 4346 M
-324 0 V
-1483 1811 M
-403 826 V
-402 890 V
-403 -129 V
-403 45 V
-403 -325 V
-403 -364 V
-403 -452 V
-402 23 V
-403 30 V
-403 -58 V
-403 -111 V
-403 156 V
-403 -2 V
-201 -40 V
-6534 4346 B
-1483 1811 B
-1886 2637 B
-2288 3527 B
-2691 3398 B
-3094 3443 B
-3497 3118 B
-3900 2754 B
-4303 2302 B
-4705 2325 B
-5108 2355 B
-5511 2297 B
-5914 2186 B
-6317 2342 B
-6720 2340 B
-LT3
-6318 4166 M
-(per_graph\(t,c\)) Rshow
-6426 4166 M
-324 0 V
-1483 1838 M
-403 884 V
-402 953 V
-403 -85 V
-403 78 V
-403 -381 V
-403 -430 V
-403 -528 V
-402 -20 V
-403 -15 V
-403 8 V
-403 -83 V
-403 138 V
-403 -37 V
-201 -22 V
-6534 4166 C
-1483 1838 C
-1886 2722 C
-2288 3675 C
-2691 3590 C
-3094 3668 C
-3497 3287 C
-3900 2857 C
-4303 2329 C
-4705 2309 C
-5108 2294 C
-5511 2302 C
-5914 2219 C
-6317 2357 C
-6720 2320 C
-LT4
-6318 3986 M
-(per_subset) Rshow
-6426 3986 M
-324 0 V
-1483 2037 M
-403 854 V
-402 885 V
-403 -162 V
-403 -27 V
-403 -529 V
-403 -624 V
-403 -898 V
-402 -203 V
-403 -118 V
-403 -196 V
-5914 752 L
-403 14 V
-6720 640 L
-201 -90 V
-6534 3986 T
-1483 2037 T
-1886 2891 T
-2288 3776 T
-2691 3614 T
-3094 3587 T
-3497 3058 T
-3900 2434 T
-4303 1536 T
-4705 1333 T
-5108 1215 T
-5511 1019 T
-5914 752 T
-6317 766 T
-6720 640 T
-LT5
-6318 3806 M
-(per_state) Rshow
-6426 3806 M
-324 0 V
-1483 2024 M
-403 828 V
-402 864 V
-403 -185 V
-403 -64 V
-403 -544 V
-403 -584 V
-403 -748 V
-402 -93 V
-403 -53 V
-403 -131 V
-403 -141 V
-403 95 V
-403 -29 V
-201 -42 V
-6534 3806 S
-1483 2024 S
-1886 2852 S
-2288 3716 S
-2691 3531 S
-3094 3467 S
-3497 2923 S
-3900 2339 S
-4303 1591 S
-4705 1498 S
-5108 1445 S
-5511 1314 S
-5914 1173 S
-6317 1268 S
-6720 1239 S
-LT6
-6318 3626 M
-(fsm) Rshow
-6426 3626 M
-324 0 V
-1483 869 M
-403 1219 V
-402 976 V
-403 -128 V
-403 161 V
-403 -161 V
-403 -187 V
-403 -428 V
-402 -6 V
-403 19 V
-403 -215 V
-403 -298 V
-403 128 V
-403 46 V
-201 -205 V
-stroke
-grestore
-end
-showpage
-
-%%EndDocument
-
- endTexFig
- 330 5311 a Fd(Figure)g(9)330 5394 y Fo(A)-7 b(verage)17
-b(amount)i(of)f(CPU-time)g(versus)f(deterministic)g(jump)h(density)f
-(for)g(each)i(of)f(the)g(algorithms,)330 5477 y(and)h(FSM.)f(Input)i
-(automata)g(have)g(100)f(states.)g(Absolute)f(transition)i(densities:)d
-(0.001-0.0035.)p Black Black 3247 5944 a Fv(12)p Black
-eop
-%%Page: 13 13
-13 12 bop Black 330 91 a Fo(van)20 b(Noor)o(d)1145 b(Epsilon)17
-b(Moves)h(in)h(Subset)g(Constr)o(uction)p Black 330 357
-a Fu(Comparison)30 b(with)g(the)g(FSM)h(library)36 b
-Fv(W)-8 b(e)31 b(also)g(pr)o(ovide)e(the)i(r)o(esults)f(for)h(A)-6
-b(T&T's)29 b(FSM)h(li-)330 457 y(brary)23 b(again.)g(FSM)g(is)h
-(designed)g(to)g(tr)o(eat)f(weighted)h(automata)f(for)h(very)f(general)
-g(weight)330 556 y(sets.)g(The)f(initial)i(implementation)g(of)e(the)h
-(library)f(consisted)i(of)e(an)h(on-the-\003y)g(computa-)330
-656 y(tion)j(of)e(the)h(epsilon-closur)o(es)g(combined)g(with)h
-(determinisation.)f(This)g(was)g(abandoned)330 756 y(for)d(two)g(r)o
-(easons:)f(it)i(could)f(not)g(be)g(generalised)f(to)h(the)g(case)g(of)g
-(general)f(weight)i(sets,)e(and)330 855 y(it)g(was)g(not)h(outputting)g
-(the)f(intermediate)g(epsilon-r)o(emoved)f(machine)i(\(which)f(might)h
-(be)330 955 y(of)f(inter)o(est)h(in)g(itself\).)e(In)i(the)g(curr)o
-(ent)e(version)i Ft(\017)p Fv(-moves)g(must)g(be)f(r)o(emoved)g(befor)o
-(e)f(deter)o(-)330 1054 y(minisation)f(is)g(possible.)f(This)g
-(mechanism)h(thus)g(is)f(comparable)f(to)h(our)g Fu(per)g(graph)f
-Fv(variant.)330 1154 y(Appar)o(ently)-9 b(,)22 b(FSM)g(employs)i(an)f
-(algorithm)h(equivalent)g(to)g(our)f Fu(per)h(graph)2799
-1124 y Fi(s;a)2888 1154 y Fv(.)g(The)f(r)o(esult-)330
-1254 y(ing)31 b(determinised)f(machines)h(ar)o(e)d(generally)i(lar)o
-(ger)f(than)i(the)f(machines)h(pr)o(oduced)e(by)330 1353
-y(our)c(integrated)f(variants)g(and)g(the)g(variants)g(which)i
-(incorporate)e Ft(\017)p Fv(-moves)g(on)h(the)g(tar)o(get)330
-1453 y(side)c(of)f(transitions.)i(The)f(timings)h(below)f(ar)o(e)e
-(obtained)i(for)f(the)h(pipe)1083 1631 y Fb(fsmrmepsilon)47
-b(|)j(fsmdeterminize)330 1808 y Fv(This)20 b(is)g(somewhat)g(unfair)f
-(since)h(this)g(includes)g(the)g(time)f(to)h(write)g(and)f(r)o(ead)f
-(the)h(interme-)330 1908 y(diate)24 b(machine.)h(Even)g(so,)h(it)f(is)g
-(inter)o(esting)h(to)f(note)h(that)f(the)g(FSM)g(library)f(is)i(a)e
-(constant)330 2008 y(factor)c(faster)f(than)i(our)g Fu(per)f(graph)1442
-1978 y Fi(s;a)1532 2008 y Fv(;)g(for)h(lar)o(ger)e(numbers)i(of)f
-(jumps)h(the)g Fu(per)g(state)f Fv(and)g Fu(per)330 2107
-y(subset)i Fv(variants)e(consistently)i(beat)e(the)h(FSM)f(library)-9
-b(.)330 2307 y Fu(Experiment:)28 b(Automata)f(generated)h(by)h(appr)o
-(oximation)d(algorithms)35 b Fv(The)29 b(automata)f(used)h(in)330
-2406 y(the)20 b(pr)o(evious)g(experiments)h(wer)o(e)e(randomly)i
-(generated.)e(However)-6 b(,)19 b(it)i(may)f(well)h(be)f(that)330
-2506 y(in)d(practice)f(the)g(automata)g(that)h(ar)o(e)e(to)i(be)g(tr)o
-(eated)d(by)j(the)g(algorithm)g(have)f(typical)h(pr)o(oper)o(-)330
-2605 y(ties)k(which)h(wer)o(e)e(not)i(r)o(e\003ected)e(in)h(this)h
-(test)f(data.)f(For)h(this)h(r)o(eason)f(r)o(esults)g(ar)o(e)e(pr)o
-(esented)330 2705 y(for)f(a)g(number)h(of)f(automata)g(that)g(wer)o(e)f
-(generated)h(using)h(appr)o(oximation)f(techniques)h(for)330
-2805 y(context-fr)o(ee)29 b(grammars.)g(In)i(particular)-6
-b(,)28 b(automata)i(have)f(been)h(used)g(which)h(wer)o(e)e(cr)o(e-)330
-2904 y(ated)18 b(by)g(Neder)o(hof,)g(using)h(the)g(technique)g
-(described)f(in)h(Neder)o(hof)e(\(1997\).)f(In)j(addition,)f(a)330
-3004 y(small)g(number)g(of)f(automata)g(have)g(been)h(used)f(which)i
-(wer)o(e)d(cr)o(eated)g(using)i(the)g(technique)330 3104
-y(of)f(Per)o(eira)e(and)h(W)-6 b(right)17 b(\(1997\))d(\(as)h
-(implemented)i(by)g(Neder)o(hof\).)e(W)-8 b(e)16 b(have)h(r)o
-(estricted)e(our)330 3203 y(attention)21 b(to)h(automata)e(with)h(at)f
-(least)h(1000)e(states)h(in)i(the)e(input.)479 3303 y(The)k(automata)f
-(typically)h(contain)g(lots)h(of)e(jumps.)i(Mor)o(eover)-6
-b(,)22 b(the)i(number)g(of)f(states)330 3402 y(of)16
-b(the)g(r)o(esulting)g(automaton)g(is)h(often)f Fu(smaller)g
-Fv(than)g(the)g(number)g(of)g(states)g(in)g(the)g(input)h(au-)330
-3502 y(tomaton.)j(Results)g(ar)o(e)e(given)h(in)h(the)f(tables)g(1)g
-(and)g(2.)f(One)i(of)f(the)g(most)h(striking)h(examples)330
-3602 y(is)f(the)h Fu(ygrim)e Fv(automaton)h(consisting)i(of)e(3382)e
-(states)i(and)g(9124)e(jumps.)j(For)f(this)h(example,)330
-3701 y(the)i Fu(per)g(graph)f Fv(implementations)j(ran)d(out)i(of)f
-(memory)h(\(after)d(a)i(long)h(time\),)f(wher)o(eas)f(the)330
-3801 y(implementation)h(of)e(the)g Fu(per)h(subset)h
-Fv(algorithm)f(pr)o(oduced)e(the)h(determinised)h(automaton)330
-3901 y(\(containing)28 b(only)g(9)f(states\))f(within)j(a)d(single)i
-(CPU-second.)e(The)h(FSM)g(implementation)330 4000 y(took)f(much)g
-(longer)g(for)f(this)h(example)e(\(wher)o(eas)g(for)h(many)g(of)h(the)f
-(other)h(examples)e(it)i(is)330 4100 y(faster)d(than)h(our)g
-(implementations\).)h(Note)f(that)f(this)i(example)e(has)h(the)g
-(highest)h(number)330 4199 y(of)20 b(jumps)h(per)e(number)h(of)g
-(states)g(ratio.)f(This)h(con\002rms)h(the)f(observation)h(that)e(the)h
-Fu(per)g(sub-)330 4299 y(set)h Fv(algorithm)h(performs)e(better)g(on)i
-(inputs)f(with)h(a)e(high)i(deterministic)f(jump)g(density)-9
-b(.)330 4498 y Fs(5)20 b(Conclusion)330 4698 y Fv(W)-8
-b(e)25 b(have)f(discussed)h(a)g(number)g(of)g(variants)f(of)h(the)g
-(subset-constr)o(uction)i(algorithm)e(for)330 4797 y(determinising)31
-b(\002nite)f(automata)f(containing)j Ft(\017)p Fv(-moves.)d(The)h
-(experiments)g(support)g(the)330 4897 y(following)22
-b(conclusions:)p Black 571 5075 a Fk(\017)p Black 16
-w Fv(The)f(integrated)f(variants)g Fu(per)h(subset)h
-Fv(and)e Fu(per)h(state)f Fv(work)i(much)f(better)f(for)629
-5174 y(automata)g(containing)i(a)e(lar)o(ge)g(number)h(of)g
-Ft(\017)p Fv(-moves.)f(The)h Fu(per)f(subset)i Fv(variant)629
-5274 y(tends)f(to)g(impr)o(ove)f(upon)i(the)f Fu(per)f(state)h
-Fv(algorithm)g(if)g(the)g(number)g(of)g Ft(\017)p Fv(-moves)629
-5373 y(incr)o(eases)f(even)g(further)-6 b(.)p Black 571
-5538 a Fk(\017)p Black 16 w Fv(W)e(e)21 b(have)f(identi\002ed)h(four)f
-(dif)o(fer)o(ent)f(variants)h(of)h(the)g Fu(per)g(graph)e
-Fv(algorithm.)i(In)629 5637 y(our)g(experiments,)f(the)h
-Fu(per)g(graph)1730 5607 y Fi(t)1779 5637 y Fv(is)g(the)g(algorithm)g
-(of)g(choice)g(for)g(automata)p Black 3247 5944 a(13)p
-Black eop
-%%Page: 14 14
-14 13 bop Black 330 91 a Fo(van)20 b(Noor)o(d)1145 b(Epsilon)17
-b(Moves)h(in)h(Subset)g(Constr)o(uction)p Black Black
-380 705 2900 4 v 378 805 4 100 v 772 805 V 772 805 V
-1193 775 a Fv(Input)p 1814 805 V 1814 805 V 1017 w(Output)p
-3278 805 V 380 808 2900 4 v 378 908 4 100 v 537 878 a(Id)p
-772 908 V 207 w(#states)p 1119 908 V 99 w(#trans)p 1445
-908 V 99 w(#jumps)p 1814 908 V 1814 908 V 659 w(#states)p
-3278 908 V 1815 911 1465 4 v 378 1007 4 100 v 772 1007
-V 1119 1007 V 1445 1007 V 1814 1007 V 1918 977 a Fo(per)e(graph)2243
-946 y Fg(s)p 2325 1007 V 2376 977 a Fo(per)h(graph)2702
-946 y Fg(t)p 2778 1007 V 2829 977 a Fo(per)g(graph)3155
-946 y Fg(t;c)p 3278 1007 V 378 1107 V 772 1107 V 1119
-1107 V 1445 1107 V 1814 1107 V 1865 1077 a Fo(per)g(graph)2191
-1045 y Fg(s;a)p 2325 1107 V 2391 1077 a Fo(per)g(subset)p
-2778 1107 V 3278 1107 V 378 1207 V 772 1207 V 1119 1207
-V 1445 1207 V 1814 1207 V 2106 1177 a Fu(FSM)p 2325 1207
-V 171 w Fo(per)g(state)p 2778 1207 V 3278 1207 V 380
-1210 2900 4 v 378 1310 4 100 v 512 1280 a Fv(g14)p 772
-1310 V 262 w(1048)p 1119 1310 V 200 w(403)p 1445 1310
-V 201 w(1272)p 1814 1310 V 385 w(137)p 2325 1310 V 327
-w(137)p 2778 1310 V 374 w(131)p 3278 1310 V 378 1409
-V 446 1379 a(ovis4.n)p 772 1409 V 196 w(1424)p 1119 1409
-V 158 w(2210)p 1445 1409 V 243 w(517)p 1814 1409 V 385
-w(164)p 2325 1409 V 327 w(133)p 2778 1409 V 374 w(107)p
-3278 1409 V 378 1509 V 512 1479 a(g13)p 772 1509 V 262
-w(1441)p 1119 1509 V 158 w(1006)p 1445 1509 V 201 w(1272)p
-1814 1509 V 385 w(337)p 2325 1509 V 327 w(337)p 2778
-1509 V 374 w(329)p 3278 1509 V 378 1608 V 476 1579 a(r)o(ene2)p
-772 1608 V 226 w(1800)p 1119 1608 V 158 w(2597)p 1445
-1608 V 284 w(96)p 1814 1608 V 386 w(846)p 2325 1608 V
-327 w(844)p 2778 1608 V 374 w(844)p 3278 1608 V 378 1708
-V 445 1678 a(ovis9.p)p 772 1708 V 195 w(1868)p 1119 1708
-V 158 w(2791)p 1445 1708 V 201 w(2688)p 1814 1708 V 344
-w(2478)p 2325 1708 V 285 w(2478)p 2778 1708 V 332 w(1386)p
-3278 1708 V 378 1808 V 466 1778 a(ygrim)p 772 1808 V
-216 w(3382)p 1119 1808 V 158 w(5422)p 1445 1808 V 201
-w(9124)p 1814 1808 V 468 w(9)p 2325 1808 V 411 w(9)p
-2778 1808 V 458 w(9)p 3278 1808 V 378 1907 V 430 1877
-a(ygrim.p)p 772 1907 V 140 w(48062)p 1119 1907 V 116
-w(63704)p 1445 1907 V 117 w(109296)p 1814 1907 V 384
-w(702)p 2325 1907 V 327 w(702)p 2778 1907 V 374 w(702)p
-3278 1907 V 378 2007 V 461 1977 a(java19)p 772 2007 V
-168 w(54369)p 1119 2007 V 116 w(28333)p 1445 2007 V 159
-w(51018)p 1814 2007 V 343 w(1971)p 2325 2007 V 285 w(1971)p
-2778 2007 V 332 w(1855)p 3278 2007 V 378 2107 V 461 2077
-a(java16)p 772 2107 V 168 w(64210)p 1119 2107 V 116 w(43935)p
-1445 2107 V 159 w(41305)p 1814 2107 V 343 w(3186)p 2325
-2107 V 285 w(3186)p 2778 2107 V 332 w(3078)p 3278 2107
-V 378 2206 V 460 2176 a(zovis3)p 772 2206 V 168 w(88156)p
-1119 2206 V 116 w(78895)p 1445 2206 V 159 w(68093)p 1814
-2206 V 343 w(5174)p 2325 2206 V 285 w(5154)p 2778 2206
-V 332 w(4182)p 3278 2206 V 378 2306 V 460 2276 a(zovis2)p
-772 2306 V 168 w(89832)p 1119 2306 V 116 w(80400)p 1445
-2306 V 159 w(69377)p 1814 2306 V 343 w(6561)p 2325 2306
-V 285 w(6541)p 2778 2306 V 332 w(5309)p 3278 2306 V 380
-2309 2900 4 v 330 2371 a Fd(T)-8 b(able)18 b(1)330 2454
-y Fo(The)h(automata)h(generated)e(by)h(appr)o(oximation)e(algorithms.)h
-(The)h(table)g(lists)f(the)h(number)g(of)f(states,)330
-2537 y(transitions)h(and)g(jumps)g(of)f(the)i(input)f(automaton,)h(and)
-f(the)g(number)g(of)f(states)h(of)g(the)330 2629 y(determinised)e
-(machine)j(using)e(r)o(espectively)e(the)k Fc(efr)o(ee)1962
-2597 y Fg(s)1995 2629 y Fo(,)e Fc(efr)o(ee)2168 2597
-y Fg(t)2196 2629 y Fo(,)g(and)h(the)g Fc(efr)o(ee)2636
-2597 y Fg(t;c)2729 2629 y Fo(variants.)p Black Black
-468 3575 2725 4 v 466 3675 4 100 v 859 3675 V 859 3675
-V 1750 3645 a Fv(CPU-time)h(\(sec\))p 3190 3675 V 861
-3678 2332 4 v 466 3775 4 100 v 859 3775 V 911 3745 a
-Fo(graph)1108 3713 y Fg(t)p 1183 3775 V 1235 3745 a Fo(graph)1432
-3713 y Fg(t;c)p 1555 3775 V 1606 3745 a Fo(graph)1803
-3713 y Fg(s)p 1884 3775 V 1936 3745 a Fo(graph)2133 3713
-y Fg(s;a)p 2267 3775 V 2318 3745 a Fo(subset)p 2576 3775
-V 133 w(state)p 2862 3775 V 158 w Fu(FSM)p 3190 3775
-V 468 3778 2725 4 v 466 3878 4 100 v 600 3848 a Fv(g14)p
-859 3878 V 302 w(0.4)p 1183 3878 V 266 w(0.4)p 1555 3878
-V 224 w(0.3)p 1884 3878 V 278 w(0.3)p 2267 3878 V 204
-w(0.4)p 2576 3878 V 182 w(0.2)p 2862 3878 V 222 w(0.1)p
-3190 3878 V 466 3977 V 533 3947 a(ovis4.n)p 859 3977
-V 237 w(0.9)p 1183 3977 V 266 w(1.1)p 1555 3977 V 224
-w(0.8)p 1884 3977 V 278 w(1.0)p 2267 3977 V 204 w(0.7)p
-2576 3977 V 182 w(0.6)p 2862 3977 V 222 w(0.6)p 3190
-3977 V 466 4077 V 600 4047 a(g13)p 859 4077 V 302 w(0.9)p
-1183 4077 V 266 w(0.8)p 1555 4077 V 224 w(0.6)p 1884
-4077 V 278 w(0.6)p 2267 4077 V 204 w(1.2)p 2576 4077
-V 182 w(0.7)p 2862 4077 V 222 w(0.2)p 3190 4077 V 466
-4177 V 564 4147 a(r)o(ene2)p 859 4177 V 266 w(0.2)p 1183
-4177 V 266 w(0.3)p 1555 4177 V 224 w(0.2)p 1884 4177
-V 278 w(0.2)p 2267 4177 V 204 w(0.2)p 2576 4177 V 182
-w(0.2)p 2862 4177 V 222 w(0.1)p 3190 4177 V 466 4276
-V 532 4246 a(ovis9.p)p 859 4276 V 194 w(36.6)p 1183 4276
-V 224 w(16.0)p 1555 4276 V 183 w(16.9)p 1884 4276 V 235
-w(17.0)p 2267 4276 V 163 w(25.2)p 2576 4276 V 139 w(20.8)p
-2862 4276 V 181 w(21.9)p 3190 4276 V 466 4376 V 553 4346
-a(ygrim)p 859 4376 V 333 w(-)p 1183 4376 V 343 w(-)p
-1555 4376 V 301 w(-)p 1884 4376 V 355 w(-)p 2267 4376
-V 205 w(0.9)p 2576 4376 V 140 w(21.0)p 2862 4376 V 139
-w(512.1)p 3190 4376 V 466 4475 V 518 4446 a(ygrim.p)p
-859 4475 V 297 w(-)p 1183 4475 V 343 w(-)p 1555 4475
-V 301 w(-)p 1884 4475 V 355 w(-)p 2267 4475 V 122 w(562.1)p
-2576 4475 V 257 w(-)p 2862 4475 V 99 w(4512.4)p 3190
-4475 V 466 4575 V 548 4545 a(java19)p 859 4575 V 208
-w(55.5)p 1183 4575 V 224 w(67.4)p 1555 4575 V 183 w(52.6)p
-1884 4575 V 235 w(45.0)p 2267 4575 V 163 w(25.8)p 2576
-4575 V 139 w(19.0)p 2862 4575 V 222 w(3.8)p 3190 4575
-V 466 4675 V 548 4645 a(java16)p 859 4675 V 208 w(30.0)p
-1183 4675 V 224 w(45.8)p 1555 4675 V 183 w(35.0)p 1884
-4675 V 235 w(29.9)p 2267 4675 V 167 w(1)-5 b(1.3)p 2576
-4675 V 140 w(12.1)p 2862 4675 V 222 w(3.0)p 3190 4675
-V 466 4774 V 547 4744 a(zovis3)p 859 4774 V 167 w(741.1)p
-1183 4774 V 182 w(557.5)p 1555 4774 V 299 w(-)p 1884
-4774 V 196 w(407.4)p 2267 4774 V 120 w(358.4)p 2576 4774
-V 98 w(302.5)p 2862 4774 V 138 w(325.6)p 3190 4774 V
-466 4874 V 547 4844 a(zovis2)p 859 4874 V 167 w(909.2)p
-1183 4874 V 182 w(627.2)p 1555 4874 V 299 w(-)p 1884
-4874 V 196 w(496.0)p 2267 4874 V 120 w(454.4)p 2576 4874
-V 98 w(369.4)p 2862 4874 V 138 w(392.1)p 3190 4874 V
-468 4877 2725 4 v 330 4939 a Fd(T)d(able)18 b(2)330 5022
-y Fo(Results)g(for)g(automata)i(generated)e(by)h(appr)o(oximation)e
-(algorithms.)h(The)h(dashes)f(in)h(the)g(table)330 5105
-y(indicate)g(that)h(the)g(corr)o(esponding)c(algorithm)i(ran)h(out)g
-(of)f(memory)g(\(after)g(a)h(long)f(period)g(of)g(time\))330
-5188 y(for)g(that)i(particular)f(example.)p Black Black
-3247 5944 a Fv(14)p Black eop
-%%Page: 15 15
-15 14 bop Black 330 91 a Fo(van)20 b(Noor)o(d)1145 b(Epsilon)17
-b(Moves)h(in)h(Subset)g(Constr)o(uction)p Black Black
-629 357 a Fv(containing)i(few)f Ft(\017)g Fv(moves,)h(because)e(it)h
-(is)h(faster)e(than)i(the)f(other)g(algorithms,)h(and)629
-457 y(because)f(it)h(pr)o(oduces)f(smaller)g(automata)g(than)h(the)g
-Fu(per)g(graph)2674 426 y Fi(s)2729 457 y Fv(and)f Fu(per)h(graph)3212
-426 y Fi(s;a)629 556 y Fv(variants.)p Black 571 722 a
-Fk(\017)p Black 16 w Fv(The)g Fu(per)f(graph)1110 692
-y Fi(t;c)1209 722 y Fv(variant)g(is)h(an)f(inter)o(esting)h
-(alternative)f(in)h(that)g(it)g(pr)o(oduces)f(the)629
-822 y(smallest)h(r)o(esults.)f(This)i(variant)e(should)h(be)g(used)f
-(if)h(the)g(input)g(automaton)g(is)629 922 y(expected)e(to)i(contain)h
-(many)f(non-co-accessible)f(states.)p Black 571 1088
-a Fk(\017)p Black 16 w Fv(Automata)g(pr)o(oduced)f(by)i(\002nite-state)
-g(appr)o(oximation)f(techniques)i(tend)f(to)629 1187
-y(contain)g(many)g Ft(\017)p Fv(-moves.)g(W)-8 b(e)21
-b(found)f(that)h(for)g(these)f(automata)h(the)f(dif)o(fer)o(ences)629
-1287 y(in)h(speed)f(between)h(the)g(various)f(algorithms)i(can)f(be)f
-(enormous.)i(The)e Fu(per)h(subset)629 1386 y Fv(and)f
-Fu(per)h(state)g Fv(algorithms)g(ar)o(e)f(good)h(candidates)f(for)g
-(this)i(application.)479 1569 y(W)-8 b(e)30 b(have)e(attempted)h(to)g
-(characterize)e(the)i(expected)f(ef)o(\002ciency)g(of)h(the)h(various)f
-(al-)330 1669 y(gorithms)f(in)f(terms)f(of)h(the)f(number)h(of)f(jumps)
-h(and)f(the)h(number)f(of)h(states)f(in)h(the)g(input)330
-1768 y(automaton.)17 b(It)f(is)g(quite)h(conceivable)f(that)g(other)h
-(simple)g(pr)o(operties)e(of)h(the)h(input)g(automa-)330
-1868 y(ton)25 b(can)g(be)f(used)g(even)h(mor)o(e)f(ef)o(fectively)f
-(for)h(this)i(purpose.)e(One)h(r)o(eviewer)e(suggests)j(to)330
-1968 y(use)21 b(the)g(number)f(of)h(str)o(ongly)g Ft(\017)p
-Fv(-connected)f(components)i(\(the)f(str)o(ongly)g(connected)g(com-)330
-2067 y(ponents)g(of)g(the)g(graph)f(of)h(all)f Ft(\017)p
-Fv(-moves\))g(for)h(this)g(purpose.)f(W)-8 b(e)21 b(leave)f(this)h(and)
-f(other)h(pos-)330 2167 y(sibilities)h(to)f(a)f(futur)o(e)g(occasion.)p
-Black 330 2367 a Fd(Acknowledgments)330 2467 y Fo(I)f(am)g(grateful)f
-(to)h(Mark-Jan)f(Neder)o(hof)f(for)330 2550 y(support,)h(and)h(for)f
-(pr)o(oviding)e(me)j(with)g(lots)g(of)330 2633 y(\(often)g(dr)o
-(eadful\))e(automata)j(generated)e(by)330 2716 y(his)h(\002nite-state)g
-(appr)o(oximation)f(tools.)g(The)330 2799 y(comments)h(of)f(the)i
-(anonymous)e(FSMNLP)330 2882 y(and)h(CL)f(r)o(eviewers)f(wer)o(e)h
-(extr)o(emely)e(useful.)330 3081 y Fd(References)p Black
-Black 330 3214 a Fo(Aho,)j(Alfr)o(ed)e(V)-10 b(.,)18
-b(Ravi)h(Sethi,)g(and)g(Jef)o(fr)o(ey)e(D.)405 3297 y(Ullman.)27
-b(1986.)h Fc(Compilers.)18 b(Principles,)405 3380 y(T)-8
-b(echniques)17 b(and)i(T)-8 b(ools)p Fo(.)26 b(Addison)18
-b(W)-7 b(esley)f(.)p Black Black 330 3480 a(Black,)18
-b(A.W)-7 b(.)26 b(1989.)i(Finite)18 b(state)i(machines)405
-3563 y(fr)o(om)d(featur)o(e)h(grammars.)26 b(In)19 b
-Fc(International)405 3646 y(W)o(orkshop)g(on)f(Parsing)h(T)-8
-b(echnologies)p Fo(,)18 b(pages)405 3729 y(277\226285,)j(Pittsbur)o
-(gh.)p Black Black 330 3829 a(Chomsky)-8 b(,)17 b(Noam.)27
-b(1963.)h(Formal)18 b(pr)o(operties)405 3912 y(of)g(grammars.)26
-b(In)19 b(R.)f(Duncan)i(Luce,)405 3995 y(Robert)e(R.)g(Bush,)h(and)g
-(Eugene)f(Galanter)-6 b(,)405 4078 y(editors,)17 b Fc(Handbook)i(of)f
-(Mathematical)405 4161 y(Psychology;)i(V)-6 b(olume)19
-b(II)p Fo(.)f(John)h(W)l(iley)-8 b(,)17 b(pages)405 4244
-y(323\226418.)p Black Black 330 4343 a(Chomsky)-8 b(,)17
-b(Noam.)27 b(1964.)h(On)19 b(the)g(notion)405 4426 y(`r)o(ule)e(of)h
-(grammar)6 b('.)25 b(In)19 b(Jerry)e(E.)g(Fodor)g(and)405
-4509 y(Jerr)o(old)f(J.)i(Katz,)i(editors,)d Fc(The)i(Structur)o(e)e(of)
-405 4592 y(Language;)h(Readings)h(in)f(the)h(Philosophy)g(of)405
-4675 y(Language)p Fo(.)f(Pr)o(entice)g(Hall,)h(pages)f(1)l(19\226136.)p
-Black Black 330 4775 a(Cormen,)g(Leiserson,)e(and)k(Rivest.)26
-b(1990.)405 4858 y Fc(Intr)o(oduction)17 b(to)i(Algorithms)p
-Fo(.)27 b(MIT)18 b(Pr)o(ess,)405 4941 y(Cambridge)f(Mass.)p
-Black Black 330 5041 a(Evans,)i(Edmund)f(Grimley)-8 b(.)25
-b(1997.)405 5124 y(Appr)o(oximating)17 b(context-fr)o(ee)h(grammars)405
-5207 y(with)h(a)g(\002nite-state)h(calculus.)27 b(In)19
-b Fc(35th)405 5290 y(Annual)e(Meeting)h(of)g(the)h(Association)g(for)
-405 5373 y(Computational)f(Linguistics)f(and)i(8th)405
-5456 y(Confer)o(ence)f(of)g(the)h(Eur)o(opean)f(Chapter)i(of)e(the)405
-5539 y(Association)g(for)h(Computational)f(Linguistics)p
-Fo(,)405 5622 y(pages)g(452\226459,)j(Madrid.)p Black
-Black 1930 2367 a(Ger)o(demann,)d(Dale)g(and)h(Gertjan)h(van)g(Noor)o
-(d.)2004 2450 y(1999.)28 b(T)-7 b(ransducers)18 b(fr)o(om)g(r)o(ewrite)
-f(r)o(ules)2004 2533 y(with)j(backr)o(efer)o(ences.)25
-b(In)19 b Fc(Ninth)f(Confer)o(ence)2004 2617 y(of)h(the)g(Eur)o(opean)f
-(Chapter)h(of)g(the)g(Association)2004 2700 y(for)g(Computational)f
-(Linguistics)p Fo(,)f(Ber)o(gen)2004 2783 y(Norway)-8
-b(.)p Black Black 1930 2882 a(Hopcr)o(oft,)17 b(John)j(E.)e(and)h(Jef)o
-(fr)o(ey)d(D.)i(Ullman.)2004 2965 y(1979.)28 b Fc(Intr)o(oduction)18
-b(to)h(Automata)f(Theory)m(,)2004 3048 y(Languages)h(and)g(Computation)
-p Fo(.)26 b(Addison)2004 3131 y(W)-7 b(esley)f(.)p Black
-Black 1930 3231 a(Johnson,)19 b(J.)f(Howar)o(d)g(and)h(Derick)e(W)-7
-b(ood.)2004 3314 y(1997.)28 b(Instr)o(uction)20 b(computation)g(in)f
-(subset)2004 3397 y(constr)o(uction.)28 b(In)19 b(Darr)o(ell)e
-(Raymond,)2004 3480 y(Derick)h(W)-7 b(ood,)17 b(and)i(Sheng)g(Y)-7
-b(u,)19 b(editors,)2004 3563 y Fc(Automata)g(Implementation)p
-Fo(.)f(Springer)2004 3646 y(V)-8 b(erlag,)17 b(pages)h(64\22671.)29
-b(Lectur)o(e)17 b(Notes)i(in)2004 3729 y(Computer)f(Science)h(1260.)p
-Black Black 1930 3829 a(Johnson,)g(Mark.)25 b(1998.)j(Finite-state)2004
-3912 y(appr)o(oximation)18 b(of)h(constraint-based)2004
-3995 y(grammars)f(using)g(left-corner)g(grammar)2004
-4078 y(transforms.)26 b(In)20 b Fc(COLING-ACL)d('98.)i(36th)2004
-4161 y(Annual)f(Meeting)f(of)i(the)g(Association)g(for)2004
-4244 y(Computational)f(Linguistics)g(and)h(17th)2004
-4327 y(International)f(Confer)o(ence)f(on)i(Computational)2004
-4410 y(Linguistics.)e(Pr)o(oceedings)i(of)g(the)g(Confer)o(ence)p
-Fo(,)2004 4493 y(Montr)o(eal.)p Black Black 1930 4592
-a(Leslie,)d(T)-7 b(ed.)26 b(1995.)i(Ef)o(\002cient)19
-b(appr)o(oaches)f(to)2004 4675 y(subset)h(constr)o(uction.)28
-b(Master)6 b('s)17 b(thesis,)2004 4758 y(Computer)h(Science,)h
-(University)f(of)2004 4842 y(W)-7 b(aterloo.)p Black
-Black 1930 4941 a(Miller)h(,)17 b(Geor)o(ge)f(and)k(Noam)f(Chomsky)-8
-b(.)25 b(1963.)2004 5024 y(Finitary)18 b(models)g(of)g(language)h
-(users.)25 b(In)2004 5107 y(R.)19 b(Luce,)f(R.)g(Bush,)g(and)h(E.)f
-(Galanter)-6 b(,)2004 5190 y(editors,)17 b Fc(Handbook)i(of)g
-(Mathematical)2004 5273 y(Psychology)m(.)i(V)-6 b(olume)18
-b(2.)h Fo(John)g(W)l(iley)-8 b(.)p Black Black 1930 5373
-a(Mohri,)17 b(Mehryar)-6 b(,)18 b(Fernando)g(C.N.)g(Per)o(eira,)2004
-5456 y(and)i(Michael)e(Riley)-8 b(.)25 b(1998.)j(A)19
-b(rational)2004 5539 y(design)f(for)g(a)h(weighted)f(\002nite-state)
-2004 5622 y(transducer)h(library)-8 b(.)25 b(In)19 b
-Fc(Automata)p Black 3247 5944 a Fv(15)p Black eop
-%%Page: 16 16
-16 15 bop Black 330 91 a Fo(van)20 b(Noor)o(d)1145 b(Epsilon)17
-b(Moves)h(in)h(Subset)g(Constr)o(uction)p Black 405 357
-a Fc(Implementation.)e(Second)i(International)405 440
-y(W)o(orkshop)g(on)f(Implementing)g(Automata,)405 523
-y(WIA)g('97)p Fo(.)h(Springer)e(V)-8 b(erlag.)25 b(Lectur)o(e)18
-b(Notes)405 606 y(in)h(Computer)f(Science)h(1436.)p Black
-Black 330 706 a(Neder)o(hof,)e(M.)h(J.)27 b(1997.)h(Regular)405
-789 y(appr)o(oximations)17 b(of)h(CFLs:)f(A)h(grammatical)405
-872 y(view)-7 b(.)26 b(In)20 b Fc(International)d(W)o(orkshop)i(on)405
-955 y(Parsing)f(T)-8 b(echnologies)p Fo(,)19 b(Massachusetts)405
-1038 y(Institute)g(of)g(T)-7 b(echnology)f(.)p Black
-Black 330 1137 a(Neder)o(hof,)17 b(Mark-Jan.)26 b(1998.)i(Context-fr)o
-(ee)405 1220 y(parsing)18 b(thr)o(ough)g(r)o(egular)f(appr)o
-(oximation.)405 1303 y(In)i Fc(Finite-state)e(Methods)i(in)f(Natural)
-405 1386 y(Language)g(Pr)o(ocessing)p Fo(,)g(pages)g(13\22624,)405
-1469 y(Ankara.)p Black Black 330 1569 a(van)i(Noor)o(d,)d(Gertjan.)27
-b(1997.)h(FSA)19 b(Utilities:)e(A)405 1652 y(toolbox)h(to)h(manipulate)
-g(\002nite-state)405 1735 y(automata.)28 b(In)19 b(Darr)o(ell)e
-(Raymond,)h(Derick)405 1818 y(W)-7 b(ood,)17 b(and)i(Sheng)h(Y)-7
-b(u,)18 b(editors,)f Fc(Automata)405 1901 y(Implementation)p
-Fo(.)g(Springer)h(V)-8 b(erlag,)17 b(pages)405 1984 y(87\226108.)28
-b(Lectur)o(e)18 b(Notes)h(in)f(Computer)405 2067 y(Science)h(1260.)p
-Black Black 330 2167 a(van)h(Noor)o(d,)d(Gertjan.)27
-b(1998.)h(The)19 b(tr)o(eatment)405 2250 y(of)f(epsilon)g(moves)g(in)h
-(subset)g(constr)o(uction.)405 2333 y(In)g Fc(Finite-state)e(Methods)i
-(in)f(Natural)405 2416 y(Language)g(Pr)o(ocessing)p Fo(,)g(Ankara.)405
-2499 y(cmp-lg/9804003.)p Black Black 330 2599 a(van)i(Noor)o(d,)d
-(Gertjan.)27 b(1999.)h(FSA6)19 b(r)o(efer)o(ence)405
-2682 y(manual.)27 b(The)19 b Fc(FSA)f(Utilities)g Fo(toolbox)g(is)405
-2765 y(available)h(fr)o(ee)e(of)i(char)o(ge)f(under)g(Gnu)405
-2848 y(General)g(Public)h(License)f(at)405 2931 y(http://www)-7
-b(.let.r)o(ug.nl/\230vannoor)o(d/Fsa/.)p Black Black
-330 3030 a(van)20 b(Noor)o(d,)d(Gertjan)i(and)g(Dale)g(Ger)o(demann.)
-405 3113 y(1999.)28 b(An)19 b(extendible)f(r)o(egular)f(expr)o(ession)
-405 3196 y(compiler)g(for)h(\002nite-state)i(appr)o(oaches)e(in)405
-3279 y(natural)h(language)g(pr)o(ocessing.)24 b(In)405
-3362 y(O.)18 b(Boldt,)f(H.)i(Juer)o(gensen,)e(and)405
-3445 y(L.)h(Robbins,)g(editors,)f Fc(W)o(orkshop)i(on)405
-3528 y(Implementing)f(Automata;)g(WIA99)405 3611 y(Pr)o(e-Pr)o
-(oceedings)p Fo(,)g(Potsdam)g(Germany)-8 b(.)p Black
-Black 330 3711 a(O'Keefe,)17 b(Richar)o(d)i(A.)26 b(1990.)i
-Fc(The)19 b(Craft)f(of)405 3794 y(Pr)o(olog)p Fo(.)26
-b(The)19 b(MIT)f(Pr)o(ess,)f(Cambridge)405 3877 y(Mass.)p
-Black Black 330 3977 a(Per)o(eira,)g(Fernando)h(C.)h(N.)f(and)h(R.)f
-(N.)h(W)-6 b(right.)405 4060 y(1991.)28 b(Finite-state)19
-b(appr)o(oximation)e(of)405 4143 y(phrase)h(str)o(uctur)o(e)g
-(grammars.)26 b(In)19 b Fc(29th)405 4226 y(Annual)e(Meeting)h(of)g(the)
-h(Association)g(for)405 4309 y(Computational)f(Linguistics)p
-Fo(,)f(Berkeley)-8 b(.)p Black Black 330 4408 a(Per)o(eira,)17
-b(Fernando)h(C.)h(N.)f(and)h(Rebecca)g(N.)405 4491 y(W)-6
-b(right.)26 b(1997.)i(Finite-state)405 4575 y(appr)o(oximation)18
-b(of)g(phrase-str)o(uctur)o(e)405 4658 y(grammars.)25
-b(In)20 b(Emmanuel)e(Roche)h(and)405 4741 y(Y)-7 b(ves)18
-b(Schabes,)i(editors,)c Fc(Finite-State)405 4824 y(Language)i(Pr)o
-(ocessing)p Fo(.)g(MIT)h(Pr)o(ess,)405 4907 y(Cambridge,)e(pages)h
-(149\226173.)p Black Black 330 5006 a(Rood,)g(C.M.)25
-b(1996.)j(Ef)o(\002cient)19 b(\002nite-state)405 5089
-y(appr)o(oximation)f(of)g(context)h(fr)o(ee)405 5172
-y(grammars.)25 b(In)20 b(A.)e(Kornai,)h(editor)-6 b(,)405
-5255 y Fc(Extended)19 b(Finite)e(State)h(Models)h(of)f(Language)p
-Fo(,)405 5338 y(Pr)o(oceedings)e(of)j(the)g(ECAI'96)g(workshop,)405
-5421 y(pages)f(58\22664,)i(Budapest)e(University)g(of)405
-5504 y(Economic)g(Sciences,)h(Hungary)-8 b(.)p Black
-3247 5944 a Fv(16)p Black eop
-%%Trailer
-end
-userdict /end-hook known{end-hook}if
-%%EOF
diff --git a/resources/graphregexpr.jar b/resources/graphregexpr.jar
deleted file mode 100644
index 99e8440..0000000
Binary files a/resources/graphregexpr.jar and /dev/null differ
diff --git a/resources/literature/RENFADFA.doc b/resources/literature/RENFADFA.doc
new file mode 100644
index 0000000..fb76173
Binary files /dev/null and b/resources/literature/RENFADFA.doc differ
diff --git a/resources/literature/fsmnlp.ps b/resources/literature/fsmnlp.ps
new file mode 100644
index 0000000..34379af
--- /dev/null
+++ b/resources/literature/fsmnlp.ps
@@ -0,0 +1,6674 @@
+%!PS-Adobe-2.0
+%%Creator: dvips(k) 5.86 Copyright 1999 Radical Eye Software
+%%Pages: 16
+%%PageOrder: Ascend
+%%BoundingBox: 0 0 596 842
+%%DocumentFonts: Palatino-Bold Palatino-Roman CMSY6 Palatino-Italic
+%%+ CMMI10 CMR7 CMSY8 CMR6 Palatino-BoldItalic CMSY7 CMSY10 CMR10 CMMI7
+%%+ CMMI6 CMEX10 Courier CMMI9
+%%DocumentPaperSizes: a4
+%%EndComments
+%DVIPSWebPage: (www.radicaleye.com)
+%DVIPSCommandLine: dvips -f
+%DVIPSParameters: dpi=600, compressed, comments removed
+%DVIPSSource:  TeX output 2003.05.08:1610
+%%BeginProcSet: texc.pro
+/TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S
+N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72
+mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0
+0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{
+landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize
+mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR[
+matrix currentmatrix{A A round sub abs 0.00001 lt{round}if}forall round
+exch round exch]setmatrix}N/@landscape{/isls true N}B/@manualfeed{
+statusdict/manualfeed true put}B/@copies{/#copies X}B/FMat[1 0 0 -1 0 0]
+N/FBB[0 0 0 0]N/nn 0 N/IEn 0 N/ctr 0 N/df-tail{/nn 8 dict N nn begin
+/FontType 3 N/FontMatrix fntrx N/FontBBox FBB N string/base X array
+/BitMaps X/BuildChar{CharBuilder}N/Encoding IEn N end A{/foo setfont}2
+array copy cvx N load 0 nn put/ctr 0 N[}B/sf 0 N/df{/sf 1 N/fntrx FMat N
+df-tail}B/dfs{div/sf X/fntrx[sf 0 0 sf neg 0 0]N df-tail}B/E{pop nn A
+definefont setfont}B/Cw{Cd A length 5 sub get}B/Ch{Cd A length 4 sub get
+}B/Cx{128 Cd A length 3 sub get sub}B/Cy{Cd A length 2 sub get 127 sub}
+B/Cdx{Cd A length 1 sub get}B/Ci{Cd A type/stringtype ne{ctr get/ctr ctr
+1 add N}if}B/id 0 N/rw 0 N/rc 0 N/gp 0 N/cp 0 N/G 0 N/CharBuilder{save 3
+1 roll S A/base get 2 index get S/BitMaps get S get/Cd X pop/ctr 0 N Cdx
+0 Cx Cy Ch sub Cx Cw add Cy setcachedevice Cw Ch true[1 0 0 -1 -.1 Cx
+sub Cy .1 sub]/id Ci N/rw Cw 7 add 8 idiv string N/rc 0 N/gp 0 N/cp 0 N{
+rc 0 ne{rc 1 sub/rc X rw}{G}ifelse}imagemask restore}B/G{{id gp get/gp
+gp 1 add N A 18 mod S 18 idiv pl S get exec}loop}B/adv{cp add/cp X}B
+/chg{rw cp id gp 4 index getinterval putinterval A gp add/gp X adv}B/nd{
+/cp 0 N rw exit}B/lsh{rw cp 2 copy get A 0 eq{pop 1}{A 255 eq{pop 254}{
+A A add 255 and S 1 and or}ifelse}ifelse put 1 adv}B/rsh{rw cp 2 copy
+get A 0 eq{pop 128}{A 255 eq{pop 127}{A 2 idiv S 128 and or}ifelse}
+ifelse put 1 adv}B/clr{rw cp 2 index string putinterval adv}B/set{rw cp
+fillstr 0 4 index getinterval putinterval adv}B/fillstr 18 string 0 1 17
+{2 copy 255 put pop}for N/pl[{adv 1 chg}{adv 1 chg nd}{1 add chg}{1 add
+chg nd}{adv lsh}{adv lsh nd}{adv rsh}{adv rsh nd}{1 add adv}{/rc X nd}{
+1 add set}{1 add clr}{adv 2 chg}{adv 2 chg nd}{pop nd}]A{bind pop}
+forall N/D{/cc X A type/stringtype ne{]}if nn/base get cc ctr put nn
+/BitMaps get S ctr S sf 1 ne{A A length 1 sub A 2 index S get sf div put
+}if put/ctr ctr 1 add N}B/I{cc 1 add D}B/bop{userdict/bop-hook known{
+bop-hook}if/SI save N @rigin 0 0 moveto/V matrix currentmatrix A 1 get A
+mul exch 0 get A mul add .99 lt{/QV}{/RV}ifelse load def pop pop}N/eop{
+SI restore userdict/eop-hook known{eop-hook}if showpage}N/@start{
+userdict/start-hook known{start-hook}if pop/VResolution X/Resolution X
+1000 div/DVImag X/IEn 256 array N 2 string 0 1 255{IEn S A 360 add 36 4
+index cvrs cvn put}for pop 65781.76 div/vsize X 65781.76 div/hsize X}N
+/p{show}N/RMat[1 0 0 -1 0 0]N/BDot 260 string N/Rx 0 N/Ry 0 N/V{}B/RV/v{
+/Ry X/Rx X V}B statusdict begin/product where{pop false[(Display)(NeXT)
+(LaserWriter 16/600)]{A length product length le{A length product exch 0
+exch getinterval eq{pop true exit}if}{pop}ifelse}forall}{false}ifelse
+end{{gsave TR -.1 .1 TR 1 1 scale Rx Ry false RMat{BDot}imagemask
+grestore}}{{gsave TR -.1 .1 TR Rx Ry scale 1 1 false RMat{BDot}
+imagemask grestore}}ifelse B/QV{gsave newpath transform round exch round
+exch itransform moveto Rx 0 rlineto 0 Ry neg rlineto Rx neg 0 rlineto
+fill grestore}B/a{moveto}B/delta 0 N/tail{A/delta X 0 rmoveto}B/M{S p
+delta add tail}B/b{S p tail}B/c{-4 M}B/d{-3 M}B/e{-2 M}B/f{-1 M}B/g{0 M}
+B/h{1 M}B/i{2 M}B/j{3 M}B/k{4 M}B/w{0 rmoveto}B/l{p -4 w}B/m{p -3 w}B/n{
+p -2 w}B/o{p -1 w}B/q{p 1 w}B/r{p 2 w}B/s{p 3 w}B/t{p 4 w}B/x{0 S
+rmoveto}B/y{3 2 roll p a}B/bos{/SS save N}B/eos{SS restore}B end
+
+%%EndProcSet
+%%BeginProcSet: pstricks.pro
+% PostScript prologue for pstricks.tex.
+% Version 97 patch 3, 98/06/01
+% For distribution, see pstricks.tex.
+%
+/tx@Dict 200 dict def tx@Dict begin
+/ADict 25 dict def
+/CM { matrix currentmatrix } bind def
+/SLW /setlinewidth load def
+/CLW /currentlinewidth load def
+/CP /currentpoint load def
+/ED { exch def } bind def
+/L /lineto load def
+/T /translate load def
+/TMatrix { } def
+/RAngle { 0 } def
+/Atan { /atan load stopped { pop pop 0 } if } def
+/Div { dup 0 eq { pop } { div } ifelse } def
+/NET { neg exch neg exch T } def
+/Pyth { dup mul exch dup mul add sqrt } def
+/PtoC { 2 copy cos mul 3 1 roll sin mul } def
+/PathLength@ { /z z y y1 sub x x1 sub Pyth add def /y1 y def /x1 x def }
+def
+/PathLength { flattenpath /z 0 def { /y1 ED /x1 ED /y2 y1 def /x2 x1 def
+} { /y ED /x ED PathLength@ } {} { /y y2 def /x x2 def PathLength@ }
+/pathforall load stopped { pop pop pop pop } if z } def
+/STP { .996264 dup scale } def
+/STV { SDict begin normalscale end STP  } def
+/DashLine { dup 0 gt { /a .5 def PathLength exch div } { pop /a 1 def
+PathLength } ifelse /b ED /x ED /y ED /z y x add def b a .5 sub 2 mul y
+mul sub z Div round z mul a .5 sub 2 mul y mul add b exch Div dup y mul
+/y ED x mul /x ED x 0 gt y 0 gt and { [ y x ] 1 a sub y mul } { [ 1 0 ]
+0 } ifelse setdash stroke } def
+/DotLine { /b PathLength def /a ED /z ED /y CLW def /z y z add def a 0 gt
+{ /b b a div def } { a 0 eq { /b b y sub def } { a -3 eq { /b b y add
+def } if } ifelse } ifelse [ 0 b b z Div round Div dup 0 le { pop 1 } if
+] a 0 gt { 0 } { y 2 div a -2 gt { neg } if } ifelse setdash 1
+setlinecap stroke } def
+/LineFill { gsave abs CLW add /a ED a 0 dtransform round exch round exch
+2 copy idtransform exch Atan rotate idtransform pop /a ED .25 .25
+% DG/SR modification begin - Dec. 12, 1997 - Patch 2
+%itransform translate pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a
+itransform pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a
+% DG/SR modification end
+Div cvi /x1 ED /y2 y2 y1 sub def clip newpath 2 setlinecap systemdict
+/setstrokeadjust known { true setstrokeadjust } if x2 x1 sub 1 add { x1
+% DG/SR modification begin - Jun.  1, 1998 - Patch 3 (from Michael Vulis)
+% a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore }
+% def
+a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore
+pop pop } def
+% DG/SR modification end
+/BeginArrow { ADict begin /@mtrx CM def gsave 2 copy T 2 index sub neg
+exch 3 index sub exch Atan rotate newpath } def
+/EndArrow { @mtrx setmatrix CP grestore end } def
+/Arrow { CLW mul add dup 2 div /w ED mul dup /h ED mul /a ED { 0 h T 1 -1
+scale } if w neg h moveto 0 0 L w h L w neg a neg rlineto gsave fill
+grestore } def
+/Tbar { CLW mul add /z ED z -2 div CLW 2 div moveto z 0 rlineto stroke 0
+CLW moveto } def
+/Bracket { CLW mul add dup CLW sub 2 div /x ED mul CLW add /y ED /z CLW 2
+div def x neg y moveto x neg CLW 2 div L x CLW 2 div L x y L stroke 0
+CLW moveto } def
+/RoundBracket { CLW mul add dup 2 div /x ED mul /y ED /mtrx CM def 0 CLW
+2 div T x y mul 0 ne { x y scale } if 1 1 moveto .85 .5 .35 0 0 0
+curveto -.35 0 -.85 .5 -1 1 curveto mtrx setmatrix stroke 0 CLW moveto }
+def
+/SD { 0 360 arc fill } def
+/EndDot { { /z DS def } { /z 0 def } ifelse /b ED 0 z DS SD b { 0 z DS
+CLW sub SD } if 0 DS z add CLW 4 div sub moveto } def
+/Shadow { [ { /moveto load } { /lineto load } { /curveto load } {
+/closepath load } /pathforall load stopped { pop pop pop pop CP /moveto
+load } if ] cvx newpath 3 1 roll T exec } def
+/NArray { aload length 2 div dup dup cvi eq not { exch pop } if /n exch
+cvi def } def
+/NArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop } if
+f { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def
+/Line { NArray n 0 eq not { n 1 eq { 0 0 /n 2 def } if ArrowA /n n 2 sub
+def n { Lineto } repeat CP 4 2 roll ArrowB L pop pop } if } def
+/Arcto { /a [ 6 -2 roll ] cvx def a r /arcto load stopped { 5 } { 4 }
+ifelse { pop } repeat a } def
+/CheckClosed { dup n 2 mul 1 sub index eq 2 index n 2 mul 1 add index eq
+and { pop pop /n n 1 sub def } if } def
+/Polygon { NArray n 2 eq { 0 0 /n 3 def } if n 3 lt { n { pop pop }
+repeat } { n 3 gt { CheckClosed } if n 2 mul -2 roll /y0 ED /x0 ED /y1
+ED /x1 ED x1 y1 /x1 x0 x1 add 2 div def /y1 y0 y1 add 2 div def x1 y1
+moveto /n n 2 sub def n { Lineto } repeat x1 y1 x0 y0 6 4 roll Lineto
+Lineto pop pop closepath } ifelse } def
+/Diamond { /mtrx CM def T rotate /h ED /w ED dup 0 eq { pop } { CLW mul
+neg /d ED /a w h Atan def /h d a sin Div h add def /w d a cos Div w add
+def } ifelse mark w 2 div h 2 div w 0 0 h neg w neg 0 0 h w 2 div h 2
+div /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx
+setmatrix } def
+% DG modification begin - Jan. 15, 1997
+%/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup 0 eq {
+%pop } { CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2
+%div dup cos exch sin Div mul sub def } ifelse mark 0 d w neg d 0 h w d 0
+%d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx
+%setmatrix } def
+/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup
+CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2
+div dup cos exch sin Div mul sub def mark 0 d w neg d 0 h w d 0
+d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx
+% DG/SR modification begin - Jun.  1, 1998 - Patch 3 (from Michael Vulis)
+% setmatrix } def
+setmatrix pop } def
+% DG/SR modification end
+/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth
+def } def
+/CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth
+def } def
+/CC { /l0 l1 def /x1 x dx sub def /y1 y dy sub def /dx0 dx1 def /dy0 dy1
+def CCA /dx dx0 l1 c exp mul dx1 l0 c exp mul add def /dy dy0 l1 c exp
+mul dy1 l0 c exp mul add def /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos
+abs b exp a mul dx dy Pyth Div 2 div def /x2 x l0 dx mul m mul sub def
+/y2 y l0 dy mul m mul sub def /dx l1 dx mul m mul neg def /dy l1 dy mul
+m mul neg def } def
+/IC { /c c 1 add def c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if }
+ifelse /a a 2 mul 3 div 45 cos b exp div def CCA /dx 0 def /dy 0 def }
+def
+/BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def
+/NC { CC x1 y1 x2 y2 x y curveto } def
+/EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def
+/BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def
+/NAC { x2 y2 x y curveto CC x1 y1 } def
+/EAC { x2 y2 x y ArrowB curveto pop pop } def
+/OpenCurve { NArray n 3 lt { n { pop pop } repeat } { BOC /n n 3 sub def
+n { NC } repeat EOC } ifelse } def
+/AltCurve { { false NArray n 2 mul 2 roll [ n 2 mul 3 sub 1 roll ] aload
+/Points ED n 2 mul -2 roll } { false NArray } ifelse n 4 lt { n { pop
+pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse } def
+/ClosedCurve { NArray n 3 lt { n { pop pop } repeat } { n 3 gt {
+CheckClosed } if 6 copy n 2 mul 6 add 6 roll IC CC x y moveto n { NC }
+repeat closepath pop pop } ifelse } def
+/SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def
+/ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def
+/SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore }
+def
+/FontDot { DS 2 mul dup matrix scale matrix concatmatrix exch matrix
+rotate matrix concatmatrix exch findfont exch makefont setfont } def
+/Rect { x1 y1 y2 add 2 div moveto x1 y2 lineto x2 y2 lineto x2 y1 lineto
+x1 y1 lineto closepath } def
+/OvalFrame { x1 x2 eq y1 y2 eq or { pop pop x1 y1 moveto x2 y2 L } { y1
+y2 sub abs x1 x2 sub abs 2 copy gt { exch pop } { pop } ifelse 2 div
+exch { dup 3 1 roll mul exch } if 2 copy lt { pop } { exch pop } ifelse
+/b ED x1 y1 y2 add 2 div moveto x1 y2 x2 y2 b arcto x2 y2 x2 y1 b arcto
+x2 y1 x1 y1 b arcto x1 y1 x1 y2 b arcto 16 { pop } repeat closepath }
+ifelse } def
+/Frame { CLW mul /a ED 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add
+/y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED 1 index 0 eq {
+pop pop Rect } { OvalFrame } ifelse } def
+/BezierNArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop
+} if n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat f { ]
+aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def
+/OpenBezier { BezierNArray n 1 eq { pop pop } { ArrowA n 4 sub 3 idiv { 6
+2 roll 4 2 roll curveto } repeat 6 2 roll 4 2 roll ArrowB curveto }
+ifelse } def
+/ClosedBezier { BezierNArray n 1 eq { pop pop } { moveto n 1 sub 3 idiv {
+6 2 roll 4 2 roll curveto } repeat closepath } ifelse } def
+/BezierShowPoints { gsave Points aload length 2 div cvi /n ED moveto n 1
+sub { lineto } repeat CLW 2 div SLW [ 4 4 ] 0 setdash stroke grestore }
+def
+/Parab { /y0 exch def /x0 exch def /y1 exch def /x1 exch def /dx x0 x1
+sub 3 div def /dy y0 y1 sub 3 div def x0 dx sub y0 dy add x1 y1 ArrowA
+x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB curveto /Points [ x1 y1 x0
+y0 x0 2 mul x1 sub y1 ] def } def
+/Grid { newpath /a 4 string def /b ED /c ED /n ED cvi dup 1 lt { pop 1 }
+if /s ED s div dup 0 eq { pop 1 } if /dy ED s div dup 0 eq { pop 1 } if
+/dx ED dy div round dy mul /y0 ED dx div round dx mul /x0 ED dy div
+round cvi /y2 ED dx div round cvi /x2 ED dy div round cvi /y1 ED dx div
+round cvi /x1 ED /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def /w x2 x1 sub
+0 gt { 1 } { -1 } ifelse def b 0 gt { /z1 b 4 div CLW 2 div add def
+/Helvetica findfont b scalefont setfont /b b .95 mul CLW 2 div add def }
+if systemdict /setstrokeadjust known { true setstrokeadjust /t { } def }
+{ /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add
+exch itransform } bind def } ifelse gsave n 0 gt { 1 setlinecap [ 0 dy n
+div ] dy n div 2 div setdash } { 2 setlinecap } ifelse /i x1 def /f y1
+dy mul n 0 gt { dy n div 2 div h mul sub } if def /g y2 dy mul n 0 gt {
+dy n div 2 div h mul add } if def x2 x1 sub w mul 1 add dup 1000 gt {
+pop 1000 } if { i dx mul dup y0 moveto b 0 gt { gsave c i a cvs dup
+stringwidth pop /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse h 0 gt {b neg}
+{z1} ifelse rmoveto show grestore } if dup t f moveto g t L stroke /i i
+w add def } repeat grestore gsave n 0 gt
+% DG/SR modification begin - Nov. 7, 1997 - Patch 1
+%{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash }
+{ 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash }
+% DG/SR modification end
+{ 2 setlinecap } ifelse /i y1 def /f x1 dx mul
+n 0 gt { dx n div 2 div w mul sub } if def /g x2 dx mul n 0 gt { dx n
+div 2 div w mul add } if def y2 y1 sub h mul 1 add dup 1000 gt { pop
+1000 } if { newpath i dy mul dup x0 exch moveto b 0 gt { gsave c i a cvs
+dup stringwidth pop /z2 ED w 0 gt {z1 z2 add neg} {z1} ifelse h 0 gt
+{z1} {b neg} ifelse rmoveto show grestore } if dup f exch t moveto g
+exch t L stroke /i i h add def } repeat grestore } def
+/ArcArrow { /d ED /b ED /a ED gsave newpath 0 -1000 moveto clip newpath 0
+1 0 0 b grestore c mul /e ED pop pop pop r a e d PtoC y add exch x add
+exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c
+mul neg d } def
+/Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def
+/Rot { CP CP translate 3 -1 roll neg rotate NET  } def
+/RotBegin { tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 }
+def } if /TMatrix [ TMatrix CM ] cvx def /a ED a Rot /RAngle [ RAngle
+dup a add ] cvx def } def
+/RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ]
+cvx def } def
+/PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def
+/PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def
+/PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def
+/Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b s
+abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b
+div w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } {
+h1 abs h sub dup s mul abs } ifelse } def
+/UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div s
+mul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q
+{ x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 add
+exch } def
+/BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible
+/IfVisible true def } if } { IfVisible { Invisible /IfVisible false def
+} if } ifelse } def
+/InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def
+/Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnit
+neg exch neg exch idtransform T moveto } def /BOL { BeginOL } def
+/IfVisible true def } def
+end
+% END pstricks.pro
+
+%%EndProcSet
+%%BeginProcSet: pst-dots.pro
+10 dict dup begin
+  /FontType 3 def
+  /FontMatrix [ .001 0 0 .001 0 0 ] def
+  /FontBBox [ 0 0 0 0 ] def
+  /Encoding 256 array def
+  0 1 255 { Encoding exch /.notdef put } for
+  Encoding
+    dup (b) 0 get /Bullet put
+    dup (c) 0 get /Circle put
+    dup (C) 0 get /BoldCircle put
+    dup (u) 0 get /SolidTriangle put
+    dup (t) 0 get /Triangle put
+    dup (T) 0 get /BoldTriangle put
+    dup (r) 0 get /SolidSquare put
+    dup (s) 0 get /Square put
+    dup (S) 0 get /BoldSquare put
+    dup (q) 0 get /SolidPentagon put
+    dup (p) 0 get /Pentagon put
+    (P) 0 get /BoldPentagon put
+  /Metrics 13 dict def
+  Metrics begin
+    /Bullet 1000 def
+    /Circle 1000 def
+    /BoldCircle 1000 def
+    /SolidTriangle 1344 def
+    /Triangle 1344 def
+    /BoldTriangle 1344 def
+    /SolidSquare 886 def
+    /Square 886 def
+    /BoldSquare 886 def
+    /SolidPentagon 1093.2 def
+    /Pentagon 1093.2 def
+    /BoldPentagon 1093.2 def
+    /.notdef 0 def
+  end
+  /BBoxes 13 dict def
+  BBoxes begin
+    /Circle { -550 -550 550 550 } def
+    /BoldCircle /Circle load def
+    /Bullet /Circle load def
+    /Triangle { -571.5 -330 571.5 660 } def
+    /BoldTriangle /Triangle load def
+    /SolidTriangle /Triangle load def
+    /Square { -450 -450 450 450 } def
+    /BoldSquare /Square load def
+    /SolidSquare /Square load def
+    /Pentagon { -546.6 -465 546.6 574.7 } def
+    /BoldPentagon /Pentagon load def
+    /SolidPentagon /Pentagon load def
+    /.notdef { 0 0 0 0 } def
+  end
+  /CharProcs 20 dict def
+  CharProcs begin
+    /Adjust {
+      2 copy dtransform floor .5 add exch floor .5 add exch idtransform
+      3 -1 roll div 3 1 roll exch div exch scale
+    } def
+    /CirclePath { 0 0 500 0 360 arc closepath } def
+    /Bullet { 500 500 Adjust CirclePath fill } def
+    /Circle { 500 500 Adjust CirclePath .9 .9 scale CirclePath eofill } def
+    /BoldCircle { 500 500 Adjust CirclePath .8 .8 scale CirclePath eofill } def
+    /BoldCircle { CirclePath .8 .8 scale CirclePath eofill } def
+    /TrianglePath {
+      0  660 moveto -571.5 -330 lineto 571.5 -330 lineto closepath
+    } def
+    /SolidTriangle { TrianglePath fill } def
+    /Triangle { TrianglePath .85 .85 scale TrianglePath eofill } def
+    /BoldTriangle { TrianglePath .7 .7 scale TrianglePath eofill } def
+    /SquarePath {
+      -450 450 moveto 450 450 lineto 450 -450 lineto -450 -450 lineto
+      closepath
+    } def
+    /SolidSquare { SquarePath fill } def
+    /Square { SquarePath .89 .89 scale SquarePath eofill } def
+    /BoldSquare { SquarePath .78 .78 scale SquarePath eofill } def
+    /PentagonPath {
+      -337.8 -465   moveto
+       337.8 -465   lineto
+       546.6  177.6 lineto
+         0    574.7 lineto
+      -546.6  177.6 lineto
+      closepath
+    } def
+    /SolidPentagon { PentagonPath fill } def
+    /Pentagon { PentagonPath .89 .89 scale PentagonPath eofill } def
+    /BoldPentagon { PentagonPath .78 .78 scale PentagonPath eofill } def
+    /.notdef { } def
+  end
+  /BuildGlyph {
+    exch
+    begin
+      Metrics 1 index get exec 0
+      BBoxes 3 index get exec
+      setcachedevice
+      CharProcs begin load exec end
+    end
+  } def
+  /BuildChar {
+    1 index /Encoding get exch get
+    1 index /BuildGlyph get exec
+  } bind def
+end
+/PSTricksDotFont exch definefont pop
+% END pst-dots.pro
+
+%%EndProcSet
+%%BeginProcSet: pst-node.pro
+% PostScript prologue for pst-node.tex.
+% Version 97 patch 1, 97/05/09.
+% For distribution, see pstricks.tex.
+%
+/tx@NodeDict 400 dict def tx@NodeDict begin
+tx@Dict begin /T /translate load def end
+/NewNode { gsave /next ED dict dup 3 1 roll def exch { dup 3 1 roll def }
+if begin tx@Dict begin STV CP T exec end /NodeMtrx CM def next end
+grestore } def
+/InitPnode { /Y ED /X ED /NodePos { NodeSep Cos mul NodeSep Sin mul } def
+} def
+/InitCnode { /r ED /Y ED /X ED /NodePos { NodeSep r add dup Cos mul exch
+Sin mul } def } def
+/GetRnodePos { Cos 0 gt { /dx r NodeSep add def } { /dx l NodeSep sub def
+} ifelse Sin 0 gt { /dy u NodeSep add def } { /dy d NodeSep sub def }
+ifelse dx Sin mul abs dy Cos mul abs gt { dy Cos mul Sin div dy } { dx
+dup Sin mul Cos Div } ifelse } def
+/InitRnode { /Y ED /X ED X sub /r ED /l X neg def Y add neg /d ED Y sub
+/u ED /NodePos { GetRnodePos } def } def
+/DiaNodePos { w h mul w Sin mul abs h Cos mul abs add Div NodeSep add dup
+Cos mul exch Sin mul } def
+/TriNodePos { Sin s lt { d NodeSep sub dup Cos mul Sin Div exch } { w h
+mul w Sin mul h Cos abs mul add Div NodeSep add dup Cos mul exch Sin mul
+} ifelse } def
+/InitTriNode { sub 2 div exch 2 div exch 2 copy T 2 copy 4 index index /d
+ED pop pop pop pop -90 mul rotate /NodeMtrx CM def /X 0 def /Y 0 def d
+sub abs neg /d ED d add /h ED 2 div h mul h d sub Div /w ED /s d w Atan
+sin def /NodePos { TriNodePos } def } def
+/OvalNodePos { /ww w NodeSep add def /hh h NodeSep add def Sin ww mul Cos
+hh mul Atan dup cos ww mul exch sin hh mul } def
+/GetCenter { begin X Y NodeMtrx transform CM itransform end } def
+/XYPos { dup sin exch cos Do /Cos ED /Sin ED /Dist ED Cos 0 gt { Dist
+Dist Sin mul Cos div } { Cos 0 lt { Dist neg Dist Sin mul Cos div neg }
+{ 0 Dist Sin mul } ifelse } ifelse Do } def
+/GetEdge { dup 0 eq { pop begin 1 0 NodeMtrx dtransform CM idtransform
+exch atan sub dup sin /Sin ED cos /Cos ED /NodeSep ED NodePos NodeMtrx
+dtransform CM idtransform end } { 1 eq {{exch}} {{}} ifelse /Do ED pop
+XYPos } ifelse } def
+/AddOffset { 1 index 0 eq { pop pop } { 2 copy 5 2 roll cos mul add 4 1
+roll sin mul sub exch } ifelse } def
+/GetEdgeA { NodeSepA AngleA NodeA NodeSepTypeA GetEdge OffsetA AngleA
+AddOffset yA add /yA1 ED xA add /xA1 ED } def
+/GetEdgeB { NodeSepB AngleB NodeB NodeSepTypeB GetEdge OffsetB AngleB
+AddOffset yB add /yB1 ED xB add /xB1 ED } def
+/GetArmA { ArmTypeA 0 eq { /xA2 ArmA AngleA cos mul xA1 add def /yA2 ArmA
+AngleA sin mul yA1 add def } { ArmTypeA 1 eq {{exch}} {{}} ifelse /Do ED
+ArmA AngleA XYPos OffsetA AngleA AddOffset yA add /yA2 ED xA add /xA2 ED
+} ifelse } def
+/GetArmB { ArmTypeB 0 eq { /xB2 ArmB AngleB cos mul xB1 add def /yB2 ArmB
+AngleB sin mul yB1 add def } { ArmTypeB 1 eq {{exch}} {{}} ifelse /Do ED
+ArmB AngleB XYPos OffsetB AngleB AddOffset yB add /yB2 ED xB add /xB2 ED
+} ifelse } def
+/InitNC { /b ED /a ED /NodeSepTypeB ED /NodeSepTypeA ED /NodeSepB ED
+/NodeSepA ED /OffsetB ED /OffsetA ED tx@NodeDict a known tx@NodeDict b
+known and dup { /NodeA a load def /NodeB b load def NodeA GetCenter /yA
+ED /xA ED NodeB GetCenter /yB ED /xB ED } if } def
+/LPutLine { 4 copy 3 -1 roll sub neg 3 1 roll sub Atan /NAngle ED 1 t sub
+mul 3 1 roll 1 t sub mul 4 1 roll t mul add /Y ED t mul add /X ED } def
+/LPutLines { mark LPutVar counttomark 2 div 1 sub /n ED t floor dup n gt
+{ pop n 1 sub /t 1 def } { dup t sub neg /t ED } ifelse cvi 2 mul { pop
+} repeat LPutLine cleartomark } def
+/BezierMidpoint { /y3 ED /x3 ED /y2 ED /x2 ED /y1 ED /x1 ED /y0 ED /x0 ED
+/t ED /cx x1 x0 sub 3 mul def /cy y1 y0 sub 3 mul def /bx x2 x1 sub 3
+mul cx sub def /by y2 y1 sub 3 mul cy sub def /ax x3 x0 sub cx sub bx
+sub def /ay y3 y0 sub cy sub by sub def ax t 3 exp mul bx t t mul mul
+add cx t mul add x0 add ay t 3 exp mul by t t mul mul add cy t mul add
+y0 add 3 ay t t mul mul mul 2 by t mul mul add cy add 3 ax t t mul mul
+mul 2 bx t mul mul add cx add atan /NAngle ED /Y ED /X ED } def
+/HPosBegin { yB yA ge { /t 1 t sub def } if /Y yB yA sub t mul yA add def
+} def
+/HPosEnd { /X Y yyA sub yyB yyA sub Div xxB xxA sub mul xxA add def
+/NAngle yyB yyA sub xxB xxA sub Atan def } def
+/HPutLine { HPosBegin /yyA ED /xxA ED /yyB ED /xxB ED HPosEnd  } def
+/HPutLines { HPosBegin yB yA ge { /check { le } def } { /check { ge } def
+} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { dup Y check { exit
+} { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark HPosEnd 
+} def
+/VPosBegin { xB xA lt { /t 1 t sub def } if /X xB xA sub t mul xA add def
+} def
+/VPosEnd { /Y X xxA sub xxB xxA sub Div yyB yyA sub mul yyA add def
+/NAngle yyB yyA sub xxB xxA sub Atan def } def
+/VPutLine { VPosBegin /yyA ED /xxA ED /yyB ED /xxB ED VPosEnd  } def
+/VPutLines { VPosBegin xB xA ge { /check { le } def } { /check { ge } def
+} ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { 1 index X check {
+exit } { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark
+VPosEnd  } def
+/HPutCurve { gsave newpath /SaveLPutVar /LPutVar load def LPutVar 8 -2
+roll moveto curveto flattenpath /LPutVar [ {} {} {} {} pathforall ] cvx
+def grestore exec /LPutVar /SaveLPutVar load def } def
+/NCCoor { /AngleA yB yA sub xB xA sub Atan def /AngleB AngleA 180 add def
+GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 xA1 yA1 ] cvx def /LPutPos {
+LPutVar LPutLine } def /HPutPos { LPutVar HPutLine } def /VPutPos {
+LPutVar VPutLine } def LPutVar } def
+/NCLine { NCCoor tx@Dict begin ArrowA CP 4 2 roll ArrowB lineto pop pop
+end } def
+/NCLines { false NArray n 0 eq { NCLine } { 2 copy yA sub exch xA sub
+Atan /AngleA ED n 2 mul dup index exch index yB sub exch xB sub Atan
+/AngleB ED GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 n 2 mul 4 add 4 roll xA1
+yA1 ] cvx def mark LPutVar tx@Dict begin false Line end /LPutPos {
+LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def }
+ifelse } def
+/NCCurve { GetEdgeA GetEdgeB xA1 xB1 sub yA1 yB1 sub Pyth 2 div dup 3 -1
+roll mul /ArmA ED mul /ArmB ED /ArmTypeA 0 def /ArmTypeB 0 def GetArmA
+GetArmB xA2 yA2 xA1 yA1 tx@Dict begin ArrowA end xB2 yB2 xB1 yB1 tx@Dict
+begin ArrowB end curveto /LPutVar [ xA1 yA1 xA2 yA2 xB2 yB2 xB1 yB1 ]
+cvx def /LPutPos { t LPutVar BezierMidpoint } def /HPutPos { { HPutLines
+} HPutCurve } def /VPutPos { { VPutLines } HPutCurve } def } def
+/NCAngles { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate
+def xA2 yA2 mtrx transform pop xB2 yB2 mtrx transform exch pop mtrx
+itransform /y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA2
+yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end /LPutVar [ xB1
+yB1 xB2 yB2 x0 y0 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { LPutLines } def
+/HPutPos { HPutLines } def /VPutPos { VPutLines } def } def
+/NCAngle { GetEdgeA GetEdgeB GetArmB /mtrx AngleA matrix rotate def xB2
+yB2 mtrx itransform pop xA1 yA1 mtrx itransform exch pop mtrx transform
+/y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA1 yA1
+tx@Dict begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA1 yA1 ]
+cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos {
+VPutLines } def } def
+/NCBar { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate def
+xA2 yA2 mtrx itransform pop xB2 yB2 mtrx itransform pop sub dup 0 mtrx
+transform 3 -1 roll 0 gt { /yB2 exch yB2 add def /xB2 exch xB2 add def }
+{ /yA2 exch neg yA2 add def /xA2 exch neg xA2 add def } ifelse mark ArmB
+0 ne { xB1 yB1 } if xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict
+begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx
+def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos {
+VPutLines } def } def
+/NCDiag { GetEdgeA GetEdgeB GetArmA GetArmB mark ArmB 0 ne { xB1 yB1 } if
+xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end
+/LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def /LPutPos {
+LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def }
+def
+/NCDiagg { GetEdgeA GetArmA yB yA2 sub xB xA2 sub Atan 180 add /AngleB ED
+GetEdgeB mark xB1 yB1 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin
+false Line end /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def /LPutPos {
+LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def }
+def
+/NCLoop { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate
+def xA2 yA2 mtrx transform loopsize add /yA3 ED /xA3 ED /xB3 xB2 yB2
+mtrx transform pop def xB3 yA3 mtrx itransform /yB3 ED /xB3 ED xA3 yA3
+mtrx itransform /yA3 ED /xA3 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2
+xB3 yB3 xA3 yA3 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false
+Line end /LPutVar [ xB1 yB1 xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 xA1 yA1 ]
+cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos {
+VPutLines } def } def
+% DG/SR modification begin - May 9, 1997 - Patch 1
+%/NCCircle { 0 0 NodesepA nodeA \tx@GetEdge pop xA sub 2 div dup 2 exp r
+%r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add
+%exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360
+%mul add dup 5 1 roll 90 sub \tx@PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED
+/NCCircle { NodeSepA 0 NodeA 0 GetEdge pop 2 div dup 2 exp r
+r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add
+exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360
+mul add dup 5 1 roll 90 sub PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED
+% DG/SR modification end
+} def /HPutPos { LPutPos } def /VPutPos { LPutPos } def r AngleA 90 sub a add
+AngleA 270 add a sub tx@Dict begin /angleB ED /angleA ED /r ED /c 57.2957 r
+Div def /y ED /x ED } def
+/NCBox { /d ED /h ED /AngleB yB yA sub xB xA sub Atan def /AngleA AngleB
+180 add def GetEdgeA GetEdgeB /dx d AngleB sin mul def /dy d AngleB cos
+mul neg def /hx h AngleB sin mul neg def /hy h AngleB cos mul def
+/LPutVar [ xA1 hx add yA1 hy add xB1 hx add yB1 hy add xB1 dx add yB1 dy
+add xA1 dx add yA1 dy add ] cvx def /LPutPos { LPutLines } def /HPutPos
+{ xB yB xA yA LPutLine } def /VPutPos { HPutPos } def mark LPutVar
+tx@Dict begin false Polygon end } def
+/NCArcBox { /l ED neg /d ED /h ED /a ED /AngleA yB yA sub xB xA sub Atan
+def /AngleB AngleA 180 add def /tA AngleA a sub 90 add def /tB tA a 2
+mul add def /r xB xA sub tA cos tB cos sub Div dup 0 eq { pop 1 } if def
+/x0 xA r tA cos mul add def /y0 yA r tA sin mul add def /c 57.2958 r div
+def /AngleA AngleA a sub 180 add def /AngleB AngleB a add 180 add def
+GetEdgeA GetEdgeB /AngleA tA 180 add yA yA1 sub xA xA1 sub Pyth c mul
+sub def /AngleB tB 180 add yB yB1 sub xB xB1 sub Pyth c mul add def l 0
+eq { x0 y0 r h add AngleA AngleB arc x0 y0 r d add AngleB AngleA arcn }
+{ x0 y0 translate /tA AngleA l c mul add def /tB AngleB l c mul sub def
+0 0 r h add tA tB arc r h add AngleB PtoC r d add AngleB PtoC 2 copy 6 2
+roll l arcto 4 { pop } repeat r d add tB PtoC l arcto 4 { pop } repeat 0
+0 r d add tB tA arcn r d add AngleA PtoC r h add AngleA PtoC 2 copy 6 2
+roll l arcto 4 { pop } repeat r h add tA PtoC l arcto 4 { pop } repeat }
+ifelse closepath /LPutVar [ x0 y0 r AngleA AngleB h d ] cvx def /LPutPos
+{ LPutVar /d ED /h ED /AngleB ED /AngleA ED /r ED /y0 ED /x0 ED t 1 le {
+r h add AngleA 1 t sub mul AngleB t mul add dup 90 add /NAngle ED PtoC }
+{ t 2 lt { /NAngle AngleB 180 add def r 2 t sub h mul t 1 sub d mul add
+add AngleB PtoC } { t 3 lt { r d add AngleB 3 t sub mul AngleA 2 t sub
+mul add dup 90 sub /NAngle ED PtoC } { /NAngle AngleA 180 add def r 4 t
+sub d mul t 3 sub h mul add add AngleA PtoC } ifelse } ifelse } ifelse
+y0 add /Y ED x0 add /X ED } def /HPutPos { LPutPos } def /VPutPos {
+LPutPos } def } def
+/Tfan { /AngleA yB yA sub xB xA sub Atan def GetEdgeA w xA1 xB sub yA1 yB
+sub Pyth Pyth w Div CLW 2 div mul 2 div dup AngleA sin mul yA1 add /yA1
+ED AngleA cos mul xA1 add /xA1 ED /LPutVar [ xA1 yA1 m { xB w add yB xB
+w sub yB } { xB yB w sub xB yB w add } ifelse xA1 yA1 ] cvx def /LPutPos
+{ LPutLines } def /VPutPos@ { LPutVar flag { 8 4 roll pop pop pop pop }
+{ pop pop pop pop 4 2 roll } ifelse } def /VPutPos { VPutPos@ VPutLine }
+def /HPutPos { VPutPos@ HPutLine } def mark LPutVar tx@Dict begin
+/ArrowA { moveto } def /ArrowB { } def false Line closepath end } def
+/LPutCoor { NAngle tx@Dict begin /NAngle ED end gsave CM STV CP Y sub neg
+exch X sub neg exch moveto setmatrix CP grestore } def
+/LPut { tx@NodeDict /LPutPos known { LPutPos } { CP /Y ED /X ED /NAngle 0
+def } ifelse LPutCoor  } def
+/HPutAdjust { Sin Cos mul 0 eq { 0 } { d Cos mul Sin div flag not { neg }
+if h Cos mul Sin div flag { neg } if 2 copy gt { pop } { exch pop }
+ifelse } ifelse s add flag { r add neg } { l add } ifelse X add /X ED }
+def
+/VPutAdjust { Sin Cos mul 0 eq { 0 } { l Sin mul Cos div flag { neg } if
+r Sin mul Cos div flag not { neg } if 2 copy gt { pop } { exch pop }
+ifelse } ifelse s add flag { d add } { h add neg } ifelse Y add /Y ED }
+def
+end
+% END pst-node.pro
+
+%%EndProcSet
+%%BeginProcSet: 8r.enc
+% @@psencodingfile@{
+%   author = "S. Rahtz, P. MacKay, Alan Jeffrey, B. Horn, K. Berry",
+%   version = "0.6",
+%   date = "1 July 1998",
+%   filename = "8r.enc",
+%   email = "tex-fonts@@tug.org",
+%   docstring = "Encoding for TrueType or Type 1 fonts
+%                to be used with TeX."
+% @}
+% 
+% Idea is to have all the characters normally included in Type 1 fonts
+% available for typesetting. This is effectively the characters in Adobe
+% Standard Encoding + ISO Latin 1 + extra characters from Lucida.
+% 
+% Character code assignments were made as follows:
+% 
+% (1) the Windows ANSI characters are almost all in their Windows ANSI
+% positions, because some Windows users cannot easily reencode the
+% fonts, and it makes no difference on other systems. The only Windows
+% ANSI characters not available are those that make no sense for
+% typesetting -- rubout (127 decimal), nobreakspace (160), softhyphen
+% (173). quotesingle and grave are moved just because it's such an
+% irritation not having them in TeX positions.
+% 
+% (2) Remaining characters are assigned arbitrarily to the lower part
+% of the range, avoiding 0, 10 and 13 in case we meet dumb software.
+% 
+% (3) Y&Y Lucida Bright includes some extra text characters; in the
+% hopes that other PostScript fonts, perhaps created for public
+% consumption, will include them, they are included starting at 0x12.
+% 
+% (4) Remaining positions left undefined are for use in (hopefully)
+% upward-compatible revisions, if someday more characters are generally
+% available.
+% 
+% (5) hyphen appears twice for compatibility with both 
+% ASCII and Windows.
+% 
+/TeXBase1Encoding [
+% 0x00 (encoded characters from Adobe Standard not in Windows 3.1)
+  /.notdef /dotaccent /fi /fl
+  /fraction /hungarumlaut /Lslash /lslash
+  /ogonek /ring /.notdef
+  /breve /minus /.notdef 
+% These are the only two remaining unencoded characters, so may as
+% well include them.
+  /Zcaron /zcaron 
+% 0x10
+ /caron /dotlessi 
+% (unusual TeX characters available in, e.g., Lucida Bright)
+ /dotlessj /ff /ffi /ffl 
+ /.notdef /.notdef /.notdef /.notdef
+ /.notdef /.notdef /.notdef /.notdef
+ % very contentious; it's so painful not having quoteleft and quoteright
+ % at 96 and 145 that we move the things normally found there to here.
+ /grave /quotesingle 
+% 0x20 (ASCII begins)
+ /space /exclam /quotedbl /numbersign
+ /dollar /percent /ampersand /quoteright
+ /parenleft /parenright /asterisk /plus /comma /hyphen /period /slash
+% 0x30
+ /zero /one /two /three /four /five /six /seven
+ /eight /nine /colon /semicolon /less /equal /greater /question
+% 0x40
+ /at /A /B /C /D /E /F /G /H /I /J /K /L /M /N /O
+% 0x50
+ /P /Q /R /S /T /U /V /W
+ /X /Y /Z /bracketleft /backslash /bracketright /asciicircum /underscore
+% 0x60
+ /quoteleft /a /b /c /d /e /f /g /h /i /j /k /l /m /n /o
+% 0x70
+ /p /q /r /s /t /u /v /w
+ /x /y /z /braceleft /bar /braceright /asciitilde
+ /.notdef % rubout; ASCII ends
+% 0x80
+ /.notdef /.notdef /quotesinglbase /florin
+ /quotedblbase /ellipsis /dagger /daggerdbl
+ /circumflex /perthousand /Scaron /guilsinglleft
+ /OE /.notdef /.notdef /.notdef
+% 0x90
+ /.notdef /.notdef /.notdef /quotedblleft
+ /quotedblright /bullet /endash /emdash
+ /tilde /trademark /scaron /guilsinglright
+ /oe /.notdef /.notdef /Ydieresis
+% 0xA0
+ /.notdef % nobreakspace
+ /exclamdown /cent /sterling
+ /currency /yen /brokenbar /section
+ /dieresis /copyright /ordfeminine /guillemotleft
+ /logicalnot
+ /hyphen % Y&Y (also at 45); Windows' softhyphen
+ /registered
+ /macron
+% 0xD0
+ /degree /plusminus /twosuperior /threesuperior
+ /acute /mu /paragraph /periodcentered
+ /cedilla /onesuperior /ordmasculine /guillemotright
+ /onequarter /onehalf /threequarters /questiondown
+% 0xC0
+ /Agrave /Aacute /Acircumflex /Atilde /Adieresis /Aring /AE /Ccedilla
+ /Egrave /Eacute /Ecircumflex /Edieresis
+ /Igrave /Iacute /Icircumflex /Idieresis
+% 0xD0
+ /Eth /Ntilde /Ograve /Oacute
+ /Ocircumflex /Otilde /Odieresis /multiply
+ /Oslash /Ugrave /Uacute /Ucircumflex
+ /Udieresis /Yacute /Thorn /germandbls
+% 0xE0
+ /agrave /aacute /acircumflex /atilde
+ /adieresis /aring /ae /ccedilla
+ /egrave /eacute /ecircumflex /edieresis
+ /igrave /iacute /icircumflex /idieresis
+% 0xF0
+ /eth /ntilde /ograve /oacute
+ /ocircumflex /otilde /odieresis /divide
+ /oslash /ugrave /uacute /ucircumflex
+ /udieresis /yacute /thorn /ydieresis
+] def
+
+%%EndProcSet
+%%BeginProcSet: texps.pro
+TeXDict begin/rf{findfont dup length 1 add dict begin{1 index/FID ne 2
+index/UniqueID ne and{def}{pop pop}ifelse}forall[1 index 0 6 -1 roll
+exec 0 exch 5 -1 roll VResolution Resolution div mul neg 0 0]/Metrics
+exch def dict begin Encoding{exch dup type/integertype ne{pop pop 1 sub
+dup 0 le{pop}{[}ifelse}{FontMatrix 0 get div Metrics 0 get div def}
+ifelse}forall Metrics/Metrics currentdict end def[2 index currentdict
+end definefont 3 -1 roll makefont/setfont cvx]cvx def}def/ObliqueSlant{
+dup sin S cos div neg}B/SlantFont{4 index mul add}def/ExtendFont{3 -1
+roll mul exch}def/ReEncodeFont{CharStrings rcheck{/Encoding false def
+dup[exch{dup CharStrings exch known not{pop/.notdef/Encoding true def}
+if}forall Encoding{]exch pop}{cleartomark}ifelse}if/Encoding exch def}
+def end
+
+%%EndProcSet
+%%BeginProcSet: special.pro
+TeXDict begin/SDict 200 dict N SDict begin/@SpecialDefaults{/hs 612 N
+/vs 792 N/ho 0 N/vo 0 N/hsc 1 N/vsc 1 N/ang 0 N/CLIP 0 N/rwiSeen false N
+/rhiSeen false N/letter{}N/note{}N/a4{}N/legal{}N}B/@scaleunit 100 N
+/@hscale{@scaleunit div/hsc X}B/@vscale{@scaleunit div/vsc X}B/@hsize{
+/hs X/CLIP 1 N}B/@vsize{/vs X/CLIP 1 N}B/@clip{/CLIP 2 N}B/@hoffset{/ho
+X}B/@voffset{/vo X}B/@angle{/ang X}B/@rwi{10 div/rwi X/rwiSeen true N}B
+/@rhi{10 div/rhi X/rhiSeen true N}B/@llx{/llx X}B/@lly{/lly X}B/@urx{
+/urx X}B/@ury{/ury X}B/magscale true def end/@MacSetUp{userdict/md known
+{userdict/md get type/dicttype eq{userdict begin md length 10 add md
+maxlength ge{/md md dup length 20 add dict copy def}if end md begin
+/letter{}N/note{}N/legal{}N/od{txpose 1 0 mtx defaultmatrix dtransform S
+atan/pa X newpath clippath mark{transform{itransform moveto}}{transform{
+itransform lineto}}{6 -2 roll transform 6 -2 roll transform 6 -2 roll
+transform{itransform 6 2 roll itransform 6 2 roll itransform 6 2 roll
+curveto}}{{closepath}}pathforall newpath counttomark array astore/gc xdf
+pop ct 39 0 put 10 fz 0 fs 2 F/|______Courier fnt invertflag{PaintBlack}
+if}N/txpose{pxs pys scale ppr aload pop por{noflips{pop S neg S TR pop 1
+-1 scale}if xflip yflip and{pop S neg S TR 180 rotate 1 -1 scale ppr 3
+get ppr 1 get neg sub neg ppr 2 get ppr 0 get neg sub neg TR}if xflip
+yflip not and{pop S neg S TR pop 180 rotate ppr 3 get ppr 1 get neg sub
+neg 0 TR}if yflip xflip not and{ppr 1 get neg ppr 0 get neg TR}if}{
+noflips{TR pop pop 270 rotate 1 -1 scale}if xflip yflip and{TR pop pop
+90 rotate 1 -1 scale ppr 3 get ppr 1 get neg sub neg ppr 2 get ppr 0 get
+neg sub neg TR}if xflip yflip not and{TR pop pop 90 rotate ppr 3 get ppr
+1 get neg sub neg 0 TR}if yflip xflip not and{TR pop pop 270 rotate ppr
+2 get ppr 0 get neg sub neg 0 S TR}if}ifelse scaleby96{ppr aload pop 4
+-1 roll add 2 div 3 1 roll add 2 div 2 copy TR .96 dup scale neg S neg S
+TR}if}N/cp{pop pop showpage pm restore}N end}if}if}N/normalscale{
+Resolution 72 div VResolution 72 div neg scale magscale{DVImag dup scale
+}if 0 setgray}N/psfts{S 65781.76 div N}N/startTexFig{/psf$SavedState
+save N userdict maxlength dict begin/magscale true def normalscale
+currentpoint TR/psf$ury psfts/psf$urx psfts/psf$lly psfts/psf$llx psfts
+/psf$y psfts/psf$x psfts currentpoint/psf$cy X/psf$cx X/psf$sx psf$x
+psf$urx psf$llx sub div N/psf$sy psf$y psf$ury psf$lly sub div N psf$sx
+psf$sy scale psf$cx psf$sx div psf$llx sub psf$cy psf$sy div psf$ury sub
+TR/showpage{}N/erasepage{}N/copypage{}N/p 3 def @MacSetUp}N/doclip{
+psf$llx psf$lly psf$urx psf$ury currentpoint 6 2 roll newpath 4 copy 4 2
+roll moveto 6 -1 roll S lineto S lineto S lineto closepath clip newpath
+moveto}N/endTexFig{end psf$SavedState restore}N/@beginspecial{SDict
+begin/SpecialSave save N gsave normalscale currentpoint TR
+@SpecialDefaults count/ocount X/dcount countdictstack N}N/@setspecial{
+CLIP 1 eq{newpath 0 0 moveto hs 0 rlineto 0 vs rlineto hs neg 0 rlineto
+closepath clip}if ho vo TR hsc vsc scale ang rotate rwiSeen{rwi urx llx
+sub div rhiSeen{rhi ury lly sub div}{dup}ifelse scale llx neg lly neg TR
+}{rhiSeen{rhi ury lly sub div dup scale llx neg lly neg TR}if}ifelse
+CLIP 2 eq{newpath llx lly moveto urx lly lineto urx ury lineto llx ury
+lineto closepath clip}if/showpage{}N/erasepage{}N/copypage{}N newpath}N
+/@endspecial{count ocount sub{pop}repeat countdictstack dcount sub{end}
+repeat grestore SpecialSave restore end}N/@defspecial{SDict begin}N
+/@fedspecial{end}B/li{lineto}B/rl{rlineto}B/rc{rcurveto}B/np{/SaveX
+currentpoint/SaveY X N 1 setlinecap newpath}N/st{stroke SaveX SaveY
+moveto}N/fil{fill SaveX SaveY moveto}N/ellipse{/endangle X/startangle X
+/yrad X/xrad X/savematrix matrix currentmatrix N TR xrad yrad scale 0 0
+1 startangle endangle arc savematrix setmatrix}N end
+
+%%EndProcSet
+%%BeginProcSet: color.pro
+TeXDict begin/setcmykcolor where{pop}{/setcmykcolor{dup 10 eq{pop
+setrgbcolor}{1 sub 4 1 roll 3{3 index add neg dup 0 lt{pop 0}if 3 1 roll
+}repeat setrgbcolor pop}ifelse}B}ifelse/TeXcolorcmyk{setcmykcolor}def
+/TeXcolorrgb{setrgbcolor}def/TeXcolorgrey{setgray}def/TeXcolorgray{
+setgray}def/TeXcolorhsb{sethsbcolor}def/currentcmykcolor where{pop}{
+/currentcmykcolor{currentrgbcolor 10}B}ifelse/DC{exch dup userdict exch
+known{pop pop}{X}ifelse}B/GreenYellow{0.15 0 0.69 0 setcmykcolor}DC
+/Yellow{0 0 1 0 setcmykcolor}DC/Goldenrod{0 0.10 0.84 0 setcmykcolor}DC
+/Dandelion{0 0.29 0.84 0 setcmykcolor}DC/Apricot{0 0.32 0.52 0
+setcmykcolor}DC/Peach{0 0.50 0.70 0 setcmykcolor}DC/Melon{0 0.46 0.50 0
+setcmykcolor}DC/YellowOrange{0 0.42 1 0 setcmykcolor}DC/Orange{0 0.61
+0.87 0 setcmykcolor}DC/BurntOrange{0 0.51 1 0 setcmykcolor}DC
+/Bittersweet{0 0.75 1 0.24 setcmykcolor}DC/RedOrange{0 0.77 0.87 0
+setcmykcolor}DC/Mahogany{0 0.85 0.87 0.35 setcmykcolor}DC/Maroon{0 0.87
+0.68 0.32 setcmykcolor}DC/BrickRed{0 0.89 0.94 0.28 setcmykcolor}DC/Red{
+0 1 1 0 setcmykcolor}DC/OrangeRed{0 1 0.50 0 setcmykcolor}DC/RubineRed{
+0 1 0.13 0 setcmykcolor}DC/WildStrawberry{0 0.96 0.39 0 setcmykcolor}DC
+/Salmon{0 0.53 0.38 0 setcmykcolor}DC/CarnationPink{0 0.63 0 0
+setcmykcolor}DC/Magenta{0 1 0 0 setcmykcolor}DC/VioletRed{0 0.81 0 0
+setcmykcolor}DC/Rhodamine{0 0.82 0 0 setcmykcolor}DC/Mulberry{0.34 0.90
+0 0.02 setcmykcolor}DC/RedViolet{0.07 0.90 0 0.34 setcmykcolor}DC
+/Fuchsia{0.47 0.91 0 0.08 setcmykcolor}DC/Lavender{0 0.48 0 0
+setcmykcolor}DC/Thistle{0.12 0.59 0 0 setcmykcolor}DC/Orchid{0.32 0.64 0
+0 setcmykcolor}DC/DarkOrchid{0.40 0.80 0.20 0 setcmykcolor}DC/Purple{
+0.45 0.86 0 0 setcmykcolor}DC/Plum{0.50 1 0 0 setcmykcolor}DC/Violet{
+0.79 0.88 0 0 setcmykcolor}DC/RoyalPurple{0.75 0.90 0 0 setcmykcolor}DC
+/BlueViolet{0.86 0.91 0 0.04 setcmykcolor}DC/Periwinkle{0.57 0.55 0 0
+setcmykcolor}DC/CadetBlue{0.62 0.57 0.23 0 setcmykcolor}DC
+/CornflowerBlue{0.65 0.13 0 0 setcmykcolor}DC/MidnightBlue{0.98 0.13 0
+0.43 setcmykcolor}DC/NavyBlue{0.94 0.54 0 0 setcmykcolor}DC/RoyalBlue{1
+0.50 0 0 setcmykcolor}DC/Blue{1 1 0 0 setcmykcolor}DC/Cerulean{0.94 0.11
+0 0 setcmykcolor}DC/Cyan{1 0 0 0 setcmykcolor}DC/ProcessBlue{0.96 0 0 0
+setcmykcolor}DC/SkyBlue{0.62 0 0.12 0 setcmykcolor}DC/Turquoise{0.85 0
+0.20 0 setcmykcolor}DC/TealBlue{0.86 0 0.34 0.02 setcmykcolor}DC
+/Aquamarine{0.82 0 0.30 0 setcmykcolor}DC/BlueGreen{0.85 0 0.33 0
+setcmykcolor}DC/Emerald{1 0 0.50 0 setcmykcolor}DC/JungleGreen{0.99 0
+0.52 0 setcmykcolor}DC/SeaGreen{0.69 0 0.50 0 setcmykcolor}DC/Green{1 0
+1 0 setcmykcolor}DC/ForestGreen{0.91 0 0.88 0.12 setcmykcolor}DC
+/PineGreen{0.92 0 0.59 0.25 setcmykcolor}DC/LimeGreen{0.50 0 1 0
+setcmykcolor}DC/YellowGreen{0.44 0 0.74 0 setcmykcolor}DC/SpringGreen{
+0.26 0 0.76 0 setcmykcolor}DC/OliveGreen{0.64 0 0.95 0.40 setcmykcolor}
+DC/RawSienna{0 0.72 1 0.45 setcmykcolor}DC/Sepia{0 0.83 1 0.70
+setcmykcolor}DC/Brown{0 0.81 1 0.60 setcmykcolor}DC/Tan{0.14 0.42 0.56 0
+setcmykcolor}DC/Gray{0 0 0 0.50 setcmykcolor}DC/Black{0 0 0 1
+setcmykcolor}DC/White{0 0 0 0 setcmykcolor}DC end
+
+%%EndProcSet
+%%BeginFont: CMMI9
+%!PS-AdobeFont-1.1: CMMI9 1.100
+%%CreationDate: 1996 Jul 23 07:53:55
+
+% Copyright (C) 1997 American Mathematical Society.  All Rights Reserved.
+
+11 dict begin
+/FontInfo 7 dict dup begin
+/version (1.100) readonly def
+/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
+/FullName (CMMI9) readonly def
+/FamilyName (Computer Modern) readonly def
+/Weight (Medium) readonly def
+/ItalicAngle -14.04 def
+/isFixedPitch false def
+end readonly def
+/FontName /CMMI9 def
+/PaintType 0 def
+/FontType 1 def
+/FontMatrix [0.001 0 0 0.001 0 0] readonly def
+/Encoding 256 array
+0 1 255 {1 index exch /.notdef put} for
+dup 15 /epsilon1 put
+readonly def
+/FontBBox{-29 -250 1075 750}readonly def
+/UniqueXX 5087384 def
+currentdict end
+currentfile eexec
+80347982ab3942d930e069a70d0d48311d725e830d1c76fba12e12486e989c98
+74c2b527f0925722787027f44470d484262c360cdfdddf3657533a57bb16f730
+48bfbbfcb73a650484015441fdc837add94ac8fbd2022e3ec8f115d4b4bb7b7f
+15388f22cc6198efe768bd9fceb3446ee4a8dc27d6cd152485384ef5f59381ff
+da43f2d20c8fb08aa27ab2015b774db10dacfdcd33e60f178c461553146ab427
+bdd7da12534ba078ad3d780414930da4f8d58abefd45db119b10eb409dd89792
+3c6e705479464a4b33ae3d31bfe98efe259f07f7950237bbaee4f7b64ffea83a
+757fa717d50c3298392891bfd60e34a056b0d6021da3fd9b8b01bf78b0b23dc4
+ea3b0605150d20b27ff9ea5f2524661019d982a2e47cd7c21ee5ca9ed9227821
+f8d07119397de26838c11d7b35bcedc43e011626e300f8249ed846d7b5ccbd89
+02550cda17ddf113df658fb13f8162681013766863784efac128e01ef997e1a4
+30312afac8f3d948edecd7d5090ab5c864b91d7f6e80256f0e1fc99f1102b74c
+61cc456e2e1bedf0e627d5f70f738f963a13666405c51ebf23ca077e97570a2f
+1118536b92e585cf1dbd5fbf36a0a5d197538c05304e93a15f3c931168d91d42
+483ef428b1a3f1b7e548fd1d23b80f5523c8b8bf450b02804fb689f915c86693
+f7dfb1c43f681627c7f027021aa3a8179148f1819cd94b8890a9ac63dc1e8a68
+f254b64f6f173c3d02e3ebc037da05074017c8b113e94f4e2d26b467ef9da07e
+afd7ea7c86e025af52c5ceeb835951e67e02a38daf1e9e698bd21996c1071e84
+ff7fbe77f6ddf9d06fa92b16ecebcbe0370b5cd9d450d0f2906a105cadf93ed0
+0abc7fcf2c996e7c15e452006e35390d99b9cfc59925f1444c20d9c3e1fc2910
+32cf9fa9d580eac1bc956334da391b870a757c3bee6aa3e005b20988d8587876
+3ced20c6edf2ac2b22890e37ff7aedeb0986d85ae05bc84339bf2116df48c5d1
+cc888bb33d409b06dd70ffd0618b2080442aac439aeb39c20a87ad74ef10629c
+f1604db8611e8e4224c5b21ab0c7ebddc77fe9a283b3a8c6a2a9508f6836e3fc
+3eae1366b4da4f44cb7a77fd81d278c17775d56cb28b70f18d894bfd1ec1827f
+fb16b0d4c1a4ce155da066810170fea53e0d24874d69366a46873838b82ece2e
+bb961c260c67b449acd29dd7613c555bdb2105bdddc2924c6064486a50e936ee
+a8c6ea5be6ee8441652dd81f930cb7c529ddee172f25588eeec791ff03753b9a
+80c10598425b6a0886d6aad2d1d973454b9c6319ac29be6b1fa97f8bbbb1c9fd
+acbda78d04e5891f78b85fcd173a827effee79a2fe5df00d2b1b4526b1858fed
+dbd207bf886ef031cdf61ad3fadfbc26cb8eb879dd17b9999d8735ee9fde3ba9
+24ce7786237f6c624563022da4d9174a9ef26e2b6baf5b3248761805f2dd2429
+7375b95ecebc05a109d87220a4e2b06b31e2c87f2f892e10c01c3801be734fac
+04300c4f912ab08adcb21b68b3fe97230cf30214cab7fe65753c1db70b401dc0
+c3
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+cleartomark
+
+%%EndFont 
+%%BeginFont: CMEX10
+%!PS-AdobeFont-1.1: CMEX10 1.00
+%%CreationDate: 1992 Jul 23 21:22:48
+
+% Copyright (C) 1997 American Mathematical Society.  All Rights Reserved.
+
+11 dict begin
+/FontInfo 7 dict dup begin
+/version (1.00) readonly def
+/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
+/FullName (CMEX10) readonly def
+/FamilyName (Computer Modern) readonly def
+/Weight (Medium) readonly def
+/ItalicAngle 0 def
+/isFixedPitch false def
+end readonly def
+/FontName /CMEX10 def
+/PaintType 0 def
+/FontType 1 def
+/FontMatrix [0.001 0 0 0.001 0 0] readonly def
+/Encoding 256 array
+0 1 255 {1 index exch /.notdef put} for
+dup 83 /uniontext put
+readonly def
+/FontBBox{-24 -2960 1454 772}readonly def
+/UniqueXX 5000774 def
+currentdict end
+currentfile eexec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+
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+cleartomark
+
+%%EndFont 
+%%BeginFont: CMMI6
+%!PS-AdobeFont-1.1: CMMI6 1.100
+%%CreationDate: 1996 Jul 23 07:53:52
+
+% Copyright (C) 1997 American Mathematical Society.  All Rights Reserved.
+
+11 dict begin
+/FontInfo 7 dict dup begin
+/version (1.100) readonly def
+/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
+/FullName (CMMI6) readonly def
+/FamilyName (Computer Modern) readonly def
+/Weight (Medium) readonly def
+/ItalicAngle -14.04 def
+/isFixedPitch false def
+end readonly def
+/FontName /CMMI6 def
+/PaintType 0 def
+/FontType 1 def
+/FontMatrix [0.001 0 0 0.001 0 0] readonly def
+/Encoding 256 array
+0 1 255 {1 index exch /.notdef put} for
+dup 59 /comma put
+dup 97 /a put
+dup 99 /c put
+dup 115 /s put
+dup 116 /t put
+readonly def
+/FontBBox{11 -250 1241 750}readonly def
+/UniqueXX 5087381 def
+currentdict end
+currentfile eexec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+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+cleartomark
+
+%%EndFont 
+%%BeginFont: CMMI7
+%!PS-AdobeFont-1.1: CMMI7 1.100
+%%CreationDate: 1996 Jul 23 07:53:53
+
+% Copyright (C) 1997 American Mathematical Society.  All Rights Reserved.
+
+11 dict begin
+/FontInfo 7 dict dup begin
+/version (1.100) readonly def
+/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
+/FullName (CMMI7) readonly def
+/FamilyName (Computer Modern) readonly def
+/Weight (Medium) readonly def
+/ItalicAngle -14.04 def
+/isFixedPitch false def
+end readonly def
+/FontName /CMMI7 def
+/PaintType 0 def
+/FontType 1 def
+/FontMatrix [0.001 0 0 0.001 0 0] readonly def
+/Encoding 256 array
+0 1 255 {1 index exch /.notdef put} for
+dup 59 /comma put
+dup 80 /P put
+dup 81 /Q put
+dup 85 /U put
+dup 88 /X put
+dup 97 /a put
+dup 99 /c put
+dup 105 /i put
+dup 106 /j put
+dup 112 /p put
+dup 115 /s put
+dup 116 /t put
+dup 117 /u put
+readonly def
+/FontBBox{0 -250 1171 750}readonly def
+/UniqueXX 5087382 def
+currentdict end
+currentfile eexec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+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+cleartomark
+
+%%EndFont 
+%%BeginFont: CMR10
+%!PS-AdobeFont-1.1: CMR10 1.00B
+%%CreationDate: 1992 Feb 19 19:54:52
+
+% Copyright (C) 1997 American Mathematical Society.  All Rights Reserved.
+
+11 dict begin
+/FontInfo 7 dict dup begin
+/version (1.00B) readonly def
+/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
+/FullName (CMR10) readonly def
+/FamilyName (Computer Modern) readonly def
+/Weight (Medium) readonly def
+/ItalicAngle 0 def
+/isFixedPitch false def
+end readonly def
+/FontName /CMR10 def
+/PaintType 0 def
+/FontType 1 def
+/FontMatrix [0.001 0 0 0.001 0 0] readonly def
+/Encoding 256 array
+0 1 255 {1 index exch /.notdef put} for
+dup 6 /Sigma put
+dup 40 /parenleft put
+dup 41 /parenright put
+dup 49 /one put
+dup 50 /two put
+dup 51 /three put
+dup 52 /four put
+dup 53 /five put
+dup 54 /six put
+dup 58 /colon put
+dup 59 /semicolon put
+dup 61 /equal put
+dup 91 /bracketleft put
+dup 93 /bracketright put
+readonly def
+/FontBBox{-251 -250 1009 969}readonly def
+/UniqueXX 5000793 def
+currentdict end
+currentfile eexec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+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+cleartomark
+
+%%EndFont 
+%%BeginFont: CMSY10
+%!PS-AdobeFont-1.1: CMSY10 1.0
+%%CreationDate: 1991 Aug 15 07:20:57
+
+% Copyright (C) 1997 American Mathematical Society.  All Rights Reserved.
+
+11 dict begin
+/FontInfo 7 dict dup begin
+/version (1.0) readonly def
+/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
+/FullName (CMSY10) readonly def
+/FamilyName (Computer Modern) readonly def
+/Weight (Medium) readonly def
+/ItalicAngle -14.035 def
+/isFixedPitch false def
+end readonly def
+/FontName /CMSY10 def
+/PaintType 0 def
+/FontType 1 def
+/FontMatrix [0.001 0 0 0.001 0 0] readonly def
+/Encoding 256 array
+0 1 255 {1 index exch /.notdef put} for
+dup 2 /multiply put
+dup 15 /bullet put
+dup 18 /reflexsubset put
+dup 19 /reflexsuperset put
+dup 33 /arrowright put
+dup 50 /element put
+dup 59 /emptyset put
+dup 91 /union put
+dup 92 /intersection put
+dup 102 /braceleft put
+dup 103 /braceright put
+dup 106 /bar put
+readonly def
+/FontBBox{-29 -960 1116 775}readonly def
+/UniqueXX 5000820 def
+currentdict end
+currentfile eexec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+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+cleartomark
+
+%%EndFont 
+%%BeginFont: CMSY7
+%!PS-AdobeFont-1.1: CMSY7 1.0
+%%CreationDate: 1991 Aug 15 07:21:52
+
+% Copyright (C) 1997 American Mathematical Society.  All Rights Reserved.
+
+11 dict begin
+/FontInfo 7 dict dup begin
+/version (1.0) readonly def
+/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
+/FullName (CMSY7) readonly def
+/FamilyName (Computer Modern) readonly def
+/Weight (Medium) readonly def
+/ItalicAngle -14.035 def
+/isFixedPitch false def
+end readonly def
+/FontName /CMSY7 def
+/PaintType 0 def
+/FontType 1 def
+/FontMatrix [0.001 0 0 0.001 0 0] readonly def
+/Encoding 256 array
+0 1 255 {1 index exch /.notdef put} for
+dup 0 /minus put
+dup 3 /asteriskmath put
+dup 48 /prime put
+dup 50 /element put
+dup 106 /bar put
+readonly def
+/FontBBox{-15 -951 1252 782}readonly def
+/UniqueXX 5000817 def
+currentdict end
+currentfile eexec
+9b9c1569015f2c1d2bf560f4c0d52257bac8ced9b09a275ab231194ecf829352
+05826f4e975dcecec72b2cf3a18899ccde1fd935d09d813b096cc6b83cdf4f23
+b9a60db41f9976ac333263c908dcefcdbd4c8402ed00a36e7487634d089fd45a
+f4a38a56a4412c3b0baffaeb717bf0de9ffb7a8460bf475a6718b0c73c571145
+d026957276530530a2fbefc6c8f73e9b697ddc0351763500e23c4d170ea8a2d2
+75ad0b6b23097f02fa803c1f46f9ac10fe0e527c431b11b1b9a50e874896cca6
+17fe3e255960846bc319ca68b9b930a45d5d0fc36b352c3443ab6f7793b38d2c
+7fb9c409ab7980ead55e9f8f6b83c70088d1fa6d7f2214da8928e40b96334ad2
+72d1b5db9d1355a579b26a8dac21f021e393d7d837a95deb8de92ed818a8b80b
+98ee9cdd8a3c57ad7d6eb7a82f43eaa6ec520eefa7302e750edc4b495f70bba2
+24a2182eec37f1a1c5dc8e20973007150237daa6bf03d498826777eeebe09014
+ebfe05a8731e1a421cfc513d47d673e3d94d805f5d0668ffa265e0962cb5a75a
+4a93d9b8763c70f88a5d87e970994617fc62f70fb0ed32c459934f23a9f150fa
+083cf9eda2757efdfc0ffcf2a563927bbad06da9fbd2cc59328c0d1cbf948664
+ff7eb9e71e42dd9eab74f6d8385bec475fbbbc5d26a9c90ef6e6050ec283a71e
+6922d272c3c23863007a9f53cbc7cdf50d3ea31622542858c80e08699eb84656
+ea41df4a8c71471000d202dff2b633a0cf98d403af763ed5240b7e301f14beb6
+0059d1ad4f936e4a3db3338958feb1fa736b970f7b9c0317b9ab2220802aea08
+22f4823816d7cdba7d977abfa1b68382e8ba20c656708ea6599d9912329b2292
+b1672afc5f9806e3aca1e593d770dc728a8798e5e26e536b128c23c131b686d7
+82a279a89e0ff3eb32ef20e5df240933d65f58bd8c79ca297191de63af012daa
+658b56745ffaf752d97f342d9ac6c2976fa2a7b56ae33f609451258b9a0cdd1c
+f78e711f1878ccbd46489c78534da7ef61aafc7b174d0ec47b78c884b5382993
+8dd2dfffd077c9e38719cb128beefbc65bb2619383071ef0041b8c85762fdba1
+2ab9ae506dd348e40ad87b15727c6729329a2a4f5b674cf802feca3cd12d7b9e
+455534b2831cd4cc04a13b890f9dafaded255d79844df6622c203cb82f840afb
+8364e5c1e72f39179d7e9dbd4b0778d82840d7ac819be3fbbb93975b34f5a2c1
+874d4112f660462027eb6912f64c049598067ddd0c51e4674034636c4bb0a833
+d50ef70b7b5889cb44a40e8173421082a5058846bde25252254f3258cd8356bc
+205f5a2ab23b1babbfe628f2b40753979b7631d163c2a94dc27092273f0382e7
+615a09eeac272e51ddbfb633f1c503ba8f2036c3fbf0608a4e523a12e1613a65
+99149acf52c8b0a077e52551fd08bcb8e7b1d2111f682425deb1e34f227e4103
+06725b89ee10a10996d0aae0d765896f910f97363b9464914c1627d6336bb8f0
+9187f280096696f0e83f7067ac2bb763046b58c206b664d37ca9afe9925055a0
+0c997a12a28cabce6e96d97f782e030ccb2c728053abc09f42
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+cleartomark
+
+%%EndFont 
+%%BeginFont: CMR6
+%!PS-AdobeFont-1.1: CMR6 1.0
+%%CreationDate: 1991 Aug 20 16:39:02
+
+% Copyright (C) 1997 American Mathematical Society.  All Rights Reserved.
+
+11 dict begin
+/FontInfo 7 dict dup begin
+/version (1.0) readonly def
+/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
+/FullName (CMR6) readonly def
+/FamilyName (Computer Modern) readonly def
+/Weight (Medium) readonly def
+/ItalicAngle 0 def
+/isFixedPitch false def
+end readonly def
+/FontName /CMR6 def
+/PaintType 0 def
+/FontType 1 def
+/FontMatrix [0.001 0 0 0.001 0 0] readonly def
+/Encoding 256 array
+0 1 255 {1 index exch /.notdef put} for
+dup 49 /one put
+dup 50 /two put
+dup 51 /three put
+dup 52 /four put
+dup 53 /five put
+dup 54 /six put
+readonly def
+/FontBBox{-20 -250 1193 750}readonly def
+/UniqueXX 5000789 def
+currentdict end
+currentfile eexec
+9b9c1569015f2c1d2bf560f4c0d52257bacdd6500abda5ed9835f6a016cfc8f0
+0b6c052ed76a87856b50f4d80dfaeb508c97f8281f3f88b17e4d3b90c0f65ec3
+79791aacdc162a66cbbc5be2f53aad8de72dd113b55a022fbfee658cb95f5bb3
+2ba0357b5e050fddf264a07470bef1c52119b6fbd5c77ebed964ac5a2bbec9d8
+b3e48ae5bb003a63d545774b922b9d5ff6b0066ece43645a131879b032137d6d
+823385fe55f3402d557fd3b4486858b2a4b5a0cc2e1bf4e2a4a0e748483c3bcf
+5de47cc5260a3a967cac70a7a35b88b54315191d0423b4065c7a432987938c6b
+edad3b72ad63c2918b6e5a2017457e0d4ebc204b031f3fc6c13d7da7277a94ba
+018e9998b3dd888011a5d7c4204989f30f908b95533bda845746b673ab71ea57
+65a0d14f4350707e47c8276305b28513cbe1bb0dbd269a53719bda46e536685d
+df78ca0146b6b93e760256b74d939d4e35b5e77238f04c92298dfdd188feea30
+e053eefbcbb52f2011772b3aae39f5805597bbc1e8bb75a446ce014030f4f2f0
+f49f9e962ee4a1024a746fa92a3628db5270732b54e43fe5ecfa524f127e5fcc
+788e77e66098336ad67fe4cccaf0253272d5df79864bf4b734cb9a5859d557d8
+bc11b8e00221ebc12e97de4b1f466ead83a4c894709363bca9040410a52d592e
+34ee40cc7e5efa920546b981aa659513a24b1b85c221a1875b62d0b89e57a368
+321b8043a5b094e0379760a443d632892b14ad6d19dacc8c78093243ad67e6a3
+08e56e6b68412ee690b10dac6e17708754a00d51fc957b500eb80175716eef4b
+2ca1ef867614659bee3f2b7319e97b6fdf1efc847bf3cee3156f72f21751da8e
+5fb6898919e6799820d3de0642d756e09d6fae4ff08dd3deda3173bff4bb11f7
+9109c97ddc05897af709ea199a90fcee8ce4c7a3c15b18170c41c04de2d3fba8
+f34296a95b8e1e8de3739b17273f8f2c85e914615e8eac5e8bd2387ba3b1edf4
+7968f06e2067d836d0f9f3e085cdfd2de06a62c81d786b304326f7002e83160a
+36598589228b4dddddc43c85e1d126f8fe81b828028e26317af5894aaccf4f69
+6301e1a9fc45935d8a414957f08febebbc3a72ada80f101e47447d019ade56e9
+f4fab969bba2b44e47399fedf5caa1bcea216d7ba713d523da5d7776ec0bb452
+fc23761a3e881b097d783e6608a001eae5a6b8bb69589902e05d9dbc92f27c27
+2348ae1f0ca880d6428de6fc0eed6c08a0a7814bd38e9bd9ea8abac49d5455ad
+f6eb7b914537823b7d84f63fceb9b4b655dc671dd1f5bbb2c0565fb9841d8f88
+c25332d81167dd2e49cbf91b8ff9aaec3caff6f74b9d057de435f022e7bce755
+85dd57330b4a524700b0a0e39d0697795b55e7b1aa507019f565f02f1d67de5f
+353296ef3feb20647e28e6e2e380bfa1ee330fe17e58c44ae95716c6a2f09f4d
+646a81965cecb7620e62b0b72a5a432364cd0560da0db5a4af5b0e8b4905fcba
+b791ddcd766688f158da449332daa27ef2ef2998b0946101bdd4a521433e0c2c
+b3ee2aa43022952dd34509c8cb57975a5332ff89b4c150ea14529eb9e7323d34
+f9a1adbb512ad2b78172df0cfb85be7f73d31fe0ac0d6cf98d7e25192196f519
+b57e599040f7c29a34a661bfbe350cbb4c050d22e10acf5380b450d073164518
+a0bf97017d5ca7f23c8b245a90b0c5876e270cd583ce2ef6932c64b9ab57109c
+3c10d0ad9e58346513442514d9f7f9829bf36a5cd2a0a4c41fcc029b3abd86e2
+342d2d4f5ad996a02b9d931b09d9b960650fc66dac32b561eddfe9f2852619bc
+a885cd130b5cdf131a421a2ceecac3cf636e8a091850e5967052f80bdc72d5a4
+40f35b29e65532db482f07d9ae5b7bf9d49064156f644072de2962c8b73b9d4a
+6814b98a16af84222ab2fb12f82b3e936036ee316f01a782734ba7285aea2ed0
+df5875cd0a781978aa6c55d34c2067529cee81accfb090c9e9ca4654cd6a9a29
+3695138f98362a46be6c8a507fc5dea916d9c64a8cda8bf3b996e6faac2358e9
+9fbb29ae326d6b3fd434957c41cb6e8b54eb000003103170093d2f927f266ce1
+f7fe2b5147028c4d41a36277f534b801aa1b28ca6aa004a692dcb5f22348c2fb
+2c25faef9ed78cad84ff3d52b3c83d2b56c4a0c2702eb526a2006b52fde7b619
+e1627a170be9eb71f2559520707ccd737002471ee8a5089040d0731a667dcabb
+bb30a6e5595695aad80742dac5ceb37924132116791565d50d86b692ce777412
+21b45baebd359adda98c084a0102d6d52f9f774c5798b0bea1ad3ae86111126a
+50da58673572778d3bec5fc0161341ad43f221713fcf5d783cc2855d7d17b376
+ee7b97b5452c7cc87c2be2fe187420969facd599b10de1578b0bad79cda626fe
+45851f43b5785ba8989cd8290791a8f40931ad8353ac077bd58cc2a99bc95f32
+fbe74ad2e8c2dad4db14612aed39c9c9fdf558eb80e6a92ee5d2fa5ff8ae4a21
+2d3cb19ef141679106b28f30dffd06d9e3a8a592f67a0407eccea6921c55d0bf
+961036adb22fbdce5a84feb3dcf64c4408087516edda733b4240e607e26607e1
+ce8b691b28d2c1741caf5d252c97831594479ac0ae2d2261d21a0f45266a9862
+d4ce67aac80573d4132a6cf7472bd3fa17f2c3deef3c7f23e7b5bfd640d4cdea
+79331fe5cfad5822352b68c29d18088367d063837b4a6c78ef1e4c3dc3795a4e
+3b2cfa5cd67c94aa65c210572001b9fef4a37bd2e557c0353e24857fc5bfb7ab
+49e709218905235efa101cde008f98f6cf896186e780ac8877bd4b0935a6
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+cleartomark
+
+%%EndFont 
+%%BeginFont: CMSY8
+%!PS-AdobeFont-1.1: CMSY8 1.0
+%%CreationDate: 1991 Aug 15 07:22:10
+
+% Copyright (C) 1997 American Mathematical Society.  All Rights Reserved.
+
+11 dict begin
+/FontInfo 7 dict dup begin
+/version (1.0) readonly def
+/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
+/FullName (CMSY8) readonly def
+/FamilyName (Computer Modern) readonly def
+/Weight (Medium) readonly def
+/ItalicAngle -14.035 def
+/isFixedPitch false def
+end readonly def
+/FontName /CMSY8 def
+/PaintType 0 def
+/FontType 1 def
+/FontMatrix [0.001 0 0 0.001 0 0] readonly def
+/Encoding 256 array
+0 1 255 {1 index exch /.notdef put} for
+dup 3 /asteriskmath put
+dup 13 /circlecopyrt put
+readonly def
+/FontBBox{-30 -955 1185 779}readonly def
+/UniqueXX 5000818 def
+currentdict end
+currentfile eexec
+9b9c1569015f2c1d2bf560f4c0d52257bac8ced9b09a275ab231194ecf829352
+05826f4e975dcecec72b2cf3a18899ccde1fd935d09d813b096cc6b83cdf4f23
+b9a60db41f9976ac333263c908dcefcdbd4c8402ed00a36e7487634d089fd45a
+f4a38a56a4412c3b0baffaeb717bf0de9ffb7a8460bf475a6718b0c73c571145
+d026957276530530a2fbefc6c8f059084178f5ab59e11b66566ca5ba42b1911a
+5d7f1bf343015eece988b7a93bce0c7aa61344d48aed9c92c8698d4b7c9951c8
+7d103f2414b39e1437f9d2e50c4ee5f218f2e6716926a79ea978f13b1f855345
+191dd7d31d8f82c2e3343c7a5894d95bdc492c28226834efcb5c12fea36ac5cc
+430e0aa604961e34888adf6c1f3954cbc2498e225d953cf5685852162346f474
+5a2a7087d5d7ad486de16d2ca8e15cee26e012671ba3bdc7d95cc8c98bb774f5
+08625e968aee27ff7d1a06e63bcfb5aa4876c3f8f13b30ccccee73c3caf4e70d
+98e6ed2f422dbb4950bf789680e064150995941a9f4dd68a575949847a7d012b
+b910bf03a69374e341e8036ff92c949f3dc6e86aaa7a2b79532b36ca1496c973
+3f5e789fa3754f83951039e765b6ef8d37389a18ca2655d971ea0ab2f6131886
+1d71a694f55fc3186d85d232f23b49634341f3d4279a84def32013aabbb89fa4
+20ba8b5a82ec05c02340bfc3e91a5db9a027ddccd503a463a6bf851d16d578a6
+b0a76a6efb49266813508e17c5b74b2890d4c8dad59c3a09170f03dc0265a344
+3356687a0d87b14590aafdc0739693bb5e81d1a98faa93a01a1b550d6ff8f53f
+06b1c4158d18ebfd24cf56f2a597d93da619a4034396e94a01a3c6b9f05cc22f
+2737d96e86155384cb35c41e2b9f34256e7d2765d1981b70b6e4937f7c0ee777
+e2b72dd324b0de03ffb857bc2d97dc2013e0a7c0a796a2ce060a1ae00065ff25
+de3f1433f60a0027f873dde7228f44d5bec99f2090494867fa9dc172a5c6b303
+5547be2f6ade63192e3cced295b049b7b61283a13eeb7a1541f72f6b1f464df9
+a6ba7d783987b571200b314418c8f132f0acc95ee967aaec1c8ee0d734dbf8cd
+6ca9e20df809650d5e92b4a48e854ec9d24e1f9a0b0d8fe52779156dabe22ce5
+11ed2afc265c8fdd73c8f73e5de20dcac79671963a66b0967d0c83f5f62240b7
+322bbd4a6f4a4532b6997ea91071c95cfab937f912ade36507ac53e60904ee66
+cd828d58a502e0dc
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+cleartomark
+
+%%EndFont 
+%%BeginFont: CMR7
+%!PS-AdobeFont-1.1: CMR7 1.0
+%%CreationDate: 1991 Aug 20 16:39:21
+
+% Copyright (C) 1997 American Mathematical Society.  All Rights Reserved.
+
+11 dict begin
+/FontInfo 7 dict dup begin
+/version (1.0) readonly def
+/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
+/FullName (CMR7) readonly def
+/FamilyName (Computer Modern) readonly def
+/Weight (Medium) readonly def
+/ItalicAngle 0 def
+/isFixedPitch false def
+end readonly def
+/FontName /CMR7 def
+/PaintType 0 def
+/FontType 1 def
+/FontMatrix [0.001 0 0 0.001 0 0] readonly def
+/Encoding 256 array
+0 1 255 {1 index exch /.notdef put} for
+dup 48 /zero put
+dup 49 /one put
+dup 50 /two put
+dup 51 /three put
+readonly def
+/FontBBox{-27 -250 1122 750}readonly def
+/UniqueXX 5000790 def
+currentdict end
+currentfile eexec
+9b9c1569015f2c1d2bf560f4c0d52257bacdd6500abda5ed9835f6a016cfc8f0
+0b6c052ed76a87856b50f4d80dfaeb508c97f8281f3f88b17e4d3b90c0f65ec3
+79791aacdc162a66cbbc5be2f53aad8de72dd113b55a022fbfee658cb95f5bb3
+2ba0357b5e050fddf264a07470bef1c52119b6fbd5c77ebed964ac5a2bbec9d8
+b3e48ae5bb003a63d545774b922b9d5ff6b0066ece43645a131879b032137d6d
+823385fe55f3402d557fd3b448685940729e6e22f4be0e08c6505cba868f7950
+93f556b64b808dd710eb936d3ac83e5783b5f7e56d363a59a026a5619a357d21
+c4e77bea121eb24b09027d1aad93158edf912940e91cd2f17922b35885894644
+7773730bb19af9e70453e1b78d5edc123b273a979891d6d5e624f4a388f3897e
+13b045e34b4ee2f5e4fc5e996d3549640010c671de14d18b0b3cd300e57dac03
+22e59bfbf7b29422230870f5897fcfaad4b50c7c1c58edcd119218163d6f6e56
+25ccb882db7b6d09a1586508e8cb642a11c29a46915e4a96e282079cb21922c1
+c2e360b487a45302fd22ec8c5fab63e54b5e844d4b17ca2fff37c69c366dd72a
+d02922c14c0932f65ed03e4219c117962edbad2dcdeaa9c10ce8af38a4ae52e2
+b377245b0be19a77d6c936e7530cc4d0b78d0cc4a92698fa2870fa54f2d8503e
+2d17b3d52fb2febb09f2b2af0c2a1892039ebe19a690098799a858e3d39631bd
+6925a154d161df3918074ada6bd52baddd0adc3f07e2d9f15e27cbf7fe8b98c4
+07205c811121fa91e059f2f99322fed63f359ac9da97aec383f067f23e5de331
+51e80f0a88ab50fe8fdae4a5de93c1ae2fdca06150b37246140c0e87cb2325a6
+0d2349162ae3ac93144eee1e665a1289105318fdfe86b6e76251cb25adc967d3
+d0b97fe5e279e1161736ab22b4ca510b964342383a840defd38f96a7280e6ac1
+34e48d740607ff2e7804164a16d47735864db847c97335e6d4215cb99911a1ec
+015a3edaac1f28fedd56d2467130d07bae9416c15f0827d27c6c79f59054282a
+418c12c157c91223a829947f47592f7cafd93ca182b25a73a9419127e3b12a9e
+5167ac3963f2b019b338ac46d63880f94dda4b538835884d2a5538c85528d6bd
+977f844d32b43b0e48caed5a4bdabcefe71695d69ca784db55ff8fd5c5c42e30
+40097ef70580328190679602afd080901928e98fe6d2dc73cac402e4e1ca6f7f
+432df214ec854aad9718714bdb6ba5281a79414d38ff3b5d49b6265ac26d3e4e
+a6c10279881a342085ea3e9bb3dd7f89bcbcfd367ff35c8e711da5022dce9399
+016902f1575ce159c868f1f9ecac906f7a5e7f60fea3c2e71a2548de75ddaf9e
+f3bd912397302b349d1897aca3279b170aee052fb7f473ac38ad55bdb638421a
+8ebb6dc9887fe398c58ff86217a35ad1bfc089e8a1dd89af1972e100ee0a289f
+4cd724cbd37d89e7b30ff19887f6dfd9332f5efe43d6cb6b4e42d9e70c79face
+5741a2d96458bb62f8ab9e12848d9bd05d0c1795a0a45b188762163a0ee14418
+476631c149aa9cc61c746cdaf335337be1e733e652d4650291d864efb26b07f2
+63644ba180e34e0fa0eccbb4f7d0372c7288301dd46dd34fb5d055757f818dd0
+e20ae31124469e7e9a345e0e6be9a0c797c9a3c726b17b1550ba3937203f5764
+2d4d44ce8dba5a13c8cbd99e44015855f93084aa67bae6fb9114361be84268fe
+6430900fa1fe389b22da19b6c3437999c1365f39c2bb6abd92eadf93c6d9fa1e
+ccdd217fc6d1c2842b5187cff6da02b1c3a9a316c414f8dffc71f0e34c35167c
+2a2514a30bb7617e533fdc4bcc453d684f5dc7a290b400c57e87a8719901c077
+4ca32a5e311fe7dab79bfe6036621b6831f817c4d7ba447997e12442fe33cfef
+f94e68847de78230a79e2841e73382efaca832c888b25d2bb81b4916dbd747fc
+172616ae399eed5be00ffcdd22a2d965ebb2adc7d97156efe60c3fb86399ba49
+ba0223ebd12c75a4d2a9cdea372376993f80992e0122f71f4f23992269b1a21e
+b6732d9f6ee4a9e584fa56dbeb6147d098ea6144be68211dd20a9c6b688bb5b6
+c9303d9e39fece40bf91e134b3811568dc7444200faf6a60e0e784df471ef31d
+de12b813811fc69ed7de6f1d8aaf407db2339d2ad24696e086d14038feec0f66
+d2e7649fc57a6396a480935be9cb7c54ec870169ce7e6c4431deb30a3e577750
+cf914d9c0c5a83919bca88f5d6f9e579
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+cleartomark
+
+%%EndFont 
+%%BeginFont: CMMI10
+%!PS-AdobeFont-1.1: CMMI10 1.100
+%%CreationDate: 1996 Jul 23 07:53:57
+
+% Copyright (C) 1997 American Mathematical Society.  All Rights Reserved.
+
+11 dict begin
+/FontInfo 7 dict dup begin
+/version (1.100) readonly def
+/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
+/FullName (CMMI10) readonly def
+/FamilyName (Computer Modern) readonly def
+/Weight (Medium) readonly def
+/ItalicAngle -14.04 def
+/isFixedPitch false def
+end readonly def
+/FontName /CMMI10 def
+/PaintType 0 def
+/FontType 1 def
+/FontMatrix [0.001 0 0 0.001 0 0] readonly def
+/Encoding 256 array
+0 1 255 {1 index exch /.notdef put} for
+dup 14 /delta put
+dup 15 /epsilon1 put
+dup 58 /period put
+dup 59 /comma put
+dup 61 /slash put
+dup 68 /D put
+dup 70 /F put
+dup 77 /M put
+dup 80 /P put
+dup 81 /Q put
+dup 83 /S put
+dup 84 /T put
+dup 85 /U put
+dup 97 /a put
+dup 98 /b put
+dup 110 /n put
+dup 112 /p put
+dup 113 /q put
+dup 114 /r put
+dup 115 /s put
+dup 116 /t put
+dup 117 /u put
+readonly def
+/FontBBox{-32 -250 1048 750}readonly def
+/UniqueXX 5087385 def
+currentdict end
+currentfile eexec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+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+cleartomark
+
+%%EndFont 
+%%BeginFont: CMSY6
+%!PS-AdobeFont-1.1: CMSY6 1.0
+%%CreationDate: 1991 Aug 15 07:21:34
+
+% Copyright (C) 1997 American Mathematical Society.  All Rights Reserved.
+
+11 dict begin
+/FontInfo 7 dict dup begin
+/version (1.0) readonly def
+/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
+/FullName (CMSY6) readonly def
+/FamilyName (Computer Modern) readonly def
+/Weight (Medium) readonly def
+/ItalicAngle -14.035 def
+/isFixedPitch false def
+end readonly def
+/FontName /CMSY6 def
+/PaintType 0 def
+/FontType 1 def
+/FontMatrix [0.001 0 0 0.001 0 0] readonly def
+/Encoding 256 array
+0 1 255 {1 index exch /.notdef put} for
+dup 3 /asteriskmath put
+readonly def
+/FontBBox{-4 -948 1329 786}readonly def
+/UniqueXX 5000816 def
+currentdict end
+currentfile eexec
+9b9c1569015f2c1d2bf560f4c0d52257bac8ced9b09a275ab231194ecf829352
+05826f4e975dcecec72b2cf3a18899ccde1fd935d09d813b096cc6b83cdf4f23
+b9a60db41f9976ac333263c908dcefcdbd4c8402ed00a36e7487634d089fd45a
+f4a38a56a4412c3b0baffaeb717bf0de9ffb7a8460bf475a6718b0c73c571145
+d026957276530530a2fbefc6c8f059084178f5ab59e11b6a18979f258b8c6ed3
+ccafbc21aca420c9c83eea371adc20e038b4d7b8ac303004b0aa205f04135140
+76407216032fdd22e6219da8f16b28ca12524deb7bca073cc5eba65c102a5e85
+fd48e6d062cd4283ee570a7774597e5bf0e3400b6be72db0115f3cb12db70ce0
+83722870cddfadee715f10f1fcaf20e06f3c54afe5ca238539bfe2b596116e83
+f5371ff18fa5003d8543226cfd4025f9940365b392a858d27f078d3abcffe4a1
+54e78c7692d1a32bf935967c64f01b24788ff8325d61145e2d4a489fd986fb77
+38e6b254522c77ca2797a504a9ce4676a77ebacb026eca94dde5922c936f8e90
+c43e28519671e8def84a1526a8b89450ef2bd624857da91e76994317b723923a
+47cb7b71e71550262a4a4eeef7e0d2eba371584b12b189f38fdb9feabf33b900
+d528bea06075d4e71d7696aa2ce7a5bf900014283045468c2625de16e2000219
+15074a97c681b3c6eee6d67ec3e481e174b53d1a3dd58da4507f93fa57f4f715
+e5df982321fae7682dcd02c3e977327fa2b9b80ef30e834269bba9c69dcd694b
+b055398be8186c0a2d19f9c101f67b30c506d8fe62dd7da5dc0d4c7abd32f9c3
+c64e081ca3cda88b1949fa64f70da6cb7a544360778ed200f21b04958bdbd70f
+044e7e611a28443d0c7b8049413c0ac989dd986086bb0b8a304c185458138b9f
+6c929aec9a804d4422ce5429d29a5c03b8a7916ed162a368650de8db6d9961ab
+cf373b396ed91d0289d26958cce7318fd7cde1bedb07347b1990557b33352b61
+b18672a53c81d8766a5260d28b9a2aaa542368e2c307cfedbb67e7a5a2b0fdfe
+8ee5f5f0c0f3cb9e7744b87ceee63dab32
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000000000000000000000
+cleartomark
+
+%%EndFont 
+TeXDict begin 39158280 55380996 1000 600 600 () @start
+/Fa 240[31 15[{}1 74.7198 /CMMI9 rf /Fb 131[50 1[50 5[50
+50 50 1[50 50 50 50 50 2[50 50 1[50 50 50 2[50 44[50
+4[50 47[{TeXBase1Encoding ReEncodeFont}18 83.022 /Courier
+rf /Fc 134[37 37 2[42 25 29 29 35 37 33 42 58 21 33 1[21
+37 37 21 29 37 30 35 33 9[71 54 58 46 42 50 1[46 58 58
+71 42 2[25 58 54 42 46 1[50 1[54 5[19 1[37 37 37 37 37
+1[37 37 37 2[19 25 19 4[21 39[{TeXBase1Encoding ReEncodeFont}53
+74.7198 /Palatino-Italic rf /Fd 136[62 1[46 25 33 29
+2[42 46 66 25 46 1[25 1[42 29 37 46 33 46 37 12[50 1[54
+11[42 4[58 7[37 37 37 37 37 37 37 37 37 49[{
+TeXBase1Encoding ReEncodeFont}31 74.7198 /Palatino-Bold
+rf /Fe 172[69 83[{}1 83.022 /CMEX10 rf /Ff 135[43 2[50
+27 35 33 1[50 45 48 73 24 46 1[24 1[46 1[40 51 37 46
+42 12[51 44 12[46 28[28 28 40[{
+.167 SlantFont TeXBase1Encoding ReEncodeFont}23 83.022
+/Palatino-Roman rf /Fg 139[24 29 15[28 1[34 37[19 59[{}5
+49.8132 /CMMI6 rf /Fh 134[33 3[37 22 26 26 1[33 29 37
+52 18 2[18 33 33 1[26 33 27 31 29 97[{TeXBase1Encoding ReEncodeFont}18
+66.4176 /Palatino-Italic rf /Fi 138[39 25 31 2[34 5[27
+23 5[30 1[36 8[54 2[45 3[52 42 20[20 59[{}13 58.1154
+/CMMI7 rf /Fj 162[23 1[23 29[65 1[23 23 3[42 42 42 42
+42 42 7[32 32 33[60 6[{}14 83.022 /CMR10 rf /Fk 149[23
+2[42 42 9[55 55 31[42 8[55 16[83 13[65 65 2[42 12[65
+2[{}12 83.022 /CMSY10 rf /Fl 149[20 55[45 1[19 44[34
+2[52{}5 58.1154 /CMSY7 rf /Fm 138[46 32 37 32 1[46 7[46
+42 1[37 2[45 46 97[{TeXBase1Encoding ReEncodeFont}10
+83.022 /Palatino-BoldItalic rf /Fn 201[30 30 30 30 30
+30 49[{}6 49.8132 /CMR6 rf /Fo 103[25 1[37 27[37 42 39
+62 42 45 24 32 30 42 45 41 43 66 22 42 17 22 43 42 25
+36 46 33 41 37 21 6[50 1[75 54 58 46 39 50 1[45 59 62
+71 46 54 25 25 62 57 42 46 58 53 46 58 5[19 19 37 37
+37 37 37 37 37 37 37 37 45 19 25 19 2[25 25 21 58 35[45
+2[{TeXBase1Encoding ReEncodeFont}73 74.7198 /Palatino-Roman
+rf /Fp 103[22 30[37 34 55 38 40 22 28 26 37 40 36 39
+59 19 37 1[19 39 37 22 32 41 29 37 33 9[66 2[41 1[44
+2[52 55 63 41 1[22 22 55 1[37 41 51 47 41 52 50 5[17
+33 33 1[33 33 33 33 33 33 33 40 17 22 17 2[22 22 18 52
+35[40 2[{TeXBase1Encoding ReEncodeFont}61 66.4176 /Palatino-Roman
+rf /Fq 242[71 9[35 3[{}2 66.4176 /CMSY8 rf /Fr 204[33
+33 33 33 48[{}4 58.1154 /CMR7 rf /Fs 135[42 69 46 51
+28 37 32 1[51 46 51 74 28 1[28 28 51 46 32 42 51 37 51
+42 10[65 2[51 2[51 2[83 51 2[32 2[46 51 1[60 1[65 11[42
+42 42 42 42 2[21 28 42[51 2[{TeXBase1Encoding ReEncodeFont}40
+83.022 /Palatino-Bold rf /Ft 138[48 30 39 37 37 42 1[50
+11[36 44 11[57 49 51 1[66 53 2[81 6[53 1[69 6[42 1[23
+23 42[34 37 14[{}22 83.022 /CMMI10 rf /Fu 133[37 42 42
+60 42 46 28 32 32 1[42 37 46 65 23 37 23 23 42 42 23
+32 42 34 38 37 11[65 51 46 55 4[78 6[46 51 65 55 1[60
+6[21 11[21 28 21 41[44 2[{TeXBase1Encoding ReEncodeFont}40
+83.022 /Palatino-Italic rf /Fv 103[28 83 28[42 46 43
+69 47 50 27 35 33 46 50 45 48 73 24 46 19 24 48 46 28
+40 51 37 46 42 23 2[28 1[28 2[55 83 60 65 51 44 55 1[50
+65 69 79 51 60 28 28 69 63 46 51 64 59 51 65 3[50 1[21
+21 42 42 42 42 42 42 42 42 42 42 50 21 28 21 50 1[28
+28 23 65 2[42 31[50 50 2[{TeXBase1Encoding ReEncodeFont}79
+83.022 /Palatino-Roman rf /Fw 252[32 3[{}1 49.8132 /CMSY6
+rf /Fx 137[56 1[32 1[39 2[54 58 3[23 4[48 61 2[50 18[83
+6[76 71[{TeXBase1Encoding ReEncodeFont}11 99.6264 /Palatino-Roman
+rf /Fy 137[80 88 48 64 56 1[88 80 88 128 48 2[48 2[56
+72 1[64 88 72 12[96 88 5[143 7[88 1[104 67[{
+TeXBase1Encoding ReEncodeFont}21 143.462 /Palatino-Bold
+rf end
+%%EndProlog
+%%BeginSetup
+%%Feature: *Resolution 600dpi
+TeXDict begin
+%%BeginPaperSize: a4
+% a4
+%%EndPaperSize
+
+%%EndSetup
+%%Page: 1 1
+1 0 bop Black Black 330 377 a Fy(T)-16 b(reatment)33
+b(of)j(Epsilon)e(Moves)h(in)g(Subset)330 543 y(Construction)330
+909 y Fx(Gertjan)26 b(van)f(Noor)n(d)1160 877 y Fw(\003)330
+997 y Fv(Rijksuniversiteit)e(Gr)o(oningen)329 1331 y
+Fu(The)29 b(paper)g(discusses)h(the)f(pr)o(oblem)g(of)h(determinising)f
+(\002nite-state)g(automata)f(containing)g(lar)o(ge)330
+1439 y(numbers)34 b(of)e Ft(\017)p Fu(-moves.)f(Experiments)h(with)f
+(\002nite-state)h(appr)o(oximations)e(of)i(natural)h(language)330
+1547 y(grammars)d(often)h(give)g(rise)h(to)e(very)h(lar)o(ge)f
+(automata)g(with)g(a)g(very)h(lar)o(ge)g(number)g(of)g
+Ft(\017)p Fu(-moves.)330 1655 y(The)21 b(paper)f(identi\002es)h(and)g
+(compar)o(es)f(a)h(number)g(of)g(subset)h(construction)f(algorithms)f
+(which)g(tr)o(eat)330 1762 y Ft(\017)p Fu(-moves.)j(Experiments)h(have)
+g(been)h(performed)f(which)g(indicate)g(that)f(the)h(algorithms)f
+(differ)i(con-)330 1870 y(siderably)19 b(in)g(practice,)f(both)g(with)h
+(r)o(espect)f(to)g(the)h(size)g(of)g(the)f(r)o(esulting)h
+(deterministic)g(automaton,)330 1978 y(and)j(with)f(r)o(espect)h(to)f
+(practical)h(ef\002ciency)m(.)f(Furthermor)o(e,)h(the)g(experiments)g
+(suggest)g(that)e(the)i(av-)330 2086 y(erage)e(number)h(of)f
+Ft(\017)p Fu(-moves)f(per)h(state)g(can)f(be)i(used)f(to)g(pr)o(edict)e
+(which)h(algorithm)f(is)j(likely)e(to)h(be)h(the)330
+2194 y(fastest)g(for)g(a)f(given)h(input)f(automaton.)330
+2393 y Fs(1)g(Introduction)330 2593 y(1.1)g(Finite-state)c(Language)j
+(Processing)330 2692 y Fv(An)29 b(important)g(pr)o(oblem)f(in)i
+(computational)f(linguistics)h(is)g(posed)e(by)h(the)g(fact)f(that)h
+(the)330 2792 y(grammars)21 b(which)i(ar)o(e)e(typically)h
+(hypothesised)h(by)f(linguists)h(ar)o(e)d(unattractive)h(fr)o(om)h(the)
+330 2892 y(point)j(of)e(view)h(of)g(computation.)g(For)g(instance,)g
+(the)g(number)g(of)g(steps)f(r)o(equir)o(ed)g(to)h(anal-)330
+2991 y(yse)18 b(a)g(sentence)g(of)g Ft(n)f Fv(wor)o(ds)h(is)h
+Ft(n)1398 2961 y Fr(3)1453 2991 y Fv(for)e(context-fr)o(ee)g(grammars.)
+g(For)h(certain)g(linguistically)330 3091 y(mor)o(e)25
+b(attractive)g(grammatical)g(formalisms)h(it)g(can)f(be)g(shown)i(that)
+f(no)g(upper)o(-bound)f(to)330 3190 y(the)31 b(number)g(of)g(steps)g(r)
+o(equir)o(ed)f(to)h(\002nd)g(an)g(analysis)g(can)f(be)h(given.)g(The)g
+(human)g(lan-)330 3290 y(guage)24 b(user)-6 b(,)25 b(however)-6
+b(,)24 b(seems)h(to)g(pr)o(ocess)f(in)i(linear)e(time;)h(humans)g
+(understand)f(longer)330 3390 y(sentences)32 b(with)g(no)f(noticeable)h
+(delay)-9 b(.)30 b(This)h(implies)h(that)g(neither)f(context-fr)o(ee)f
+(gram-)330 3489 y(mars)17 b(nor)h(mor)o(e)f(powerful)h(grammatical)f
+(formalisms)h(ar)o(e)e(likely)i(models)g(for)f(human)h(lan-)330
+3589 y(guage)23 b(pr)o(ocessing.)g(An)g(important)h(issue)g(ther)o
+(efor)o(e)d(is)j(how)g(the)f(linearity)h(of)f(pr)o(ocessing)330
+3689 y(by)e(humans)g(can)g(be)f(accounted)g(for)-6 b(.)479
+3788 y(A)26 b(potential)g(solution)h(to)f(this)h(pr)o(oblem)e(concerns)
+h(the)g(possibility)h(of)f Fu(appr)o(oximating)330 3888
+y Fv(an)17 b(underlying)h(general)e(and)h(abstract)f(grammar)h(by)g
+(techniques)h(of)f(a)g(much)g(simpler)h(sort.)330 3987
+y(The)g(idea)g(that)g(a)g(competence)g(grammar)g(might)h(be)f(appr)o
+(oximated)e(by)j(\002nite-state)f(means)330 4087 y(goes)24
+b(back)g(to)g(early)f(work)h(by)g(Chomsky)i(\(Chomsky)-9
+b(,)24 b(1963;)e(Chomsky)-9 b(,)24 b(1964\).)e(Ther)o(e)g(ar)o(e)330
+4187 y(essentially)h(thr)o(ee)e(observations)i(which)g(motivate)f(the)h
+(view)f(that)g(the)h(pr)o(ocessing)f(of)g(nat-)330 4286
+y(ural)e(language)h(is)g(\002nite-state:)p Black 571
+4469 a(1.)p Black -5 w(humans)g(have)g(a)f(\002nite)h(\(small,)g
+(limited,)g(\002xed\))e(amount)j(of)f(memory)g(available)629
+4569 y(for)f(language)h(pr)o(ocessing)p Black 571 4735
+a(2.)p Black -5 w(humans)g(have)g(pr)o(oblems)f(with)i(certain)e
+(grammatical)g(constr)o(uctions,)j(such)e(as)629 4834
+y(center)o(-embedding,)e(which)j(ar)o(e)d(impossible)j(to)f(describe)f
+(by)h(\002nite-state)f(means)629 4934 y(\(Miller)g(and)g(Chomsky)-9
+b(,)22 b(1963\))p Black 571 5100 a(3.)p Black -5 w(humans)f(pr)o(ocess)
+g(natural)f(language)g(very)h(ef)o(\002ciently)f(\(in)h(linear)f
+(time\))p Black 330 5293 1495 4 v 371 5371 a Fq(\003)d
+Fp(Alfa-informatica)h(&)e(BCN.)h(E-mail:)f(vannoor)o(d@let.r)o(ug.nl)p
+Black Black 351 5942 a(c)330 5944 y Fq(\015)g Fp(2000)i(Association)f
+(for)h(Computational)e(Linguistics)p Black eop
+%%Page: 2 2
+2 1 bop Black 330 91 a Fo(van)20 b(Noor)o(d)1145 b(Epsilon)17
+b(Moves)h(in)h(Subset)g(Constr)o(uction)p Black 330 357
+a Fs(1.2)h(Finite-state)c(Approximation)i(and)i Ft(\017)p
+Fs(-moves)330 457 y Fv(In)27 b(experimenting)f(with)h(\002nite-state)f
+(appr)o(oximation)g(techniques)i(for)e(context-fr)o(ee)e(and)330
+556 y(mor)o(e)17 b(powerful)h(grammatical)f(formalisms)h(\(such)g(as)f
+(the)h(techniques)h(pr)o(esented)d(in)j(Black)330 656
+y(\(1989\),)24 b(Per)o(eira)i(and)h(W)-6 b(right)28 b(\(1991\),)d(Rood)
+j(\(1996\),)c(Per)o(eira)i(and)h(W)-6 b(right)28 b(\(1997\),)c(Evans)
+330 756 y(\(1997\),)31 b(Neder)o(hof)h(\(1997\),)f(Neder)o(hof)i
+(\(1998\),)e(Johnson)k(\(1998\))c(\))i(we)h(have)f(found)h(that)330
+855 y(the)24 b(r)o(esulting)f(automata)g(often)h(ar)o(e)e(extr)o(emely)
+g(lar)o(ge.)g(Mor)o(eover)-6 b(,)22 b(the)i(automata)e(contain)330
+955 y(many)f Ft(\017)p Fv(-moves)g(\()p Fu(jumps)p Fv(\).)e(And)i
+(\002nally)-9 b(,)21 b(if)f(such)i(automata)e(ar)o(e)f(determinised)i
+(then)g(the)g(r)o(e-)330 1054 y(sulting)h(automata)d(ar)o(e)h(often)g
+Fu(smaller)p Fv(.)h(It)f(turns)h(out)g(that)g(a)f(straightforwar)o(d)f
+(implementa-)330 1154 y(tion)j(of)f(the)g(subset)h(constr)o(uction)h
+(determinisation)e(algorithm)h(performs)f(badly)g(for)g(such)330
+1254 y(inputs.)k(In)f(this)h(paper)e(we)h(consider)g(a)g(number)g(of)g
+(variants)g(of)g(the)g(subset-constr)o(uction)330 1353
+y(algorithm)e(which)f(dif)o(fer)e(in)i(their)g(tr)o(eatment)f(of)h
+Ft(\017)p Fv(-moves.)479 1453 y(Although)30 b(we)e(have)g(observed)g
+(that)g(\002nite-state)h(appr)o(oximation)f(techniques)h(typi-)330
+1553 y(cally)h(yield)g(automata)g(with)g(lar)o(ge)f(amounts)i(of)f
+Ft(\017)p Fv(-moves,)g(this)h(is)f(obviously)i(not)f(a)e(ne-)330
+1652 y(cessity)-9 b(.)21 b(Instead)f(of)g(trying)h(to)g(impr)o(ove)g
+(upon)g(determinisation)g(techniques)g(for)g(such)g(au-)330
+1752 y(tomata)k(it)g(might)i(be)d(mor)o(e)h(fr)o(uitful,)g(per)o(haps,)
+f(to)i(try)f(to)g(impr)o(ove)g(these)g(appr)o(oximation)330
+1851 y(techniques)g(in)g(such)g(a)e(way)h(that)h(mor)o(e)f(compact)g
+(automata)f(ar)o(e)g(pr)o(oduced.)2914 1820 y Fn(1)2973
+1851 y Fv(However)-6 b(,)330 1951 y(because)26 b(r)o(esear)o(ch)f(into)
+i(\002nite-state)g(appr)o(oximation)f(is)h(still)h(of)e(an)h
+(exploratory)f(and)h(ex-)330 2051 y(perimental)g(natur)o(e,)e(it)j(can)
+e(be)h(ar)o(gued)e(that)i(mor)o(e)g(r)o(obust)f(determinisation)i
+(algorithms)330 2150 y(do)e(still)h(have)f(a)g(r)o(ole)g(to)h(play:)e
+(it)i(can)f(be)g(expected)f(that)h(appr)o(oximation)g(techniques)h(ar)o
+(e)330 2250 y(much)f(easier)f(to)h(de\002ne)f(and)g(implement)h(if)g
+(the)f(r)o(esulting)h(automaton)g(is)g(allowed)f(to)h(be)330
+2350 y(non-deterministic)c(and)e(to)h(contain)g Ft(\017)p
+Fv(-moves.)479 2449 y(Note)f(furthermor)o(e)e(that)h(even)g(if)g(our)g
+(primary)g(motivation)h(is)g(in)g(\002nite-state)f(appr)o(ox-)330
+2549 y(imation,)24 b(the)f(pr)o(oblem)g(of)g(determinising)h
+(\002nite-state)f(automata)f(with)i Ft(\017)p Fv(-moves)f(may)g(be)330
+2648 y(r)o(elevant)d(in)h(other)g(ar)o(eas)e(of)i(language)f(r)o(esear)
+o(ch)f(as)h(well.)330 2848 y Fs(1.3)g(Subset)e(construction)i(and)f
+Ft(\017)p Fs(-moves)330 2947 y Fv(The)50 b(experiments)g(wer)o(e)f
+(performed)g(using)h(the)h Fu(FSA)f(Utilities)p Fv(.)f(The)h
+Fu(FSA)g(Utilities)330 3047 y Fv(tool-box)j(\(van)e(Noor)o(d,)h(1997;)e
+(van)h(Noor)o(d,)h(1999;)e(Ger)o(demann)h(and)h(van)g(Noor)o(d,)330
+3147 y(1999;)44 b(van)i(Noor)o(d)g(and)f(Ger)o(demann,)g(1999\))f(is)j
+(a)e(collection)i(of)f(tools)i(to)e(manipu-)330 3246
+y(late)36 b(r)o(egular)f(expr)o(essions,)h(\002nite-state)h(automata)e
+(and)i(\002nite-state)f(transducers.)f(Ma-)330 3346 y(nipulations)40
+b(include)e(determinisation,)h(minimisation,)i(composition,)f
+(complementa-)330 3445 y(tion,)g(intersection,)g(Kleene)g(closur)o(e,)f
+(etc.)g(V)-8 b(arious)40 b(visualisation)h(tools)f(ar)o(e)e(available)
+330 3545 y(to)i(br)o(owse)g(\002nite-state)g(automata.)f(The)h
+(tool-box)g(is)h(implemented)f(in)g(SICStus)g(Pr)o(o-)330
+3645 y(log,)49 b(and)g(is)g(available)f(fr)o(ee)f(of)i(char)o(ge)f
+(under)g(Gnu)i(General)e(Public)i(License)e(via)330 3744
+y(anonymous)35 b(ftp)e(at)g(ftp://ftp.let.r)o(ug.nl/pub/vannoor)o
+(d/Fsa/,)h(and)f(via)g(the)h(web)f(at)330 3844 y(http://www)-8
+b(.let.r)o(ug.nl/\230vannoor)o(d/Fsa/.)38 b(At)e(the)g(time)h(of)f(our)
+g(initial)h(experiments)330 3944 y(with)31 b(\002nite-state)f(appr)o
+(oximation,)g(an)g(old)h(version)g(of)f(the)h(tool-box)g(was)f(used,)g
+(which)330 4043 y(ran)d(into)h(memory)f(pr)o(oblems)g(for)g(some)h(of)e
+(these)i(automata.)e(For)h(this)h(r)o(eason,)e(the)h(sub-)330
+4143 y(set)i(constr)o(uction)i(algorithm)f(has)f(been)f(r)o
+(e-implemented,)g(paying)h(special)g(attention)h(to)330
+4242 y(the)25 b(tr)o(eatment)f(of)h Ft(\017)p Fv(-moves.)f(Thr)o(ee)g
+(variants)g(of)h(the)g(subset)g(constr)o(uction)i(algorithm)e(ar)o(e)
+330 4342 y(identi\002ed)c(which)g(dif)o(fer)e(in)j(the)e(way)h
+Ft(\017)p Fv(-moves)g(ar)o(e)e(tr)o(eated:)p Black 330
+4525 a Fm(per)i(graph)p Black 42 w Fv(The)d(most)h(obvious)h(and)d
+(straightforwar)o(d)h(appr)o(oach)e(is)j(sequential)g(in)g(the)f(fol-)
+629 4624 y(lowing)33 b(sense.)g(Firstly)-9 b(,)32 b(an)g(equivalent)g
+(automaton)h(without)g Ft(\017)p Fv(-moves)f(is)h(con-)629
+4724 y(str)o(ucted)16 b(for)g(the)h(input.)f(In)h(or)o(der)e(to)i(do)g
+(this,)g(the)f(transitive)g(closur)o(e)g(of)h(the)f(graph)629
+4824 y(consisting)27 b(of)e(all)g Ft(\017)p Fv(-moves)f(is)i(computed.)
+f(Secondly)-9 b(,)24 b(the)h(r)o(esulting)h(automaton)629
+4923 y(is)20 b(then)g(tr)o(eated)e(by)i(a)f(subset)h(constr)o(uction)i
+(algorithm)e(for)g Ft(\017)p Fv(-fr)o(ee)d(automata.)i(Dif-)629
+5023 y(fer)o(ent)g(variants)h(of)g Fu(per)g(graph)f Fv(can)h(be)g
+(identi\002ed,)f(depending)i(on)f(the)h(implemen-)629
+5122 y(tation)g(of)g(the)g Ft(\017)p Fv(-r)o(emoval)e(step.)p
+Black 330 5289 a Fm(per)i(state)p Black 42 w Fv(For)d(each)g
+Fu(state)g Fv(which)h(occurs)f(in)h(a)f(subset)g(pr)o(oduced)f(during)h
+(subset)h(constr)o(uc-)p Black 330 5458 1495 4 v 373
+5536 a Fp(1)e(Indeed,)e(a)i(later)g(implementation)e(by)h(Neder)o(hof)h
+(avoids)f(constr)o(uction)i(of)f(the)f(complete)g(non-determistic)423
+5611 y(automaton)g(by)g(minimising)h(sub-automata)g(befor)o(e)f(they)g
+(ar)o(e)g(embedded)e(into)j(lar)o(ger)g(sub-automata.)p
+Black Black 3288 5944 a Fv(2)p Black eop
+%%Page: 3 3
+3 2 bop Black 330 91 a Fo(van)20 b(Noor)o(d)1145 b(Epsilon)17
+b(Moves)h(in)h(Subset)g(Constr)o(uction)p Black 629 357
+a Fv(tion,)i(compute)f(the)h(states)f(which)h(ar)o(e)e(r)o(eachable)f
+(using)j Ft(\017)p Fv(-moves.)f(The)g(r)o(esults)g(of)629
+457 y(this)25 b(computation)g(can)g(be)f(memorised,)g(or)h(computed)f
+(for)h(each)e(state)i(in)f(a)g(pr)o(e-)629 556 y(pr)o(ocessing)31
+b(step.)g(This)h(is)f(the)g(appr)o(oach)f(mentioned)i(brie\003y)f(in)h
+(Johnson)g(and)629 656 y(W)-8 b(ood)21 b(\(1997\).)1111
+624 y Fn(2)p Black 330 822 a Fm(per)g(subset)p Black
+43 w Fv(For)35 b(each)e Fu(subset)j Ft(Q)e Fv(of)h(states)f(which)h
+(arises)f(during)h(subset)g(constr)o(uction,)629 922
+y(compute)19 b Ft(Q)1036 891 y Fl(0)1082 922 y Fk(\023)k
+Ft(Q)18 b Fv(which)i(extends)e Ft(Q)h Fv(with)g(all)g(states)f(which)i
+(ar)o(e)e(r)o(eachable)e(fr)o(om)629 1021 y(any)25 b(member)f(of)h
+Ft(Q)f Fv(using)i Ft(\017)p Fv(-moves.)e(Such)h(an)f(algorithm)i(is)f
+(described)f(in)h(Aho,)629 1121 y(Sethi,)20 b(and)h(Ullman)f(\(1986\).)
+479 1303 y(The)d(motivation)i(for)d(this)i(paper)e(is)h(the)g
+(experience)f(that)h(the)g(\002rst)h(appr)o(oach)d(turns)j(out)330
+1403 y(to)h(be)f(impractical)g(for)g(automata)f(with)j(very)e(lar)o(ge)
+f(numbers)i(of)f Ft(\017)p Fv(-moves.)g(An)g(integration)330
+1503 y(of)32 b(the)g(subset)f(constr)o(uction)j(algorithm)e(with)h(the)
+f(computation)g(of)g Ft(\017)p Fv(-r)o(eachable)d(states)330
+1602 y(performs)20 b(much)i(better)e(in)h(practice)f(for)g(such)i
+(automata.)479 1702 y(Section)35 b(2)f(pr)o(esents)f(a)h(short)h
+(statement)f(of)h(the)f(pr)o(oblem)g(\(how)h(to)f(determinise)g(a)330
+1802 y(given)c(\002nite-state)g(automaton\),)g(and)g(a)f(subset)i
+(constr)o(uction)h(algorithm)e(which)h(solves)330 1901
+y(this)23 b(pr)o(oblem)g(in)g(the)g(absence)f(of)h Ft(\017)p
+Fv(-moves.)f(Section)h(3)f(de\002nes)h(a)f(number)h(of)g(subset)g(con-)
+330 2001 y(str)o(uction)28 b(algorithms)g(which)f(dif)o(fer)e(with)j(r)
+o(espect)e(to)h(the)g(tr)o(eatment)f(of)g Ft(\017)p Fv(-moves.)h(Most)
+330 2100 y(aspects)21 b(of)g(the)g(algorithms)h(ar)o(e)e(not)i(new)f
+(and)g(have)g(been)g(described)f(elsewher)o(e,)g(and/or)330
+2200 y(wer)o(e)j(incorporated)g(in)h(pr)o(evious)g(implementations;)h
+(a)e(comparison)h(of)g(the)g(dif)o(fer)o(ent)e(al-)330
+2300 y(gorithms)28 b(had)e(not)h(been)f(performed)g(pr)o(eviously)-9
+b(.)26 b(W)-8 b(e)26 b(pr)o(ovide)g(a)g(comparison)h(with)g(r)o(e-)330
+2399 y(spect)e(to)h(the)g(size)f(of)g(the)h(r)o(esulting)f
+(deterministic)h(automaton)g(\(in)g(section)g(3\))e(and)h(prac-)330
+2499 y(tical)d(ef)o(\002ciency)g(\(in)h(section)h(4\).)d(Section)i(4)f
+(pr)o(ovides)g(experimental)g(r)o(esults)h(both)g(for)g(ran-)330
+2599 y(domly)30 b(generated)f(automata)g(and)g(for)g(automata)g
+(generated)f(by)i(appr)o(oximation)f(algo-)330 2698 y(rithms.)j(Our)f
+(implementations)h(of)f(the)g(various)g(algorithms)i(ar)o(e)c(also)i
+(compar)o(ed)f(with)330 2798 y(A)-6 b(T&T's)20 b(FSM)g(utilities)h
+(\(Mohri,)g(Per)o(eira,)e(and)h(Riley)-9 b(,)21 b(1998\),)d(to)j
+(establish)g(that)g(the)g(experi-)330 2897 y(mental)g(dif)o(fer)o
+(ences)d(we)j(\002nd)g(between)f(the)h(algorithms)g(ar)o(e)f(tr)o(uly)h
+(caused)f(by)g(dif)o(fer)o(ences)330 2997 y(in)h(the)g(algorithm)h
+(\(as)e(opposed)h(to)g(accidental)f(implementation)h(details\).)330
+3196 y Fs(2)f(Subset)f(Construction)330 3396 y(2.1)h(Problem)f
+(statement)330 3495 y Fv(Let)30 b(a)h(\002nite-state)f(machine)h
+Ft(M)39 b Fv(be)31 b(speci\002ed)f(by)h(a)f(tuple)h Fj(\()p
+Ft(Q;)14 b Fj(\006)p Ft(;)g(\016)o(;)g(S;)g(F)e Fj(\))30
+b Fv(wher)o(e)g Ft(Q)g Fv(is)h(a)330 3595 y(\002nite)24
+b(set)f(of)h(states,)f Fj(\006)g Fv(is)h(a)f(\002nite)h(alphabet,)e
+Ft(\016)k Fv(is)e(a)f(function)h(fr)o(om)f Ft(Q)d Fk(\002)g
+Fj(\(\006)h Fk([)f(f)p Ft(\017)p Fk(g)p Fj(\))27 b Fk(!)h
+Fj(2)3253 3565 y Fi(Q)3309 3595 y Fv(.)330 3694 y(Furthermor)o(e,)20
+b Ft(S)28 b Fk(\022)23 b Ft(Q)d Fv(is)h(a)f(set)h(of)g(start)f(states)h
+(and)f Ft(F)35 b Fk(\022)23 b Ft(Q)d Fv(is)h(a)g(set)f(of)h(\002nal)g
+(states.)3075 3663 y Fn(3)479 3794 y Fv(Let)30 b Ft(\017)p
+Fv(-move)g(be)g(the)g(r)o(elation)g Fk(f)p Fj(\()p Ft(q)1608
+3806 y Fi(i)1635 3794 y Ft(;)14 b(q)1709 3806 y Fi(j)1744
+3794 y Fj(\))p Fk(j)p Ft(q)1836 3806 y Fi(j)1912 3794
+y Fk(2)40 b Ft(\016)s Fj(\()p Ft(q)2116 3806 y Fi(i)2145
+3794 y Ft(;)14 b(\017)p Fj(\))p Fk(g)p Fv(.)29 b Ft(\017)p
+Fv(-r)o(eachable)e(is)k(the)f(r)o(e\003exive)330 3894
+y(and)21 b(transitive)g(closur)o(e)f(of)i Ft(\017)p Fv(-move.)e(Let)h
+Ft(\017)p Fv(-CLOSURE:)e Fj(2)2219 3864 y Fi(Q)2299 3894
+y Fk(!)k Fj(2)2447 3864 y Fi(Q)2524 3894 y Fv(be)e(a)g(function)h
+(which)g(is)330 3993 y(de\002ned)e(as:)896 4093 y Ft(\017)p
+Fv(-CLOSURE)n Fj(\()p Ft(Q)1444 4059 y Fl(0)1468 4093
+y Fj(\))j(=)g Fk(f)p Ft(q)s Fk(j)p Ft(q)1756 4059 y Fl(0)1802
+4093 y Fk(2)g Ft(Q)1946 4059 y Fl(0)1969 4093 y Ft(;)14
+b Fj(\()p Ft(q)2078 4059 y Fl(0)2101 4093 y Ft(;)g(q)s
+Fj(\))24 b Fk(2)f Ft(\017)p Fv(-r)o(eachable)n Fk(g)330
+4242 y Fv(Furthermor)o(e,)50 b(we)g(write)g Ft(\017)p
+Fv(-CLOSURE)1721 4204 y Fl(\000)p Fr(1)1810 4242 y Fj(\()p
+Ft(Q)1908 4212 y Fl(0)1931 4242 y Fj(\))h Fv(for)f(the)g(set)h
+Fk(f)p Ft(q)s Fk(j)p Ft(q)2633 4212 y Fl(0)2733 4242
+y Fk(2)78 b Ft(Q)2932 4212 y Fl(0)2955 4242 y Ft(;)14
+b Fj(\()p Ft(q)s(;)g(q)3141 4212 y Fl(0)3165 4242 y Fj(\))78
+b Fk(2)330 4342 y Ft(\017)p Fv(-r)o(eachable)m Fk(g)p
+Fv(.)479 4442 y(For)21 b(any)g(given)g(\002nite-state)f(automaton)h
+Ft(M)32 b Fj(=)22 b(\()p Ft(Q;)14 b Fj(\006)p Ft(;)g(\016)o(;)g(S;)g(F)
+e Fj(\))20 b Fv(ther)o(e)g(is)g(an)h(equivalent)330 4541
+y(deterministic)i(automaton)h Ft(M)1349 4511 y Fl(0)1399
+4541 y Fj(=)j(\(2)1565 4511 y Fi(Q)1621 4541 y Ft(;)14
+b Fj(\006)p Ft(;)g(\016)1795 4511 y Fl(0)1818 4541 y
+Ft(;)g Fk(f)p Ft(Q)1963 4553 y Fr(0)1999 4541 y Fk(g)p
+Ft(;)g(F)2143 4511 y Fl(0)2166 4541 y Fj(\))p Fv(.)23
+b Ft(F)2307 4511 y Fl(0)2353 4541 y Fv(is)h(the)f(set)g(of)g(all)g
+(states)g(in)g Fj(2)3274 4511 y Fi(Q)330 4641 y Fv(containing)k(a)d
+(\002nal)i(state)f(of)g Ft(M)9 b Fv(,)25 b(i.e.,)f(the)i(set)f(of)h
+(subsets)f Fk(f)p Ft(Q)2351 4653 y Fi(i)2410 4641 y Fk(2)31
+b Fj(2)2538 4611 y Fi(Q)2594 4641 y Fk(j)p Ft(q)k Fk(2)d
+Ft(Q)2842 4653 y Fi(i)2869 4641 y Ft(;)14 b(q)35 b Fk(2)d
+Ft(F)12 b Fk(g)p Fv(.)24 b Ft(M)3307 4611 y Fl(0)330
+4741 y Fv(has)e(a)g(single)h(start)f(state)g Ft(Q)1226
+4753 y Fr(0)1286 4741 y Fv(which)h(is)g(the)f(epsilon)i(closur)o(e)e
+(of)g(the)g(start)h(states)f(of)g Ft(M)9 b Fv(,)22 b(i.e.,)330
+4840 y Ft(Q)396 4852 y Fr(0)456 4840 y Fj(=)h Ft(\017)p
+Fv(-CLOSURE)n Fj(\()p Ft(S)5 b Fj(\))p Fv(.)21 b(Finally)-9
+b(,)582 5046 y Ft(\016)622 5012 y Fl(0)646 5046 y Fj(\()p
+Fk(f)p Ft(q)757 5058 y Fr(1)794 5046 y Ft(;)14 b(q)868
+5058 y Fr(2)905 5046 y Ft(;)g(:)g(:)g(:)g(;)g(q)1127
+5058 y Fi(i)1154 5046 y Fk(g)p Ft(;)g(a)p Fj(\))23 b(=)f
+Ft(\017)p Fv(-CLOSURE)o Fj(\()p Ft(\016)s Fj(\()p Ft(q)2011
+5058 y Fr(1)2049 5046 y Ft(;)14 b(a)p Fj(\))k Fk([)h
+Ft(\016)s Fj(\()p Ft(q)2363 5058 y Fr(2)2401 5046 y Ft(;)14
+b(a)p Fj(\))k Fk([)h Ft(:)14 b(:)g(:)k Fk([)h Ft(\016)s
+Fj(\()p Ft(q)2904 5058 y Fi(i)2932 5046 y Ft(;)14 b(a)p
+Fj(\)\))p Black 330 5216 1495 4 v 373 5294 a Fp(2)j(Accor)o(ding)g(to)g
+(Derick)g(W)-6 b(ood)17 b(\(p.c.\),)f(this)h(appr)o(oach)g(has)g(been)e
+(implemented)g(in)i(several)f(systems,)423 5369 y(including)h(Howar)o
+(d)g(Johnson's)g(INR)h(system.)373 5439 y(3)f(Note)g(that)e(a)i(set)f
+(of)h(start)g(states)f(is)h(r)o(equir)o(ed,)f(rather)h(than)e(a)i
+(single)g(start)g(state.)e(Many)h(operations)i(on)423
+5514 y(automata)e(can)h(be)g(de\002ned)e(somewhat)h(mor)o(e)h
+(elegantly)f(in)g(this)h(way)g(\(including)g Fh(per)f(graph)2853
+5491 y Fg(t)2899 5514 y Fp(discussed)423 5589 y(below\).)h(Obviously)-7
+b(,)16 b(for)h(deterministic)g(automata)f(this)h(set)f(should)g(be)h(a)
+f(singleton)h(set.)p Black Black 3288 5944 a Fv(3)p Black
+eop
+%%Page: 4 4
+4 3 bop Black 330 91 a Fo(van)20 b(Noor)o(d)1145 b(Epsilon)17
+b(Moves)h(in)h(Subset)g(Constr)o(uction)p Black Black
+Black Black Black Black Black 705 344 a Fs(funct)p Black
+705 357 199 4 v 20 w Ff(subset)p 1162 344 25 4 v 30 w(constr)o(uction)8
+b Fj(\(\()p Ft(Q;)14 b Fj(\006)p Ft(;)g(\016)o(;)g(S;)g(F)e
+Fj(\)\))788 443 y Ff(index)p 999 443 V 30 w(transitions\(\))e
+Fj(;)37 b Ff(T)-7 b(rans)29 b Fj(:=)23 b Fk(;)p Fj(;)36
+b Ff(Finals)30 b Fj(:=)23 b Fk(;)p Fj(;)36 b Ff(States)29
+b Fj(:=)23 b Fk(;)p Fj(;)788 543 y Ff(Start)31 b Fj(:=)22
+b Ff(epsilon)p 1373 543 V 31 w(closur)o(e)6 b Fj(\()p
+Ft(S)f Fj(\))788 643 y Ff(add)k Fj(\()p Ft(S)c(tar)r(t)p
+Fj(\))p Black 788 742 a Fs(while)p Black 788 755 217
+4 v 40 w Fv(ther)o(e)20 b(is)h(an)g(unmarked)f(subset)h
+Ft(T)34 b Fk(2)24 b Ff(States)p Black 26 w Fs(do)p Black
+2504 755 97 4 v 1025 842 a Ff(mark)10 b Fj(\()p Ft(T)i
+Fj(\))p Black 1025 941 a Fs(foreach)p Black 1025 954
+282 4 v 21 w Fj(\()p Ft(a;)i(U)9 b Fj(\))23 b Fk(2)g
+Ff(instr)o(uctions)8 b Fj(\()p Ft(T)k Fj(\))p Black 21
+w Fs(do)p Black 2226 954 97 4 v 1108 1041 a Ft(U)32 b
+Fj(:=)23 b Ff(epsilon)p 1579 1041 25 4 v 31 w(closur)o(e)6
+b Fj(\()p Ft(U)j Fj(\))1108 1141 y Ff(T)-7 b(rans)6 b
+Fj([)p Ft(T)h(;)14 b(a)p Fj(])23 b(:=)f Fk(f)p Ft(U)9
+b Fk(g)1108 1240 y Ff(add)g Fj(\()p Ft(U)g Fj(\))p Black
+1025 1340 a Fs(od)p Black 1025 1353 97 4 v Black 788
+1440 a(od)p Black 788 1453 V Black 788 1539 a(return)p
+Black 788 1552 236 4 v 20 w Fj(\()p Ff(States)d Ft(;)14
+b Fj(\006)p Ft(;)g Ff(T)-7 b(rans)5 b Ft(;)14 b Fk(f)p
+Ff(Start)7 b Fk(g)p Ft(;)14 b Ff(Finals)7 b Fj(\))p Black
+705 1639 a Fs(end)p Black 705 1652 143 4 v Black 705
+1838 a(proc)p Black 705 1851 167 4 v 21 w Ff(add)i Fj(\()p
+Ft(U)g Fj(\))584 b Fv(Reachable-state-set)19 b(Maintenance)p
+Black 788 1938 a Fs(if)p Black 788 1951 60 4 v 21 w Ft(U)41
+b(=)-51 b Fk(2)23 b Ff(States)p Black 869 2037 a Fs(then)p
+Black 869 2050 171 4 v 40 w Fv(add)d Ft(U)29 b Fv(unmarked)20
+b(to)i Ff(States)p Black 1060 2137 a Fs(if)p Black 1060
+2150 60 4 v 21 w Ft(U)27 b Fk(\\)19 b Ft(F)p Black 32
+w Fs(then)p Black 1384 2150 171 4 v 20 w Ff(Finals)30
+b Fj(:=)23 b Ff(Finals)i Fk([)19 b(f)p Ft(U)9 b Fk(g)p
+Black 19 w Fs(\002)p Black 2423 2150 51 4 v Black 788
+2237 a(\002)p Black 788 2250 V Black 705 2336 a(end)p
+Black 705 2349 143 4 v Black 705 2535 a(funct)p Black
+705 2548 199 4 v 20 w Ff(instr)o(uctions)f Fj(\()p Ft(P)k
+Fj(\))548 b Fv(Instr)o(uction)22 b(Computation)p Black
+788 2635 a Fs(return)p Black 788 2648 236 4 v 20 w Ff(mer)o(ge)6
+b Fj(\()1313 2573 y Fe(S)1382 2660 y Fi(p)p Fl(2)p Fi(P)1530
+2635 y Ff(transitions)i Fj(\()p Ft(p)p Fj(\)\))p Black
+705 2741 a Fs(end)p Black 705 2754 143 4 v Black 705
+2940 a(funct)p Black 705 2953 199 4 v 20 w Ff(epsilon)p
+1195 2940 25 4 v 31 w(closur)o(e)e Fj(\()p Ft(U)j Fj(\))532
+b Fv(variant)20 b(1:)g(No)h Ft(\017)p Fv(-moves)p Black
+788 3040 a Fs(return)p Black 788 3053 236 4 v 20 w Ft(U)p
+Black 705 3140 a Fs(end)p Black 705 3153 143 4 v 330
+3313 a Fd(Figure)d(1)330 3396 y Fo(Subset-constr)o(uction)i(algorithm.)
+p Black 479 3699 a Fv(An)27 b(algorithm)h(which)g(computes)g
+Ft(M)1738 3669 y Fl(0)1788 3699 y Fv(for)f(a)f(given)i
+Ft(M)35 b Fv(will)28 b(only)g(need)f(to)h(take)e(into)330
+3799 y(account)c(states)f(in)h Fj(2)1001 3769 y Fi(Q)1079
+3799 y Fv(which)g(ar)o(e)e(r)o(eachable)g(fr)o(om)h(the)h(start)f
+(state)g Ft(Q)2611 3811 y Fr(0)2648 3799 y Fv(.)h(This)g(is)g(the)g(r)o
+(eason)330 3899 y(that)27 b(for)f(many)h(input)h(automata)e(the)h
+(algorithm)h(does)e(not)i(need)e(to)i(tr)o(eat)d(all)i(subsets)g(of)330
+3998 y(states)33 b(\(but)g(note)g(that)g(ther)o(e)f(ar)o(e)g(automata)g
+(for)h(which)h(all)f(subsets)g(ar)o(e)f(r)o(elevant,)f(and)330
+4098 y(hence)21 b(exponential)g(behaviour)f(cannot)h(be)g(avoided)f(in)
+h(general\).)479 4198 y(Consider)28 b(the)g(subset)h(constr)o(uction)g
+(algorithm)g(in)f(\002gur)o(e)f(1.)h(The)f(algorithm)i(main-)330
+4297 y(tains)23 b(a)e(set)i(of)f(subsets)h Fu(States)p
+Fv(.)f(Each)g(subset)g(can)g(be)g(either)g(marked)g(or)h(unmarked)e
+(\(to)i(in-)330 4397 y(dicate)e(whether)g(the)h(subset)g(has)f(been)g
+(tr)o(eated)f(by)i(the)f(algorithm\);)h(the)f(set)h(of)f(unmarked)330
+4497 y(subsets)28 b(is)f(sometimes)i(r)o(eferr)o(ed)24
+b(to)k(as)f(the)g(agenda.)g(The)g(algorithm)h(takes)f(such)h(an)f(un-)
+330 4596 y(marked)21 b(subset)h Ft(T)32 b Fv(and)21 b(computes)h(all)g
+(transitions)g(leaving)g Ft(T)12 b Fv(.)20 b(This)i(computation)h(is)e
+(per)o(-)330 4696 y(formed)d(by)h(the)f(function)i Fu(instructions)f
+Fv(and)f(is)h(called)e Fu(instruction)i(computation)e
+Fv(by)i(Johnson)330 4795 y(and)h(W)-8 b(ood)22 b(\(1997\).)479
+4895 y(The)j(function)g Fu(index)p 1165 4895 25 4 v 29
+w(transitions)g Fv(constr)o(ucts)g(the)g(function)g Fu(transitions)p
+Fv(:)f Ft(Q)30 b Fk(!)f Fj(\006)21 b Fk(\002)g Fj(2)3274
+4865 y Fi(Q)330 4995 y Fv(which)i(r)o(eturns)e(for)g(a)h(given)g(state)
+f Ft(p)g Fv(the)h(set)g(of)g(pairs)f Fj(\()p Ft(s;)14
+b(T)e Fj(\))21 b Fv(r)o(epr)o(esenting)g(the)h(transitions)330
+5094 y(leaving)f Ft(p)p Fv(.)g(Furthermor)o(e,)g(the)g(function)h
+Fu(mer)o(ge)f Fv(takes)g(such)h(a)f(set)g(of)h(pairs)e(and)h(mer)o(ges)
+g(all)330 5194 y(pairs)d(with)i(the)e(same)h(\002rst)g(element)g(\(by)f
+(taking)h(the)g(union)h(of)e(the)h(corr)o(esponding)g(second)330
+5294 y(elements\).)i(For)g(example:)p Black Black 330
+5538 a Ff(mer)o(ge)6 b Fj(\()p Fk(f)p Fj(\()p Ft(a;)14
+b Fk(f)p Fj(1)p Ft(;)g Fj(2)p Ft(;)g Fj(4)p Fk(g)p Fj(\))p
+Ft(;)g Fj(\()p Ft(b;)g Fk(f)p Fj(2)p Ft(;)g Fj(4)p Fk(g)p
+Fj(\))p Ft(;)g Fj(\()p Ft(a;)g Fk(f)p Fj(3)p Ft(;)g Fj(4)p
+Fk(g)o Fj(\))p Ft(;)g Fj(\()p Ft(b;)g Fk(f)p Fj(5)o Ft(;)g
+Fj(6)p Fk(g)o Fj(\))p Fk(g)p Fj(\))j(=)538 5637 y Fk(f)p
+Fj(\()p Ft(a;)d Fk(f)p Fj(1)p Ft(;)g Fj(2)p Ft(;)g Fj(3)p
+Ft(;)g Fj(4)p Fk(g)p Fj(\))p Ft(;)g Fj(\()p Ft(b;)g Fk(f)p
+Fj(2)p Ft(;)g Fj(4)p Ft(;)g Fj(5)p Ft(;)g Fj(6)o Fk(g)p
+Fj(\))p Fk(g)p Black 3288 5944 a Fv(4)p Black eop
+%%Page: 5 5
+5 4 bop Black 330 91 a Fo(van)20 b(Noor)o(d)1145 b(Epsilon)17
+b(Moves)h(in)h(Subset)g(Constr)o(uction)p Black 479 357
+a Fv(The)24 b(pr)o(ocedur)o(e)e Fu(add)g Fv(is)i(r)o(esponsible)f(for)h
+(`r)o(eachable-state-set)c(maintenance',)k(by)f(en-)330
+457 y(suring)h(that)f(tar)o(get)g(subsets)g(ar)o(e)f(added)g(to)i(the)f
+(set)h(of)f(subsets)h(if)f(these)g(subsets)h(wer)o(e)e(not)330
+556 y(encounter)o(ed)d(befor)o(e.)g(Mor)o(eover)-6 b(,)18
+b(if)i(such)h(a)f(new)g(subset)g(contains)h(a)f(\002nal)g(state,)g
+(then)g(this)330 656 y(subset)h(is)g(added)e(to)i(the)g(set)g(of)g
+(\002nal)g(states.)330 855 y Fs(3)f(V)-9 b(ariants)19
+b(for)i Ft(\017)p Fs(-Moves)330 1054 y Fv(The)31 b(algorithm)i(pr)o
+(esented)d(in)i(the)f(pr)o(evious)h(section)g(does)f(not)h(tr)o(eat)e
+Ft(\017)p Fv(-moves.)i(In)f(this)330 1154 y(section,)21
+b(possible)h(extensions)f(of)g(the)g(algorithm)h(ar)o(e)d(identi\002ed)
+i(to)g(tr)o(eat)e Ft(\017)p Fv(-moves.)330 1353 y Fs(3.1)h(Per)g(graph)
+330 1453 y Fv(In)h(the)f Fu(per)g(graph)f Fv(variant)h(two)h(steps)f
+(can)g(be)g(identi\002ed.)g(In)g(the)h(\002rst)f(step,)g
+Fu(efr)o(ee)p Fv(,)h(an)f(equiv-)330 1553 y(alent)26
+b Ft(\017)p Fv(-fr)o(ee)f(automaton)h(is)h(constr)o(ucted.)g(In)g(the)f
+(second)h(step)f(this)h Ft(\017)p Fv(-fr)o(ee)e(automaton)i(is)330
+1652 y(determinised)g(using)h(the)g(subset)f(constr)o(uction)i
+(algorithm.)f(The)f(advantage)f(of)h(this)h(ap-)330 1752
+y(pr)o(oach)i(is)h(that)g(the)g(subset)g(constr)o(uction)i(algorithm)f
+(can)e(r)o(emain)g(simple)i(because)e(the)330 1851 y(input)21
+b(automaton)h(is)f Ft(\017)p Fv(-fr)o(ee.)479 1951 y(An)43
+b(algorithm)h(for)f Fu(efr)o(ee)h Fv(is)g(described)e(for)h(instance)g
+(in)h(Hopcr)o(oft)e(and)h(Ullman)330 2051 y(\(1979\)[page)29
+b(26-27].)h(The)i(main)h(ingr)o(edient)g(of)f Fu(efr)o(ee)i
+Fv(is)f(the)g(constr)o(uction)h(of)f(the)f(func-)330
+2150 y(tion)c Ft(\017)p Fv(-CLOSURE,)d(which)j(can)f(be)g(computed)g
+(by)g(using)h(a)f(standar)o(d)e(transitive)i(closur)o(e)330
+2250 y(algorithm)22 b(for)f(dir)o(ected)f(graphs:)g(this)i(algorithm)g
+(is)g(applied)e(to)i(the)f(dir)o(ected)f(graph)h(con-)330
+2350 y(sisting)27 b(of)e(all)h Ft(\017)p Fv(-moves)f(of)h
+Ft(M)9 b Fv(.)25 b(Such)g(an)h(algorithm)g(can)g(be)f(found)h(in)g
+(several)e(textbooks)330 2449 y(\(see,)c(for)g(instance,)h(Cormen,)g
+(Leiserson,)g(and)f(Rivest)h(\(1990\)\).)479 2549 y(For)31
+b(a)f(given)g(\002nite-state)g(automaton)h Ft(M)49 b
+Fj(=)40 b(\()p Ft(Q;)14 b Fj(\006)p Ft(;)g(\016)o(;)g(S;)g(F)e
+Fj(\))29 b Fu(efr)o(ee)i Fv(computes)g Ft(M)3202 2519
+y Fl(0)3265 2549 y Fj(=)330 2648 y(\()p Ft(Q;)14 b Fj(\006)p
+Ft(;)g(\016)602 2618 y Fl(0)625 2648 y Ft(;)g(S)718 2618
+y Fl(0)741 2648 y Ft(;)g(F)843 2618 y Fl(0)866 2648 y
+Fj(\))p Fv(,)46 b(wher)o(e)g Ft(S)1296 2618 y Fl(0)1389
+2648 y Fj(=)69 b Ft(\017)p Fv(-CLOSURE)o Fj(\()p Ft(S)5
+b Fj(\))p Fv(,)46 b Ft(F)2226 2618 y Fl(0)2319 2648 y
+Fj(=)69 b Ft(\017)p Fv(-CLOSURE)2904 2610 y Fl(\000)p
+Fr(1)2993 2648 y Fj(\()p Ft(F)12 b Fj(\))p Fv(,)46 b(and)330
+2748 y Ft(\016)370 2718 y Fl(0)393 2748 y Fj(\()p Ft(p;)14
+b(a)p Fj(\))42 b(=)f Fk(f)p Ft(q)s Fk(j)p Ft(q)873 2718
+y Fl(0)938 2748 y Fk(2)h Ft(\016)s Fj(\()p Ft(p)1149
+2718 y Fl(0)1172 2748 y Ft(;)14 b(a)p Fj(\))p Ft(;)g(p)1364
+2718 y Fl(0)1429 2748 y Fk(2)42 b Ft(\017)p Fv(-CLOSURE)1977
+2710 y Fl(\000)p Fr(1)2066 2748 y Fj(\()p Ft(p)p Fj(\))p
+Ft(;)14 b(q)45 b Fk(2)d Ft(\017)p Fv(-CLOSURE)n Fj(\()p
+Ft(q)2910 2718 y Fl(0)2934 2748 y Fj(\))p Fk(g)p Fv(.)30
+b(Instead)330 2848 y(of)20 b(using)h Ft(\017)p Fv(-CLOSURE)e(on)i(both)
+g(the)f(sour)o(ce)g(and)g(tar)o(get)f(side)h(of)g(a)g(transition,)g
+Fu(efr)o(ee)h Fv(can)f(be)330 2947 y(optimised)h(in)h(two)f(dif)o(fer)o
+(ent)e(ways)i(by)f(using)i Ft(\017)p Fv(-CLOSURE)d(only)j(on)f(one)h
+(side:)p Black 571 3130 a Fk(\017)p Black 16 w Fu(efr)o(ee)779
+3100 y Fi(t)809 3130 y Fu(:)e Ft(M)940 3100 y Fl(0)986
+3130 y Fj(=)j(\()p Ft(Q;)14 b Fj(\006)p Ft(;)g(\016)1346
+3100 y Fl(0)1369 3130 y Ft(;)g(S)1462 3100 y Fl(0)1485
+3130 y Ft(;)g(F)e Fj(\))p Fv(,)20 b(wher)o(e)h Ft(S)1966
+3100 y Fl(0)2012 3130 y Fj(=)h Ft(\017)p Fv(-CLOSURE)o
+Fj(\()p Ft(S)5 b Fj(\))p Fv(,)21 b(and)629 3230 y Ft(\016)669
+3199 y Fl(0)692 3230 y Fj(\()p Ft(p;)14 b(a)p Fj(\))23
+b(=)g Fk(f)p Ft(q)s Fk(j)p Ft(q)1135 3199 y Fl(0)1181
+3230 y Fk(2)g Ft(\016)s Fj(\()p Ft(p;)14 b(a)p Fj(\))p
+Ft(;)g(q)27 b Fk(2)c Ft(\017)p Fv(-CLOSURE)o Fj(\()p
+Ft(q)2188 3199 y Fl(0)2211 3230 y Fj(\))p Fk(g)p Fv(.)p
+Black 571 3396 a Fk(\017)p Black 16 w Fu(efr)o(ee)779
+3365 y Fi(s)815 3396 y Fu(:)e Ft(M)947 3365 y Fl(0)993
+3396 y Fj(=)h(\()p Ft(Q;)14 b Fj(\006)p Ft(;)g(\016)1352
+3365 y Fl(0)1375 3396 y Ft(;)g(S;)g(F)1565 3365 y Fl(0)1588
+3396 y Fj(\))p Fv(,)21 b(wher)o(e)f Ft(F)1976 3365 y
+Fl(0)2023 3396 y Fj(=)i Ft(\017)p Fv(-CLOSURE)2561 3357
+y Fl(\000)p Fr(1)2650 3396 y Fj(\()p Ft(F)12 b Fj(\))p
+Fv(,)21 b(and)629 3495 y Ft(\016)669 3465 y Fl(0)692
+3495 y Fj(\()p Ft(p;)14 b(a)p Fj(\))23 b(=)g Fk(f)p Ft(q)s
+Fk(j)p Ft(q)j Fk(2)d Ft(\016)s Fj(\()p Ft(p)1350 3465
+y Fl(0)1374 3495 y Ft(;)14 b(a)p Fj(\))p Ft(;)g(p)1566
+3465 y Fl(0)1612 3495 y Fk(2)23 b Ft(\017)p Fv(-CLOSURE)2141
+3457 y Fl(\000)p Fr(1)2230 3495 y Fj(\()p Ft(p)p Fj(\))p
+Fk(g)p Fv(.)479 3678 y(Although)d(both)e(variants)g(appear)f(very)g
+(similar)-6 b(,)18 b(ther)o(e)g(ar)o(e)e(some)j(dif)o(fer)o(ences.)d
+(Firstly)-9 b(,)330 3778 y Fu(efr)o(ee)480 3747 y Fi(t)533
+3778 y Fv(might)24 b(intr)o(oduce)e(states)h(which)g(ar)o(e)f(not)h
+Fu(co-accessible)p Fv(:)g(states)g(fr)o(om)f(which)i(no)f(path)330
+3877 y(exists)g(to)g(a)f(\002nal)h(state;)f(in)h(contrast,)g
+Fu(efr)o(ee)1700 3847 y Fi(s)1759 3877 y Fv(might)g(intr)o(oduce)g
+(states)f(which)i(ar)o(e)d(not)i Fu(acces-)330 3977 y(sible)p
+Fv(:)e(states)g(fr)o(om)e(which)j(no)f(path)f(exists)h(fr)o(om)f(the)g
+(start)g(state.)g(A)g(straightforwar)o(d)f(mod-)330 4076
+y(i\002cation)27 b(of)g(both)g(algorithms)g(is)g(possible)g(to)g(ensur)
+o(e)f(that)g(these)h(states)f(ar)o(e)f(not)j(pr)o(esent)330
+4176 y(in)i(the)g(output.)f(Thus)h Fu(efr)o(ee)1240 4146
+y Fi(t;c)1349 4176 y Fv(ensur)o(es)f(that)h(all)f(states)g(in)h(the)g
+(r)o(esulting)f(automaton)h(ar)o(e)330 4276 y(co-accessible;)24
+b Fu(efr)o(ee)995 4246 y Fi(s;a)1111 4276 y Fv(ensur)o(es)g(that)h(all)
+g(states)f(in)h(the)g(r)o(esulting)g(automaton)g(ar)o(e)e
+Fu(accessi-)330 4375 y(ble)p Fv(.)k(As)f(a)f(consequence,)i(the)f(size)
+g(of)g(the)g(determinised)g(machine)g(is)h(in)g(general)e(smaller)330
+4475 y(if)j Fu(efr)o(ee)560 4445 y Fi(t;c)667 4475 y
+Fv(is)g(employed,)g(because)f(states)h(which)h(wer)o(e)e(not)i
+(co-accessible)e(\(in)h(the)g(input\))330 4575 y(ar)o(e)c(r)o(emoved)h
+(\(this)h(is)g(ther)o(efor)o(e)e(an)h(additional)g(bene\002t)h(of)f
+Fu(efr)o(ee)2493 4544 y Fi(t;c)2573 4575 y Fv(;)g(the)h(fact)e(that)i
+Fu(efr)o(ee)3238 4544 y Fi(s;a)330 4674 y Fv(r)o(emoves)31
+b(accessible)f(states)h(has)g(no)g(ef)o(fect)f(on)h(the)g(size)g(of)g
+(the)g(determinised)g(machine)330 4774 y(because)20 b(the)h(subset)g
+(constr)o(uction)h(algorithm)g(alr)o(eady)d(ensur)o(es)h(accessibility)
+h(anyway\).)479 4873 y(Secondly)-9 b(,)37 b(it)g(turns)g(out)g(that)g
+(applying)g Fu(efr)o(ee)2038 4843 y Fi(t)2105 4873 y
+Fv(in)g(combination)i(with)e(the)g(subset-)330 4973 y(constr)o(uction)
+32 b(algorithm)g(generally)e(pr)o(oduces)f(smaller)i(automata)f(than)h
+Fu(efr)o(ee)2979 4943 y Fi(s)3045 4973 y Fv(\(even)f(if)330
+5073 y(we)21 b(ignor)o(e)g(the)g(bene\002t)g(of)g(ensuring)g
+(co-accessibility\).)g(An)f(example)h(is)g(pr)o(esented)f(in)h(\002g-)
+330 5172 y(ur)o(e)f(2.)g(The)h(dif)o(fer)o(ences)d(can)j(be)f(quite)h
+(signi\002cant.)h(This)f(is)g(illustrated)g(in)g(\002gur)o(e)f(3.)479
+5272 y(Below)g(we)f(will)h(write)f Fu(per)h(graph)1550
+5242 y Fi(X)1631 5272 y Fv(to)f(indicate)g(the)h(non-integrated)f
+(algorithm)h(based)330 5372 y(on)h Fu(efr)o(ee)594 5341
+y Fi(X)658 5372 y Fv(.)p Black 3288 5944 a(5)p Black
+eop
+%%Page: 6 6
+6 5 bop Black 330 91 a Fo(van)20 b(Noor)o(d)1145 b(Epsilon)17
+b(Moves)h(in)h(Subset)g(Constr)o(uction)p Black Black
+Black Black 1101 592 a
+ tx@Dict begin tx@NodeDict begin {5.0 2 div 6.8299 0.15997 add 2 div
+2 copy 0.15997 sub 4 2 roll Pyth 3.0 add 0.8 add} false /N@0 11 {InitCnode
+} NewNode end end
+ 1101 592 a @beginspecial @setspecial
+ tx@Dict begin STP newpath 0.8 SLW 0  setgray  5.0 2 div 6.8299 0.15997
+add 2 div 2 copy 0.15997 sub 4 2 roll Pyth 3.0 add CLW 2 div add 0
+360 arc closepath gsave 0.8 SLW 0  setgray 0 setlinecap stroke  grestore
+end
+
+
+@endspecial Fv(0)1121 565 y
+ tx@Dict begin tx@NodeDict begin {-28.44543 0.0 } false /N@start0 10
+{InitPnode } NewNode end end
+ 1121 565 a 1121 565 a
+ tx@Dict begin gsave STV newpath 0.8 SLW 0  setgray  /ArrowA { moveto
+} def /ArrowB { BeginArrow 1.  1.  scale false 0.4 1.4 1.5 2. Arrow
+ EndArrow  } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 0.0
+0 0 /N@start0 /N@0 InitNC { yB yA sub xB xA sub Atan dup 0.  add /AngleA
+ED 0.  sub 180 add /AngleB ED 0.67  0.67  NCCurve  } if end gsave 0.8
+SLW 0  setgray 0 setlinecap stroke  grestore  grestore end
+ 1121
+565 a 2281 593 a
+ tx@Dict begin tx@NodeDict begin {5.0 2 div 6.97992 0.05994 add 2 div
+2 copy 0.05994 sub 4 2 roll Pyth 3.0 add 2.6 add} false /N@1 11 {InitCnode
+} NewNode end end
+ 2281 593 a @beginspecial @setspecial
+ tx@Dict begin STP newpath 2.6 SLW 0  setgray  5.0 2 div 6.97992 0.05994
+add 2 div 2 copy 0.05994 sub 4 2 roll Pyth 3.0 add CLW 2 div add 0
+360 arc closepath gsave 2.6 SLW 0  setgray 0 setlinecap stroke  grestore
+gsave 1.0 SLW 1  setgray stroke grestore end
+
+
+@endspecial Fv(1)1691 593 y
+ tx@Dict begin tx@NodeDict begin {5.0 2 div 6.8299 0.05994 add 2 div
+2 copy 0.05994 sub 4 2 roll Pyth 3.0 add 0.8 add} false /N@2 11 {InitCnode
+} NewNode end end
+ 1691 593 a @beginspecial
+@setspecial
+ tx@Dict begin STP newpath 0.8 SLW 0  setgray  5.0 2 div 6.8299 0.05994
+add 2 div 2 copy 0.05994 sub 4 2 roll Pyth 3.0 add CLW 2 div add 0
+360 arc closepath gsave 0.8 SLW 0  setgray 0 setlinecap stroke  grestore
+end
+ 
+@endspecial Fv(2)1121 565 y
+ tx@Dict begin gsave STV newpath 0.8 SLW 0  setgray  /ArrowA { moveto
+} def /ArrowB { BeginArrow 1.  1.  scale false 0.4 1.4 1.5 2. Arrow
+ EndArrow  } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 0.0
+0 0 /N@0 /N@2 InitNC { yB yA sub xB xA sub Atan dup 15.0  add /AngleA
+ED 15.0  sub 180 add /AngleB ED 0.67  0.67  NCCurve  } if end gsave
+0.8 SLW 0  setgray 0 setlinecap stroke  grestore  grestore end
+ 1121 565 a 1121
+565 a
+ tx@Dict begin tx@NodeDict begin /t .5 def LPut end PutBegin  end
+ 1121 565 a 1121 565 a
+ tx@Dict begin { 5.0 tx@Dict /NCLW known { NCLW add } if 11.55904 4.71497
+0.15997 NAngle 90 add  Uput exch pop add a PtoC h1 add exch w1 add
+exch } PutCoor PutBegin  end
+ 1121 565 a 1073 583 a
+ tx@Dict begin tx@NodeDict begin {4.71497 0.15997 11.55904 5.77951
+2.2775 } false /N@x 16 {InitRnode } NewNode end end
+ 1073
+583 a Ft(\017)i Fv(a)1121 565 y
+ tx@Dict begin PutEnd  end
+ 1121 565 a 1121 565 a
+ tx@Dict begin PutEnd  end
+
+1121 565 a 1121 565 a
+ tx@Dict begin gsave STV newpath 0.8 SLW 0  setgray  /ArrowA { moveto
+} def /ArrowB { BeginArrow 1.  1.  scale false 0.4 1.4 1.5 2. Arrow
+ EndArrow  } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 0.0
+0 0 /N@1 /N@2 InitNC { yB yA sub xB xA sub Atan dup 15.0  add /AngleA
+ED 15.0  sub 180 add /AngleB ED 0.67  0.67  NCCurve  } if end gsave
+0.8 SLW 0  setgray 0 setlinecap stroke  grestore  grestore end
+ 1121 565 a 1121 565 a
+ tx@Dict begin tx@NodeDict begin /t .5 def LPut end PutBegin  end
+ 1121 565
+a 1121 565 a
+ tx@Dict begin { 5.0 tx@Dict /NCLW known { NCLW add } if 4.05904 4.30554
+0.0 NAngle 90 add  Uput exch pop add a PtoC h1 add exch w1 add exch
+} PutCoor PutBegin  end
+ 1121 565 a 1104 582 a
+ tx@Dict begin tx@NodeDict begin {4.30554 0.0 4.05904 2.02951 2.15277
+} false /N@x 16 {InitRnode } NewNode end end
+ 1104 582 a Ft(\017)1121
+565 y
+ tx@Dict begin PutEnd  end
+ 1121 565 a 1121 565 a
+ tx@Dict begin PutEnd  end
+ 1121 565 a 1121 565 a
+ tx@Dict begin gsave STV newpath 0.8 SLW 0  setgray  /ArrowA { moveto
+} def /ArrowB { BeginArrow 1.  1.  scale false 0.4 1.4 1.5 2. Arrow
+ EndArrow  } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 0.0
+0 0 /N@2 /N@1 InitNC { yB yA sub xB xA sub Atan dup 15.0  add /AngleA
+ED 15.0  sub 180 add /AngleB ED 0.67  0.67  NCCurve  } if end gsave
+0.8 SLW 0  setgray 0 setlinecap stroke  grestore  grestore end
+ 1121
+565 a 1121 565 a
+ tx@Dict begin tx@NodeDict begin /t .5 def LPut end PutBegin  end
+ 1121 565 a 1121 565 a
+ tx@Dict begin { 5.0 tx@Dict /NCLW known { NCLW add } if 5.0 4.71497
+0.15997 NAngle 90 add  Uput exch pop add a PtoC h1 add exch w1 add
+exch } PutCoor PutBegin  end
+ 1121 565 a 1100
+583 a
+ tx@Dict begin tx@NodeDict begin {4.71497 0.15997 5.0 2.5 2.2775 }
+false /N@x 16 {InitRnode } NewNode end end
+ 1100 583 a Fv(a)1121 565 y
+ tx@Dict begin PutEnd  end
+ 1121 565 a 1121 565
+a
+ tx@Dict begin PutEnd  end
+ 1121 565 a 1653 860 a Fv(\(1\))869 1073 y
+ tx@Dict begin tx@NodeDict begin {5.0 2 div 6.8299 0.15997 add 2 div
+2 copy 0.15997 sub 4 2 roll Pyth 3.0 add 0.8 add} false /N@0 11 {InitCnode
+} NewNode end end
+ 869 1073
+a @beginspecial @setspecial
+ tx@Dict begin STP newpath 0.8 SLW 0  setgray  5.0 2 div 6.8299 0.15997
+add 2 div 2 copy 0.15997 sub 4 2 roll Pyth 3.0 add CLW 2 div add 0
+360 arc closepath gsave 0.8 SLW 0  setgray 0 setlinecap stroke  grestore
+end
+ 
+@endspecial Fv(0)890 1748
+y
+ tx@Dict begin tx@NodeDict begin {-28.44543 84.62517 } false /N@start0
+10 {InitPnode } NewNode end end
+ 890 1748 a 890 1748 a
+ tx@Dict begin gsave STV newpath 0.8 SLW 0  setgray  /ArrowA { moveto
+} def /ArrowB { BeginArrow 1.  1.  scale false 0.4 1.4 1.5 2. Arrow
+ EndArrow  } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 0.0
+0 0 /N@start0 /N@0 InitNC { yB yA sub xB xA sub Atan dup 0.  add /AngleA
+ED 0.  sub 180 add /AngleB ED 0.67  0.67  NCCurve  } if end gsave 0.8
+SLW 0  setgray 0 setlinecap stroke  grestore  grestore end
+ 890 1748 a 1312 1777 a
+ tx@Dict begin tx@NodeDict begin {5.0 2 div 6.97992 0.05994 add 2 div
+2 copy 0.05994 sub 4 2 roll Pyth 3.0 add 2.6 add} false /N@1 11 {InitCnode
+} NewNode end end
+ 1312 1777
+a @beginspecial @setspecial
+ tx@Dict begin STP newpath 2.6 SLW 0  setgray  5.0 2 div 6.97992 0.05994
+add 2 div 2 copy 0.05994 sub 4 2 roll Pyth 3.0 add CLW 2 div add 0
+360 arc closepath gsave 2.6 SLW 0  setgray 0 setlinecap stroke  grestore
+gsave 1.0 SLW 1  setgray stroke grestore end
+ 
+@endspecial Fv(1)1312 1251
+y
+ tx@Dict begin tx@NodeDict begin {5.0 2 div 6.8299 0.05994 add 2 div
+2 copy 0.05994 sub 4 2 roll Pyth 3.0 add 0.8 add} false /N@2 11 {InitCnode
+} NewNode end end
+ 1312 1251 a @beginspecial @setspecial
+ tx@Dict begin STP newpath 0.8 SLW 0  setgray  5.0 2 div 6.8299 0.05994
+add 2 div 2 copy 0.05994 sub 4 2 roll Pyth 3.0 add CLW 2 div add 0
+360 arc closepath gsave 0.8 SLW 0  setgray 0 setlinecap stroke  grestore
+end
+ 
+@endspecial
+Fv(2)890 1748 y
+ tx@Dict begin tx@NodeDict begin {24.88976 63.29109 } false /N@start2
+10 {InitPnode } NewNode end end
+ 890 1748 a 890 1748 a
+ tx@Dict begin gsave STV newpath 0.8 SLW 0  setgray  /ArrowA { moveto
+} def /ArrowB { BeginArrow 1.  1.  scale false 0.4 1.4 1.5 2. Arrow
+ EndArrow  } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 0.0
+0 0 /N@start2 /N@2 InitNC { yB yA sub xB xA sub Atan dup 0.  add /AngleA
+ED 0.  sub 180 add /AngleB ED 0.67  0.67  NCCurve  } if end gsave 0.8
+SLW 0  setgray 0 setlinecap stroke  grestore  grestore end
+ 890 1748 a 890
+1748 a
+ tx@Dict begin gsave STV newpath 0.8 SLW 0  setgray  /ArrowA { moveto
+} def /ArrowB { BeginArrow 1.  1.  scale false 0.4 1.4 1.5 2. Arrow
+ EndArrow  } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 0.0
+0 0 /N@0 /N@2 InitNC { yB yA sub xB xA sub Atan dup 15.0  add /AngleA
+ED 15.0  sub 180 add /AngleB ED 0.67  0.67  NCCurve  } if end gsave
+0.8 SLW 0  setgray 0 setlinecap stroke  grestore  grestore end
+ 890 1748 a 890 1748 a
+ tx@Dict begin tx@NodeDict begin /t .5 def LPut end PutBegin  end
+ 890 1748 a 890 1748 a
+ tx@Dict begin { 5.0 tx@Dict /NCLW known { NCLW add } if 5.0 4.71497
+0.15997 NAngle 90 add  Uput exch pop add a PtoC h1 add exch w1 add
+exch } PutCoor PutBegin  end
+ 890
+1748 a 869 1767 a
+ tx@Dict begin tx@NodeDict begin {4.71497 0.15997 5.0 2.5 2.2775 }
+false /N@x 16 {InitRnode } NewNode end end
+ 869 1767 a Fv(a)890 1748 y
+ tx@Dict begin PutEnd  end
+ 890 1748
+a 890 1748 a
+ tx@Dict begin PutEnd  end
+ 890 1748 a 890 1748 a
+ tx@Dict begin gsave STV newpath 0.8 SLW 0  setgray  /ArrowA { moveto
+} def /ArrowB { BeginArrow 1.  1.  scale false 0.4 1.4 1.5 2. Arrow
+ EndArrow  } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 0.0
+0 0 /N@2 /N@1 InitNC { yB yA sub xB xA sub Atan dup 15.0  add /AngleA
+ED 15.0  sub 180 add /AngleB ED 0.67  0.67  NCCurve  } if end gsave
+0.8 SLW 0  setgray 0 setlinecap stroke  grestore  grestore end
+ 890 1748 a 890 1748
+a
+ tx@Dict begin tx@NodeDict begin /t .5 def LPut end PutBegin  end
+ 890 1748 a 890 1748 a
+ tx@Dict begin { 5.0 tx@Dict /NCLW known { NCLW add } if 5.0 4.71497
+0.15997 NAngle 90 add  Uput exch pop add a PtoC h1 add exch w1 add
+exch } PutCoor PutBegin  end
+ 890 1748 a 869 1767 a
+ tx@Dict begin tx@NodeDict begin {4.71497 0.15997 5.0 2.5 2.2775 }
+false /N@x 16 {InitRnode } NewNode end end
+ 869 1767
+a Fv(a)890 1748 y
+ tx@Dict begin PutEnd  end
+ 890 1748 a 890 1748 a
+ tx@Dict begin PutEnd  end
+ 890 1748 a 890
+1748 a
+ tx@Dict begin gsave STV newpath 0.8 SLW 0  setgray  /ArrowA { BeginArrow
+1.  1.  scale false 0.4 1.4 1.5 2. Arrow  EndArrow  moveto } def /ArrowB
+{ } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 0.0 0 0 /N@2
+/N@2 InitNC { /AngleA -90. def /r 14.22636 def NCCircle x y r angleA
+{ ArrowA CP } { add } ArcArrow angleB arc end } if end gsave 0.8 SLW
+0  setgray 0 setlinecap stroke  grestore  grestore end
+ 890 1748 a 890 1748 a
+ tx@Dict begin tx@NodeDict begin /t 0.5 def tx@NodeDict /HPutPos known
+{ HPutPos } { CP /Y ED /X ED /NAngle 0 def /NCLW 0 def } ifelse /Sin
+NAngle sin def /Cos NAngle cos def /s 5.0 NCLW add def /l 2.5 def /r
+2.5 def /h 1.43202 def /d 3.44292 def /flag false def HPutAdjust LPutCoor
+end PutBegin  end
+ 890 1748 a 869 1775 a
+ tx@Dict begin tx@NodeDict begin {4.71497 0.15997 5.0 2.5 2.2775 }
+false /N@x 16 {InitRnode } NewNode end end
+ 869
+1775 a Fv(a)890 1748 y
+ tx@Dict begin PutEnd  end
+ 890 1748 a 1185 1925 a Fv(\(2\))2041
+1539 y
+ tx@Dict begin tx@NodeDict begin {5.0 2 div 6.8299 0.15997 add 2 div
+2 copy 0.15997 sub 4 2 roll Pyth 3.0 add 0.8 add} false /N@0 11 {InitCnode
+} NewNode end end
+ 2041 1539 a @beginspecial @setspecial
+ tx@Dict begin STP newpath 0.8 SLW 0  setgray  5.0 2 div 6.8299 0.15997
+add 2 div 2 copy 0.15997 sub 4 2 roll Pyth 3.0 add CLW 2 div add 0
+360 arc closepath gsave 0.8 SLW 0  setgray 0 setlinecap stroke  grestore
+end
+ 
+@endspecial
+Fv(0)2062 1748 y
+ tx@Dict begin tx@NodeDict begin {-22.76672 28.4584 } false /N@start0
+10 {InitPnode } NewNode end end
+ 2062 1748 a 2062 1748 a
+ tx@Dict begin gsave STV newpath 0.8 SLW 0  setgray  /ArrowA { moveto
+} def /ArrowB { BeginArrow 1.  1.  scale false 0.4 1.4 1.5 2. Arrow
+ EndArrow  } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 0.0
+0 0 /N@start0 /N@0 InitNC { yB yA sub xB xA sub Atan dup 0.  add /AngleA
+ED 0.  sub 180 add /AngleB ED 0.67  0.67  NCCurve  } if end gsave 0.8
+SLW 0  setgray 0 setlinecap stroke  grestore  grestore end
+ 2062 1748 a
+2514 1304 a
+ tx@Dict begin tx@NodeDict begin {5.0 2 div 6.97992 0.05994 add 2 div
+2 copy 0.05994 sub 4 2 roll Pyth 3.0 add 2.6 add} false /N@1 11 {InitCnode
+} NewNode end end
+ 2514 1304 a @beginspecial @setspecial
+ tx@Dict begin STP newpath 2.6 SLW 0  setgray  5.0 2 div 6.97992 0.05994
+add 2 div 2 copy 0.05994 sub 4 2 roll Pyth 3.0 add CLW 2 div add 0
+360 arc closepath gsave 2.6 SLW 0  setgray 0 setlinecap stroke  grestore
+gsave 1.0 SLW 1  setgray stroke grestore end
+ 
+@endspecial
+Fv(1)2514 1776 y
+ tx@Dict begin tx@NodeDict begin {5.0 2 div 6.8299 0.05994 add 2 div
+2 copy 0.05994 sub 4 2 roll Pyth 3.0 add 0.8 add} false /N@2 11 {InitCnode
+} NewNode end end
+ 2514 1776 a @beginspecial @setspecial
+ tx@Dict begin STP newpath 0.8 SLW 0  setgray  5.0 2 div 6.8299 0.05994
+add 2 div 2 copy 0.05994 sub 4 2 roll Pyth 3.0 add CLW 2 div add 0
+360 arc closepath gsave 0.8 SLW 0  setgray 0 setlinecap stroke  grestore
+end
+
+
+@endspecial Fv(2)2062 1748 y
+ tx@Dict begin gsave STV newpath 0.8 SLW 0  setgray  /ArrowA { moveto
+} def /ArrowB { BeginArrow 1.  1.  scale false 0.4 1.4 1.5 2. Arrow
+ EndArrow  } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 0.0
+0 0 /N@0 /N@1 InitNC { yB yA sub xB xA sub Atan dup 20.0  add /AngleA
+ED 20.0  sub 180 add /AngleB ED 0.67  0.67  NCCurve  } if end gsave
+0.8 SLW 0  setgray 0 setlinecap stroke  grestore  grestore end
+ 2062 1748 a 2062 1748 a
+ tx@Dict begin tx@NodeDict begin /t .5 def LPut end PutBegin  end
+
+2062 1748 a 2062 1748 a
+ tx@Dict begin { 5.0 tx@Dict /NCLW known { NCLW add } if 5.0 4.71497
+0.15997 NAngle 90 add  Uput exch pop add a PtoC h1 add exch w1 add
+exch } PutCoor PutBegin  end
+ 2062 1748 a 2041 1767 a
+ tx@Dict begin tx@NodeDict begin {4.71497 0.15997 5.0 2.5 2.2775 }
+false /N@x 16 {InitRnode } NewNode end end
+ 2041
+1767 a Fv(a)2062 1748 y
+ tx@Dict begin PutEnd  end
+ 2062 1748 a 2062 1748 a
+ tx@Dict begin PutEnd  end
+ 2062
+1748 a 2062 1748 a
+ tx@Dict begin gsave STV newpath 0.8 SLW 0  setgray  /ArrowA { moveto
+} def /ArrowB { BeginArrow 1.  1.  scale false 0.4 1.4 1.5 2. Arrow
+ EndArrow  } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 0.0
+0 0 /N@0 /N@2 InitNC { yB yA sub xB xA sub Atan dup 20.0  add /AngleA
+ED 20.0  sub 180 add /AngleB ED 0.67  0.67  NCCurve  } if end gsave
+0.8 SLW 0  setgray 0 setlinecap stroke  grestore  grestore end
+ 2062 1748 a 2062 1748 a
+ tx@Dict begin tx@NodeDict begin /t .5 def LPut end PutBegin  end
+ 2062 1748
+a 2062 1748 a
+ tx@Dict begin { 5.0 tx@Dict /NCLW known { NCLW add } if 5.0 4.71497
+0.15997 NAngle 90 add  Uput exch pop add a PtoC h1 add exch w1 add
+exch } PutCoor PutBegin  end
+ 2062 1748 a 2041 1767 a
+ tx@Dict begin tx@NodeDict begin {4.71497 0.15997 5.0 2.5 2.2775 }
+false /N@x 16 {InitRnode } NewNode end end
+ 2041 1767 a Fv(a)2062
+1748 y
+ tx@Dict begin PutEnd  end
+ 2062 1748 a 2062 1748 a
+ tx@Dict begin PutEnd  end
+ 2062 1748 a 2062 1748
+a
+ tx@Dict begin gsave STV newpath 0.8 SLW 0  setgray  /ArrowA { BeginArrow
+1.  1.  scale false 0.4 1.4 1.5 2. Arrow  EndArrow  moveto } def /ArrowB
+{ } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 0.0 0 0 /N@1
+/N@1 InitNC { /AngleA -90. def /r 14.22636 def NCCircle x y r angleA
+{ ArrowA CP } { add } ArcArrow angleB arc end } if end gsave 0.8 SLW
+0  setgray 0 setlinecap stroke  grestore  grestore end
+ 2062 1748 a 2062 1748 a
+ tx@Dict begin tx@NodeDict begin /t 0.5 def tx@NodeDict /HPutPos known
+{ HPutPos } { CP /Y ED /X ED /NAngle 0 def /NCLW 0 def } ifelse /Sin
+NAngle sin def /Cos NAngle cos def /s 5.0 NCLW add def /l 2.5 def /r
+2.5 def /h 1.43202 def /d 3.44292 def /flag false def HPutAdjust LPutCoor
+end PutBegin  end
+ 2062 1748 a 2041 1775 a
+ tx@Dict begin tx@NodeDict begin {4.71497 0.15997 5.0 2.5 2.2775 }
+false /N@x 16 {InitRnode } NewNode end end
+ 2041
+1775 a Fv(a)2062 1748 y
+ tx@Dict begin PutEnd  end
+ 2062 1748 a 2062 1748 a
+ tx@Dict begin gsave STV newpath 0.8 SLW 0  setgray  /ArrowA { moveto
+} def /ArrowB { BeginArrow 1.  1.  scale false 0.4 1.4 1.5 2. Arrow
+ EndArrow  } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 0.0
+0 0 /N@2 /N@1 InitNC { yB yA sub xB xA sub Atan dup 20.0  add /AngleA
+ED 20.0  sub 180 add /AngleB ED 0.67  0.67  NCCurve  } if end gsave
+0.8 SLW 0  setgray 0 setlinecap stroke  grestore  grestore end
+ 2062
+1748 a 2062 1748 a
+ tx@Dict begin tx@NodeDict begin /t .5 def LPut end PutBegin  end
+ 2062 1748 a 2062 1748 a
+ tx@Dict begin { 5.0 tx@Dict /NCLW known { NCLW add } if 5.0 4.71497
+0.15997 NAngle 90 add  Uput exch pop add a PtoC h1 add exch w1 add
+exch } PutCoor PutBegin  end
+ 2062 1748
+a 2041 1767 a
+ tx@Dict begin tx@NodeDict begin {4.71497 0.15997 5.0 2.5 2.2775 }
+false /N@x 16 {InitRnode } NewNode end end
+ 2041 1767 a Fv(a)2062 1748 y
+ tx@Dict begin PutEnd  end
+ 2062 1748
+a 2062 1748 a
+ tx@Dict begin PutEnd  end
+ 2062 1748 a 2298 1890 a Fv(\(3\))653 2209
+y
+ tx@Dict begin tx@NodeDict begin {5.0 2 div 6.8299 0.15997 add 2 div
+2 copy 0.15997 sub 4 2 roll Pyth 3.0 add 0.8 add} false /N@0 11 {InitCnode
+} NewNode end end
+ 653 2209 a @beginspecial @setspecial
+ tx@Dict begin STP newpath 0.8 SLW 0  setgray  5.0 2 div 6.8299 0.15997
+add 2 div 2 copy 0.15997 sub 4 2 roll Pyth 3.0 add CLW 2 div add 0
+360 arc closepath gsave 0.8 SLW 0  setgray 0 setlinecap stroke  grestore
+end
+ 
+@endspecial Fv(0)674
+2182 y
+ tx@Dict begin tx@NodeDict begin {-22.76672 0.0 } false /N@start0 10
+{InitPnode } NewNode end end
+ 674 2182 a 674 2182 a
+ tx@Dict begin gsave STV newpath 0.8 SLW 0  setgray  /ArrowA { moveto
+} def /ArrowB { BeginArrow 1.  1.  scale false 0.4 1.4 1.5 2. Arrow
+ EndArrow  } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 0.0
+0 0 /N@start0 /N@0 InitNC { yB yA sub xB xA sub Atan dup 0.  add /AngleA
+ED 0.  sub 180 add /AngleB ED 0.67  0.67  NCCurve  } if end gsave 0.8
+SLW 0  setgray 0 setlinecap stroke  grestore  grestore end
+ 674 2182 a 1126 2210 a
+ tx@Dict begin tx@NodeDict begin {5.0 2 div 6.97992 0.05994 add 2 div
+2 copy 0.05994 sub 4 2 roll Pyth 3.0 add 2.6 add} false /N@1 11 {InitCnode
+} NewNode end end
+ 1126
+2210 a @beginspecial @setspecial
+ tx@Dict begin STP newpath 2.6 SLW 0  setgray  5.0 2 div 6.97992 0.05994
+add 2 div 2 copy 0.05994 sub 4 2 roll Pyth 3.0 add CLW 2 div add 0
+360 arc closepath gsave 2.6 SLW 0  setgray 0 setlinecap stroke  grestore
+gsave 1.0 SLW 1  setgray stroke grestore end
+ 
+@endspecial Fv(1)674
+2182 y
+ tx@Dict begin gsave STV newpath 0.8 SLW 0  setgray  /ArrowA { moveto
+} def /ArrowB { BeginArrow 1.  1.  scale false 0.4 1.4 1.5 2. Arrow
+ EndArrow  } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 0.0
+0 0 /N@0 /N@1 InitNC { yB yA sub xB xA sub Atan dup 20.0  add /AngleA
+ED 20.0  sub 180 add /AngleB ED 0.67  0.67  NCCurve  } if end gsave
+0.8 SLW 0  setgray 0 setlinecap stroke  grestore  grestore end
+ 674 2182 a 674 2182 a
+ tx@Dict begin tx@NodeDict begin /t .5 def LPut end PutBegin  end
+ 674 2182 a 674 2182 a
+ tx@Dict begin { 5.0 tx@Dict /NCLW known { NCLW add } if 5.0 4.71497
+0.15997 NAngle 90 add  Uput exch pop add a PtoC h1 add exch w1 add
+exch } PutCoor PutBegin  end
+ 674
+2182 a 653 2200 a
+ tx@Dict begin tx@NodeDict begin {4.71497 0.15997 5.0 2.5 2.2775 }
+false /N@x 16 {InitRnode } NewNode end end
+ 653 2200 a Fv(a)674 2182 y
+ tx@Dict begin PutEnd  end
+ 674 2182
+a 674 2182 a
+ tx@Dict begin PutEnd  end
+ 674 2182 a 674 2182 a
+ tx@Dict begin gsave STV newpath 0.8 SLW 0  setgray  /ArrowA { BeginArrow
+1.  1.  scale false 0.4 1.4 1.5 2. Arrow  EndArrow  moveto } def /ArrowB
+{ } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 0.0 0 0 /N@1
+/N@1 InitNC { /AngleA -90. def /r 14.22636 def NCCircle x y r angleA
+{ ArrowA CP } { add } ArcArrow angleB arc end } if end gsave 0.8 SLW
+0  setgray 0 setlinecap stroke  grestore  grestore end
+ 674 2182 a 674 2182
+a
+ tx@Dict begin tx@NodeDict begin /t 0.5 def tx@NodeDict /HPutPos known
+{ HPutPos } { CP /Y ED /X ED /NAngle 0 def /NCLW 0 def } ifelse /Sin
+NAngle sin def /Cos NAngle cos def /s 5.0 NCLW add def /l 2.5 def /r
+2.5 def /h 1.43202 def /d 3.44292 def /flag false def HPutAdjust LPutCoor
+end PutBegin  end
+ 674 2182 a 653 2209 a
+ tx@Dict begin tx@NodeDict begin {4.71497 0.15997 5.0 2.5 2.2775 }
+false /N@x 16 {InitRnode } NewNode end end
+ 653 2209 a Fv(a)674 2182 y
+ tx@Dict begin PutEnd  end
+ 674
+2182 a 910 2323 a Fv(\(4\))1855 2209 y
+ tx@Dict begin tx@NodeDict begin {5.0 2 div 6.8299 0.15997 add 2 div
+2 copy 0.15997 sub 4 2 roll Pyth 3.0 add 0.8 add} false /N@0 11 {InitCnode
+} NewNode end end
+ 1855 2209 a @beginspecial
+@setspecial
+ tx@Dict begin STP newpath 0.8 SLW 0  setgray  5.0 2 div 6.8299 0.15997
+add 2 div 2 copy 0.15997 sub 4 2 roll Pyth 3.0 add CLW 2 div add 0
+360 arc closepath gsave 0.8 SLW 0  setgray 0 setlinecap stroke  grestore
+end
+ 
+@endspecial Fv(0)1876 2182 y
+ tx@Dict begin tx@NodeDict begin {-22.76672 0.0 } false /N@start0 10
+{InitPnode } NewNode end end
+ 1876 2182 a
+1876 2182 a
+ tx@Dict begin gsave STV newpath 0.8 SLW 0  setgray  /ArrowA { moveto
+} def /ArrowB { BeginArrow 1.  1.  scale false 0.4 1.4 1.5 2. Arrow
+ EndArrow  } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 0.0
+0 0 /N@start0 /N@0 InitNC { yB yA sub xB xA sub Atan dup 0.  add /AngleA
+ED 0.  sub 180 add /AngleB ED 0.67  0.67  NCCurve  } if end gsave 0.8
+SLW 0  setgray 0 setlinecap stroke  grestore  grestore end
+ 1876 2182 a 2328 2210 a
+ tx@Dict begin tx@NodeDict begin {5.0 2 div 6.97992 0.05994 add 2 div
+2 copy 0.05994 sub 4 2 roll Pyth 3.0 add 2.6 add} false /N@1 11 {InitCnode
+} NewNode end end
+ 2328 2210 a @beginspecial
+@setspecial
+ tx@Dict begin STP newpath 2.6 SLW 0  setgray  5.0 2 div 6.97992 0.05994
+add 2 div 2 copy 0.05994 sub 4 2 roll Pyth 3.0 add CLW 2 div add 0
+360 arc closepath gsave 2.6 SLW 0  setgray 0 setlinecap stroke  grestore
+gsave 1.0 SLW 1  setgray stroke grestore end
+ 
+@endspecial Fv(1)2800 2210 y
+ tx@Dict begin tx@NodeDict begin {5.0 2 div 6.8299 0.05994 add 2 div
+2 copy 0.05994 sub 4 2 roll Pyth 3.0 add 2.6 add} false /N@2 11 {InitCnode
+} NewNode end end
+ 2800 2210 a
+@beginspecial @setspecial
+ tx@Dict begin STP newpath 2.6 SLW 0  setgray  5.0 2 div 6.8299 0.05994
+add 2 div 2 copy 0.05994 sub 4 2 roll Pyth 3.0 add CLW 2 div add 0
+360 arc closepath gsave 2.6 SLW 0  setgray 0 setlinecap stroke  grestore
+gsave 1.0 SLW 1  setgray stroke grestore end
+ 
+@endspecial Fv(2)1876 2182
+y
+ tx@Dict begin gsave STV newpath 0.8 SLW 0  setgray  /ArrowA { moveto
+} def /ArrowB { BeginArrow 1.  1.  scale false 0.4 1.4 1.5 2. Arrow
+ EndArrow  } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 0.0
+0 0 /N@0 /N@1 InitNC { yB yA sub xB xA sub Atan dup 20.0  add /AngleA
+ED 20.0  sub 180 add /AngleB ED 0.67  0.67  NCCurve  } if end gsave
+0.8 SLW 0  setgray 0 setlinecap stroke  grestore  grestore end
+ 1876 2182 a 1876 2182 a
+ tx@Dict begin tx@NodeDict begin /t .5 def LPut end PutBegin  end
+ 1876 2182 a 1876 2182 a
+ tx@Dict begin { 5.0 tx@Dict /NCLW known { NCLW add } if 5.0 4.71497
+0.15997 NAngle 90 add  Uput exch pop add a PtoC h1 add exch w1 add
+exch } PutCoor PutBegin  end
+ 1876
+2182 a 1855 2200 a
+ tx@Dict begin tx@NodeDict begin {4.71497 0.15997 5.0 2.5 2.2775 }
+false /N@x 16 {InitRnode } NewNode end end
+ 1855 2200 a Fv(a)1876 2182 y
+ tx@Dict begin PutEnd  end
+ 1876
+2182 a 1876 2182 a
+ tx@Dict begin PutEnd  end
+ 1876 2182 a 1876 2182 a
+ tx@Dict begin gsave STV newpath 0.8 SLW 0  setgray  /ArrowA { moveto
+} def /ArrowB { BeginArrow 1.  1.  scale false 0.4 1.4 1.5 2. Arrow
+ EndArrow  } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 0.0
+0 0 /N@1 /N@2 InitNC { yB yA sub xB xA sub Atan dup 20.0  add /AngleA
+ED 20.0  sub 180 add /AngleB ED 0.67  0.67  NCCurve  } if end gsave
+0.8 SLW 0  setgray 0 setlinecap stroke  grestore  grestore end
+ 1876 2182
+a 1876 2182 a
+ tx@Dict begin tx@NodeDict begin /t .5 def LPut end PutBegin  end
+ 1876 2182 a 1876 2182 a
+ tx@Dict begin { 5.0 tx@Dict /NCLW known { NCLW add } if 5.0 4.71497
+0.15997 NAngle 90 add  Uput exch pop add a PtoC h1 add exch w1 add
+exch } PutCoor PutBegin  end
+ 1876 2182 a 1855
+2200 a
+ tx@Dict begin tx@NodeDict begin {4.71497 0.15997 5.0 2.5 2.2775 }
+false /N@x 16 {InitRnode } NewNode end end
+ 1855 2200 a Fv(a)1876 2182 y
+ tx@Dict begin PutEnd  end
+ 1876 2182 a 1876
+2182 a
+ tx@Dict begin PutEnd  end
+ 1876 2182 a 1876 2182 a
+ tx@Dict begin gsave STV newpath 0.8 SLW 0  setgray  /ArrowA { BeginArrow
+1.  1.  scale false 0.4 1.4 1.5 2. Arrow  EndArrow  moveto } def /ArrowB
+{ } def /NCLW CLW def tx@NodeDict begin 0.0 0.0 neg 0.0 0.0 0 0 /N@2
+/N@2 InitNC { /AngleA -90. def /r 14.22636 def NCCircle x y r angleA
+{ ArrowA CP } { add } ArcArrow angleB arc end } if end gsave 0.8 SLW
+0  setgray 0 setlinecap stroke  grestore  grestore end
+ 1876 2182 a 1876 2182
+a
+ tx@Dict begin tx@NodeDict begin /t 0.5 def tx@NodeDict /HPutPos known
+{ HPutPos } { CP /Y ED /X ED /NAngle 0 def /NCLW 0 def } ifelse /Sin
+NAngle sin def /Cos NAngle cos def /s 5.0 NCLW add def /l 2.5 def /r
+2.5 def /h 1.43202 def /d 3.44292 def /flag false def HPutAdjust LPutCoor
+end PutBegin  end
+ 1876 2182 a 1855 2209 a
+ tx@Dict begin tx@NodeDict begin {4.71497 0.15997 5.0 2.5 2.2775 }
+false /N@x 16 {InitRnode } NewNode end end
+ 1855 2209 a Fv(a)1876 2182
+y
+ tx@Dict begin PutEnd  end
+ 1876 2182 a 2348 2371 a Fv(\(5\))330 2584 y Fd(Figure)d(2)330
+2667 y Fo(Illustration)h(of)f(the)h(dif)o(fer)o(ence)e(in)i(size)f
+(between)i(two)f(variants)g(of)g Fc(efr)o(ee)p Fo(.)f(\(1\))h(is)f(the)
+h(input)330 2759 y(automaton.)h(The)f(r)o(esult)e(of)i
+Fc(efr)o(ee)1297 2727 y Fg(t)1343 2759 y Fo(is)f(given)g(in)h(\(2\);)g
+(\(3\))g(is)f(the)h(r)o(esult)e(of)i Fc(efr)o(ee)2553
+2727 y Fg(s)2586 2759 y Fo(.)f(\(4\))h(and)g(\(5\))g(ar)o(e)f(the)330
+2850 y(r)o(esult)f(of)i(applying)f(the)h(subset)g(constr)o(uction)g(to)
+g(the)g(r)o(esult)f(of)g Fc(efr)o(ee)2348 2819 y Fg(t)2395
+2850 y Fo(and)h Fc(efr)o(ee)2676 2819 y Fg(s)2709 2850
+y Fo(,)f(r)o(espectively)-8 b(.)p Black Black 330 3047
+a
+ 23681433 16577003 3289088 3289088 26970521 19866091 startTexFig
+ 330 3047 a
+%%BeginDocument: csizes.ps
+/gnudict 40 dict def
+gnudict begin
+/Color false def
+/Solid true def
+/gnulinewidth 5.000 def
+/vshift -60 def
+/dl {10 mul} def
+/hpt 31.5 def
+/vpt 31.5 def
+/M {moveto} bind def
+/L {lineto} bind def
+/R {rmoveto} bind def
+/V {rlineto} bind def
+/vpt2 vpt 2 mul def
+/hpt2 hpt 2 mul def
+/Lshow { currentpoint stroke M
+  0 vshift R show } def
+/Rshow { currentpoint stroke M
+  dup stringwidth pop neg vshift R show } def
+/Cshow { currentpoint stroke M
+  dup stringwidth pop -2 div vshift R show } def
+/DL { Color {setrgbcolor Solid {pop []} if 0 setdash }
+ {pop pop pop Solid {pop []} if 0 setdash} ifelse } def
+/BL { stroke gnulinewidth 2 mul setlinewidth } def
+/AL { stroke gnulinewidth 2 div setlinewidth } def
+/PL { stroke gnulinewidth setlinewidth } def
+/LTb { BL [] 0 0 0 DL } def
+/LTa { AL [1 dl 2 dl] 0 setdash 0 0 0 setrgbcolor } def
+/LT0 { PL [] 0 1 0 DL } def
+/LT1 { PL [4 dl 2 dl] 0 0 1 DL } def
+/LT2 { PL [2 dl 3 dl] 1 0 0 DL } def
+/LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def
+/LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def
+/LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def
+/LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def
+/LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def
+/LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def
+/P { stroke [] 0 setdash
+  currentlinewidth 2 div sub M
+  0 currentlinewidth V stroke } def
+/D { stroke [] 0 setdash 2 copy vpt add M
+  hpt neg vpt neg V hpt vpt neg V
+  hpt vpt V hpt neg vpt V closepath stroke
+  P } def
+/A { stroke [] 0 setdash vpt sub M 0 vpt2 V
+  currentpoint stroke M
+  hpt neg vpt neg R hpt2 0 V stroke
+  } def
+/B { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M
+  0 vpt2 neg V hpt2 0 V 0 vpt2 V
+  hpt2 neg 0 V closepath stroke
+  P } def
+/C { stroke [] 0 setdash exch hpt sub exch vpt add M
+  hpt2 vpt2 neg V currentpoint stroke M
+  hpt2 neg 0 R hpt2 vpt2 V stroke } def
+/T { stroke [] 0 setdash 2 copy vpt 1.12 mul add M
+  hpt neg vpt -1.62 mul V
+  hpt 2 mul 0 V
+  hpt neg vpt 1.62 mul V closepath stroke
+  P  } def
+/S { 2 copy A C} def
+end
+gnudict begin
+gsave
+50 50 translate
+0.050 0.050 scale
+0 setgray
+/Palatino-Roman findfont 180 scalefont setfont
+newpath
+LTa
+1080 451 M
+5841 0 V
+-5841 0 R
+0 4498 V
+LTb
+1080 451 M
+63 0 V
+5778 0 R
+-63 0 V
+972 451 M
+(0) Rshow
+1080 901 M
+63 0 V
+5778 0 R
+-63 0 V
+972 901 M
+(2000) Rshow
+1080 1351 M
+63 0 V
+5778 0 R
+-63 0 V
+-5886 0 R
+(4000) Rshow
+1080 1800 M
+63 0 V
+5778 0 R
+-63 0 V
+-5886 0 R
+(6000) Rshow
+1080 2250 M
+63 0 V
+5778 0 R
+-63 0 V
+-5886 0 R
+(8000) Rshow
+1080 2700 M
+63 0 V
+5778 0 R
+-63 0 V
+-5886 0 R
+(10000) Rshow
+1080 3150 M
+63 0 V
+5778 0 R
+-63 0 V
+-5886 0 R
+(12000) Rshow
+1080 3600 M
+63 0 V
+5778 0 R
+-63 0 V
+-5886 0 R
+(14000) Rshow
+1080 4049 M
+63 0 V
+5778 0 R
+-63 0 V
+-5886 0 R
+(16000) Rshow
+1080 4499 M
+63 0 V
+5778 0 R
+-63 0 V
+-5886 0 R
+(18000) Rshow
+1080 4949 M
+63 0 V
+5778 0 R
+-63 0 V
+-5886 0 R
+(20000) Rshow
+1080 451 M
+0 63 V
+0 4435 R
+0 -63 V
+0 -4615 R
+(0) Cshow
+1664 451 M
+0 63 V
+0 4435 R
+0 -63 V
+0 -4615 R
+(0.2) Cshow
+2248 451 M
+0 63 V
+0 4435 R
+0 -63 V
+0 -4615 R
+(0.4) Cshow
+2832 451 M
+0 63 V
+0 4435 R
+0 -63 V
+0 -4615 R
+(0.6) Cshow
+3416 451 M
+0 63 V
+0 4435 R
+0 -63 V
+0 -4615 R
+(0.8) Cshow
+4001 451 M
+0 63 V
+0 4435 R
+0 -63 V
+0 -4615 R
+(1) Cshow
+4585 451 M
+0 63 V
+0 4435 R
+0 -63 V
+0 -4615 R
+(1.2) Cshow
+5169 451 M
+0 63 V
+0 4435 R
+0 -63 V
+0 -4615 R
+(1.4) Cshow
+5753 451 M
+0 63 V
+0 4435 R
+0 -63 V
+0 -4615 R
+(1.6) Cshow
+6337 451 M
+0 63 V
+0 4435 R
+0 -63 V
+0 -4615 R
+(1.8) Cshow
+6921 451 M
+0 63 V
+0 4435 R
+0 -63 V
+0 -4615 R
+(2) Cshow
+1080 451 M
+5841 0 V
+0 4498 V
+-5841 0 V
+0 -4498 V
+180 2700 M
+currentpoint gsave translate 90 rotate 0 0 M
+(Number of States) Cshow
+grestore
+4000 91 M
+(Deterministic Jump Density \(mean\)) Cshow
+LT0
+6318 4706 M
+(efree-source) Rshow
+6426 4706 M
+324 0 V
+1372 880 M
+292 26 V
+1956 574 L
+292 1055 V
+292 1381 V
+292 1873 V
+3124 2334 L
+292 792 V
+3708 1439 L
+293 1469 V
+4293 1550 L
+4585 714 L
+292 645 V
+5169 541 L
+292 20 V
+292 -48 V
+292 -31 V
+292 3 V
+292 11 V
+292 -19 V
+6534 4706 D
+1372 880 D
+1664 906 D
+1956 574 D
+2248 1629 D
+2540 3010 D
+2832 4883 D
+3124 2334 D
+3416 3126 D
+3708 1439 D
+4001 2908 D
+4293 1550 D
+4585 714 D
+4877 1359 D
+5169 541 D
+5461 561 D
+5753 513 D
+6045 482 D
+6337 485 D
+6629 496 D
+6921 477 D
+LT1
+6318 4526 M
+(efree-target) Rshow
+6426 4526 M
+324 0 V
+1372 877 M
+292 25 V
+1956 571 L
+292 1012 V
+292 1218 V
+292 1409 V
+3124 2002 L
+292 428 V
+3708 1114 L
+293 830 V
+4293 999 L
+4585 571 L
+292 254 V
+5169 483 L
+292 3 V
+292 -17 V
+292 -9 V
+292 0 V
+292 1 V
+292 -3 V
+6534 4526 A
+1372 877 A
+1664 902 A
+1956 571 A
+2248 1583 A
+2540 2801 A
+2832 4210 A
+3124 2002 A
+3416 2430 A
+3708 1114 A
+4001 1944 A
+4293 999 A
+4585 571 A
+4877 825 A
+5169 483 A
+5461 486 A
+5753 469 A
+6045 460 A
+6337 460 A
+6629 461 A
+6921 458 A
+stroke
+grestore
+end
+showpage
+
+%%EndDocument
+
+ endTexFig
+ 330 5230 a Fd(Figure)18 b(3)330 5313 y Fo(Dif)o(fer)o(ence)f(in)i
+(sizes)f(of)g(deterministic)g(automata)i(constr)o(ucted)f(with)h
+(either)e Fc(efr)o(ee)2740 5281 y Fg(s)2792 5313 y Fo(or)g
+Fc(efr)o(ee)3017 5281 y Fg(t)3044 5313 y Fo(,)h(for)330
+5396 y(randomly)f(generated)g(input)h(automata)h(consisting)f(of)f(100)
+i(states,)e(15)i(symbols,)d(and)i(various)330 5479 y(numbers)g(of)f
+(transitions)h(and)g(jumps)g(\(cf.)f(section)h(4\).)f(Note)h(that)h
+(all)f(states)g(in)g(the)g(input)g(ar)o(e)330 5562 y(co-accessible;)f
+(the)h(dif)o(fer)o(ence)e(in)i(size)f(is)g(due)g(solely)f(to)i(the)g
+(ef)o(fect)f(illustrated)g(in)h(\002gur)o(e)e(2.)p Black
+Black 3288 5944 a Fv(6)p Black eop
+%%Page: 7 7
+7 6 bop Black 330 91 a Fo(van)20 b(Noor)o(d)1145 b(Epsilon)17
+b(Moves)h(in)h(Subset)g(Constr)o(uction)p Black Black
+Black Black Black Black Black 933 344 a Fs(funct)p Black
+933 357 199 4 v 20 w Ff(closur)o(e)7 b Fj(\()p Ft(T)12
+b Fj(\))1016 443 y Ft(D)26 b Fj(:=)c Fk(;)p Black 1016
+543 a Fs(foreach)p Black 1016 556 282 4 v 21 w Ft(t)h
+Fk(2)g Ft(T)p Black 32 w Fs(do)p Black 1531 556 97 4
+v 41 w Fv(add)d Ft(t)h Fv(unmarked)f(to)h Ft(D)p Black
+23 w Fs(od)p Black 2472 556 V Black 1016 643 a(while)p
+Black 1016 656 217 4 v 41 w Fv(ther)o(e)f(is)h(an)f(unmarked)h(state)f
+Ft(t)j Fk(2)h Ft(D)p Black 22 w Fs(do)p Black 2490 656
+97 4 v 1254 742 a Ff(mark)10 b Fj(\()p Ft(t)p Fj(\))p
+Black 1254 842 a Fs(foreach)p Black 1254 855 282 4 v
+20 w Ft(q)26 b Fk(2)d Ft(\016)s Fj(\()p Ft(t;)14 b(\017)p
+Fj(\))p Black 21 w Fs(do)p Black 1923 855 97 4 v Black
+1337 941 a(if)p Black 1337 954 60 4 v 21 w Ft(q)35 b(=)-51
+b Fk(2)23 b Ft(D)p Black 23 w Fs(then)p Black 1651 954
+171 4 v 40 w Fv(add)d Ft(q)k Fv(unmarked)c(to)h Ft(D)p
+Black 23 w Fs(\002)p Black 2676 954 51 4 v Black 1254
+1041 a(od)p Black 1254 1054 97 4 v Black 1016 1141 a(od)p
+Black 1016 1154 V Black 1016 1240 a(return)p Black 1016
+1253 236 4 v 20 w Ft(D)p Black 933 1340 a Fs(end)p Black
+933 1353 143 4 v 330 1514 a Fd(Figure)d(4)330 1597 y
+Fo(Epsilon-closur)o(e)e(Algorithm)p Black 330 1900 a
+Fs(3.2)k(Per)g(subset)f(and)h(per)g(state)330 2000 y
+Fv(Next)i(we)f(discuss)i(two)f(variants)f(\()p Fu(per)h(subset)h
+Fv(and)e Fu(per)h(state)p Fv(\))g(in)g(which)h(the)f(tr)o(eatment)f(of)
+h Ft(\017)p Fv(-)330 2099 y(moves)17 b(is)g(integrated)g(with)g(the)g
+(subset)g(constr)o(uction)h(algorithm.)g(W)-8 b(e)17
+b(will)g(show)h(later)e(that)330 2199 y(such)27 b(an)g(integrated)f
+(appr)o(oach)f(is)i(in)g(practice)f(often)g(mor)o(e)h(ef)o(\002cient)f
+(than)h(the)g Fu(per)f(graph)330 2298 y Fv(appr)o(oach)i(if)h(ther)o(e)
+g(ar)o(e)f(many)i Ft(\017)p Fv(-moves.)f(The)g Fu(per)h(subset)h
+Fv(and)e Fu(per)g(state)g Fv(appr)o(oaches)f(ar)o(e)330
+2398 y(also)c(mor)o(e)g(suitable)g(for)f(a)h Fu(lazy)f
+Fv(implementation)i(of)f(the)g(subset)h(constr)o(uction)g(algorithm)330
+2498 y(\(in)d(such)g(a)f(lazy)g(implementation)i(subsets)f(ar)o(e)f
+(only)h(computed)g(with)h(r)o(espect)d(to)i(a)g(given)330
+2597 y(input)f(string\).)479 2697 y(The)i Fu(per)f(subset)i
+Fv(and)e(the)g Fu(per)h(state)f Fv(algorithms)i(use)e(a)g(simpli\002ed)
+h(variant)f(of)g(the)h(tran-)330 2797 y(sitive)g(closur)o(e)g
+(algorithm)h(for)f(graphs.)g(Instead)f(of)i(computing)g(the)f
+(transitive)g(closur)o(e)g(of)330 2896 y(a)i(given)i(graph,)e(this)i
+(algorithm)f(only)h(computes)g(the)f(closur)o(e)f(for)h(a)f(given)i
+(set)f(of)f(states.)330 2996 y(Such)c(an)f(algorithm)i(is)f(given)g(in)
+g(\002gur)o(e)f(4.)479 3095 y(In)i(both)g(of)f(the)g(two)h(integrated)f
+(appr)o(oaches,)e(the)i(subset)h(constr)o(uction)h(algorithm)f(is)330
+3195 y(initialised)k(with)g(an)f(agenda)f(containing)i(a)f(single)h
+(subset)f(which)h(is)g(the)f Ft(\017)p Fv(-CLOSURE)f(of)330
+3295 y(the)h(set)f(of)g(start-states)g(of)g(the)h(input;)g(furthermor)o
+(e,)e(the)i(way)f(in)h(which)g(new)g(transitions)330
+3394 y(ar)o(e)j(computed)i(also)g(takes)f(the)h(ef)o(fect)e(of)i
+Ft(\017)p Fv(-moves)f(into)i(account.)e(Both)h(dif)o(fer)o(ences)d(ar)o
+(e)330 3494 y(accounted)20 b(for)h(by)g(an)f(alternative)g
+(de\002nition)i(of)f(the)f Fu(epsilon)p 2339 3494 25
+4 v 31 w(closur)o(e)h Fv(function.)479 3594 y(The)c(appr)o(oach)d(in)j
+(which)g(the)f(transitive)g(closur)o(e)g(is)h(computed)f(for)g(one)h
+(state)e(at)h(a)g(time)330 3693 y(is)25 b(de\002ned)e(by)h(the)h
+(following)g(de\002nition)h(of)e(the)g Fu(epsilon)p 2210
+3693 V 30 w(closur)o(e)h Fv(function.)g(Note)f(that)g(we)330
+3793 y(make)c(sur)o(e)g(that)h(the)g(transitive)f(closur)o(e)h
+(computation)g(is)g(only)h(performed)d(once)i(for)g(each)330
+3892 y(input)f(state,)e(by)i(memorising)g(the)g Fu(closur)o(e)f
+Fv(function;)h(the)g(full)f(computation)h(is)g(memorised)330
+3992 y(as)g(well.)626 3960 y Fn(4)p Black Black Black
+330 4258 a Fs(funct)p Black 330 4271 199 4 v 20 w Ff(epsilon)p
+820 4258 25 4 v 31 w(closur)o(e)6 b Fj(\()p Ft(U)j Fj(\))1405
+b Fv(variant)20 b(2:)g(per)g(state)p Black 413 4357 a
+Fs(return)p Black 413 4370 236 4 v 20 w Ff(memo)7 b Fj(\()939
+4295 y Fe(S)1009 4382 y Fi(u)p Fl(2)p Fi(U)1162 4357
+y Ff(memo)g Fj(\()p Ff(closur)o(e)g Fj(\()p Fk(f)p Ft(u)p
+Fk(g)p Fj(\)\)\))p Black 330 4457 a Fs(end)p Black 330
+4470 143 4 v 479 4623 a Fv(In)23 b(the)g(case)f(of)h(the)g
+Fu(per)g(subset)h Fv(appr)o(oach,)d(the)i(closur)o(e)f(algorithm)i(is)f
+(applied)e(to)j(each)330 4723 y(subset.)f(W)-8 b(e)24
+b(also)f(memorise)h(the)g(closur)o(e)f(function,)h(in)g(or)o(der)e(to)i
+(ensur)o(e)e(that)i(the)f(closur)o(e)330 4822 y(computation)j(is)f
+(performed)f(only)h(once)g(for)g(each)f(subset.)h(This)g(can)g(be)f
+(useful)h(since)g(the)330 4922 y(same)d(subset)h(can)f(be)g(generated)g
+(many)g(times)h(during)g(subset)g(constr)o(uction.)h(The)e(de\002ni-)
+330 5022 y(tion)g(simply)f(is:)p Black Black Black 330
+5287 a Fs(funct)p Black 330 5300 199 4 v 20 w Ff(epsilon)p
+820 5287 25 4 v 31 w(closur)o(e)6 b Fj(\()p Ft(U)j Fj(\))1343
+b Fv(variant)20 b(3:)g(per)g(subset)p Black 330 5457
+1495 4 v 373 5535 a Fp(4)d(This)f(is)i(an)e(impr)o(ovement)f(over)h
+(the)g(algorithm)h(given)f(in)g(a)h(pr)o(eliminary)g(version)g(of)g
+(this)f(paper)h(\(van)423 5610 y(Noor)o(d,)g(1998\).)p
+Black Black 3288 5944 a Fv(7)p Black eop
+%%Page: 8 8
+8 7 bop Black 330 91 a Fo(van)20 b(Noor)o(d)1145 b(Epsilon)17
+b(Moves)h(in)h(Subset)g(Constr)o(uction)p Black Black
+413 357 a Fs(return)p Black 413 370 236 4 v 20 w Ff(memo)7
+b Fj(\()p Ff(closur)o(e)g Fj(\()p Ft(U)i Fj(\)\))p Black
+330 457 a Fs(end)p Black 330 470 143 4 v 479 606 a Fv(The)17
+b(motivation)h(for)f(the)g Fu(per)g(state)f Fv(variant)g(is)h(the)g
+(insight)i(that)d(in)i(this)f(case)f(the)h(closur)o(e)330
+706 y(algorithm)31 b(is)g(called)e(at)h(most)i Fk(j)p
+Ft(Q)p Fk(j)e Fv(times.)h(In)f(contrast,)g(in)h(the)g
+Fu(per)f(subset)i Fv(appr)o(oach)d(the)330 806 y(transitive)c(closur)o
+(e)f(algorithm)i(may)f(need)f(to)i(be)e(called)g Fj(2)2258
+776 y Fl(j)p Fi(Q)p Fl(j)2379 806 y Fv(times.)h(On)g(the)g(other)g
+(hand,)330 905 y(in)19 b(the)f Fu(per)g(state)g Fv(appr)o(oach)f(some)h
+(over)o(head)f(must)i(be)f(accepted)e(for)i(computing)i(the)e(union)330
+1005 y(of)27 b(the)g(r)o(esults)f(for)h(each)f(state.)g(Mor)o(eover)-6
+b(,)26 b(in)h(practice)f(the)h(number)g(of)f(subsets)i(is)f(often)330
+1105 y(much)c(smaller)f(than)h Fj(2)1084 1074 y Fl(j)p
+Fi(Q)p Fl(j)1179 1105 y Fv(.)g(In)f(some)h(cases,)f(the)h(number)f(of)h
+(r)o(eachable)d(subsets)j(is)g(smaller)330 1204 y(than)e(the)g(number)g
+(of)g(states)f(encounter)o(ed)g(in)h(those)h(subsets.)330
+1403 y Fs(3.3)e(Implementation)330 1503 y Fv(In)f(or)o(der)f(to)i
+(implement)g(the)f(algorithms)h(ef)o(\002ciently)f(in)h(Pr)o(olog,)f
+(it)g(is)h(important)f(to)h(use)f(ef-)330 1603 y(\002cient)g(data-str)o
+(uctur)o(es.)e(In)i(particular)-6 b(,)17 b(we)i(use)g(an)g
+(implementation)h(of)e(\(non-updatable\))330 1702 y(arrays)h(based)g
+(on)i(the)f(N+K)h(tr)o(ees)e(of)h(O'Keefe)g(\(1990,)e(pp.142-145\))e
+(with)21 b(N=95)e(and)h(K=32.)330 1802 y(On)f(top)f(of)g(this)g
+(datastr)o(uctur)o(e,)e(a)i(hash)g(array)f(is)h(implemented)g(using)h
+(the)f(SICStus)g(library)330 1902 y(pr)o(edicate)23 b
+Fb(term)p 901 1902 25 4 v 29 w(hash/4)g Fv(which)j(constr)o(ucts)f(a)f
+(key)h(for)f(a)g(given)h(term.)f(In)h(such)g(hashes,)330
+2001 y(a)h(value)f(in)i(the)g(underlying)f(array)f(is)i(a)f(partial)f
+(list)i(of)f(key-value)g(pairs;)f(thus)i(collisions)330
+2101 y(ar)o(e)22 b(r)o(esolved)h(by)h(chaining.)g(This)g(pr)o(ovides)f
+(ef)o(\002cient)g(access)g(in)i(practice,)d(although)j(such)330
+2200 y(arrays)17 b(ar)o(e)f(quite)j(memory-intensive:)f(car)o(e)e(must)
+j(be)e(taken)h(to)g(ensur)o(e)g(that)f(the)h(determin-)330
+2300 y(istic)f(algorithms)h(indeed)e(ar)o(e)f(implemented)i(without)h
+(intr)o(oducing)f(choice-points)h(during)330 2400 y(r)o(untime.)330
+2599 y Fs(4)i(Experiments)330 2798 y Fv(T)-7 b(wo)22
+b(sets)f(of)h(experiments)f(have)g(been)h(performed.)e(In)i(the)g
+(\002rst)f(set)h(of)g(experiments,)f(ran-)330 2898 y(dom)33
+b(automata)e(ar)o(e)g(generated)g(accor)o(ding)h(to)g(a)g(number)g(of)h
+(criteria)e(based)g(on)i(Leslie)330 2997 y(\(1995\).)13
+b(In)j(the)g(second)g(set)g(of)f(experiments,)h(r)o(esults)f(ar)o(e)g
+(pr)o(ovided)f(for)i(a)f(number)h(of)g(\(much)330 3097
+y(lar)o(ger\))i(automata)h(that)h(surfaced)f(during)h(actual)f
+(development)g(work)i(on)f(\002nite-state)g(ap-)330 3197
+y(pr)o(oximation)h(techniques.)1241 3165 y Fn(5)330 3396
+y Fu(Random)34 b(automata.)d Fv(Firstly)-9 b(,)35 b(we)g(r)o(eport)g
+(on)g(a)g(number)g(of)g(experiments)g(for)g(randomly)330
+3496 y(generated)30 b(automata.)g(Following)j(Leslie)d(\(1995\),)e(the)
+j Fu(absolute)h(transition)f(density)f Fv(of)h(an)330
+3595 y(automaton)g(is)f(de\002ned)g(as)f(the)i(number)f(of)g
+(transitions)h(divided)e(by)h(the)g(squar)o(e)g(of)g(the)330
+3695 y(number)25 b(of)f(states)h(multiplied)g(by)g(the)f(number)h(of)g
+(symbols)h(\(i.e.)d(the)i(number)g(of)f(transi-)330 3794
+y(tions)19 b(divided)e(by)i(the)f(maximum)g(number)h(of)f(`possible')h
+(transitions,)g(or)-6 b(,)17 b(in)i(other)f(wor)o(ds,)330
+3894 y(the)k(pr)o(obability)f(that)h(a)f(possible)i(transition)f(in)h
+(fact)e(exists\).)g Fu(Deterministic)h(transition)f(den-)330
+3994 y(sity)f Fv(is)h(the)g(number)g(of)g(transitions)h(divided)e(by)h
+(the)g(number)f(of)h(states)g(multiplied)g(by)g(the)330
+4093 y(number)26 b(of)g(symbols)h(\(i.e.)e(the)i(ratio)e(of)h(the)h
+(number)f(of)g(transitions)h(and)e(the)i(maximum)330
+4193 y(number)21 b(of)g(`possible')g(transitions)h(in)f(a)g
+(deterministic)g(machine\).)479 4293 y(In)28 b(both)g(of)f(these)g
+(de\002nitions,)h(the)f(number)h(of)f(transitions)h(should)g(be)f
+(understood)330 4392 y(as)f(the)g(the)h(number)f(of)h(non-duplicate)f
+(transitions)h(which)g(do)g(not)g(lead)e(to)i(a)f(sink)h(state.)330
+4492 y(A)c(sink)h(state)f(is)h(a)f(state)g(fr)o(om)g(which)h(ther)o(e)f
+(exists)g(no)i(sequence)e(of)h(transitions)g(to)g(a)f(\002nal)330
+4591 y(state.)g(In)g(the)h(randomly)f(generated)g(automata,)f(states)h
+(ar)o(e)f(accessible)h(and)g(co-accessible)330 4691 y(by)e(constr)o
+(uction;)h(sink)g(states)e(and)h(associated)f(transitions)h(ar)o(e)f
+(not)h(r)o(epr)o(esented.)479 4791 y(Leslie)g(\(1995\))e(shows)k(that)e
+Fu(deterministic)g(transition)g(density)g Fv(is)g(a)g(r)o(eliable)f
+(measur)o(e)g(for)330 4890 y(the)k(dif)o(\002culty)g(of)g(subset)h
+(constr)o(uction.)g(Exponential)g(blow-up)f(can)g(be)g(expected)f(for)h
+(in-)330 4990 y(put)34 b(automata)e(with)j(deterministic)f(transition)g
+(density)g(of)f(ar)o(ound)g(2.)2753 4958 y Fn(6)2820
+4990 y Fv(He)h(concludes)330 5090 y(\(page)20 b(66\):)p
+Black Black 629 5252 a([.)12 b(.)g(.)g(])27 b(randomly)g(generated)f
+(automata)g(exhibit)i(the)f(maximum)g(execu-)p Black
+330 5413 1495 4 v 373 5491 a Fp(5)17 b(All)g(the)f(automata)g(used)g
+(in)h(the)f(experiments)g(ar)o(e)g(fr)o(eely)h(available)g(fr)o(om)423
+5566 y(http://www)-6 b(.let.r)o(ug.nl/\230vannoor)o(d/Fsa/.)373
+5637 y(6)17 b(Leslie)g(uses)f(the)g(terms)g Fh(absolute)i(density)f
+Fp(and)f Fh(deterministic)h(density)p Fp(.)p Black Black
+3288 5944 a Fv(8)p Black eop
+%%Page: 9 9
+9 8 bop Black 330 91 a Fo(van)20 b(Noor)o(d)1145 b(Epsilon)17
+b(Moves)h(in)h(Subset)g(Constr)o(uction)p Black Black
+330 1687 a
+ 23681433 16577003 3289088 3289088 26970521 19866091 startTexFig
+ 330 1687 a
+%%BeginDocument: dts25n.ps
+/gnudict 40 dict def
+gnudict begin
+/Color false def
+/Solid true def
+/gnulinewidth 5.000 def
+/vshift -60 def
+/dl {10 mul} def
+/hpt 31.5 def
+/vpt 31.5 def
+/M {moveto} bind def
+/L {lineto} bind def
+/R {rmoveto} bind def
+/V {rlineto} bind def
+/vpt2 vpt 2 mul def
+/hpt2 hpt 2 mul def
+/Lshow { currentpoint stroke M
+  0 vshift R show } def
+/Rshow { currentpoint stroke M
+  dup stringwidth pop neg vshift R show } def
+/Cshow { currentpoint stroke M
+  dup stringwidth pop -2 div vshift R show } def
+/DL { Color {setrgbcolor Solid {pop []} if 0 setdash }
+ {pop pop pop Solid {pop []} if 0 setdash} ifelse } def
+/BL { stroke gnulinewidth 2 mul setlinewidth } def
+/AL { stroke gnulinewidth 2 div setlinewidth } def
+/PL { stroke gnulinewidth setlinewidth } def
+/LTb { BL [] 0 0 0 DL } def
+/LTa { AL [1 dl 2 dl] 0 setdash 0 0 0 setrgbcolor } def
+/LT0 { PL [] 0 1 0 DL } def
+/LT1 { PL [4 dl 2 dl] 0 0 1 DL } def
+/LT2 { PL [2 dl 3 dl] 1 0 0 DL } def
+/LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def
+/LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def
+/LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def
+/LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def
+/LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def
+/LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def
+/P { stroke [] 0 setdash
+  currentlinewidth 2 div sub M
+  0 currentlinewidth V stroke } def
+/D { stroke [] 0 setdash 2 copy vpt add M
+  hpt neg vpt neg V hpt vpt neg V
+  hpt vpt V hpt neg vpt V closepath stroke
+  P } def
+/A { stroke [] 0 setdash vpt sub M 0 vpt2 V
+  currentpoint stroke M
+  hpt neg vpt neg R hpt2 0 V stroke
+  } def
+/B { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M
+  0 vpt2 neg V hpt2 0 V 0 vpt2 V
+  hpt2 neg 0 V closepath stroke
+  P } def
+/C { stroke [] 0 setdash exch hpt sub exch vpt add M
+  hpt2 vpt2 neg V currentpoint stroke M
+  hpt2 neg 0 R hpt2 vpt2 V stroke } def
+/T { stroke [] 0 setdash 2 copy vpt 1.12 mul add M
+  hpt neg vpt -1.62 mul V
+  hpt 2 mul 0 V
+  hpt neg vpt 1.62 mul V closepath stroke
+  P  } def
+/S { 2 copy A C} def
+end
+gnudict begin
+gsave
+50 50 translate
+0.050 0.050 scale
+0 setgray
+/Palatino-Roman findfont 180 scalefont setfont
+newpath
+LTa
+LTb
+1080 451 M
+63 0 V
+5778 0 R
+-63 0 V
+972 451 M
+(1) Rshow
+1080 677 M
+31 0 V
+5810 0 R
+-31 0 V
+1080 975 M
+31 0 V
+5810 0 R
+-31 0 V
+1080 1128 M
+31 0 V
+5810 0 R
+-31 0 V
+-5810 73 R
+63 0 V
+5778 0 R
+-63 0 V
+-5886 0 R
+(10) Rshow
+1080 1426 M
+31 0 V
+5810 0 R
+-31 0 V
+1080 1725 M
+31 0 V
+5810 0 R
+-31 0 V
+1080 1878 M
+31 0 V
+5810 0 R
+-31 0 V
+-5810 72 R
+63 0 V
+5778 0 R
+-63 0 V
+-5886 0 R
+(100) Rshow
+1080 2176 M
+31 0 V
+5810 0 R
+-31 0 V
+1080 2474 M
+31 0 V
+5810 0 R
+-31 0 V
+1080 2627 M
+31 0 V
+5810 0 R
+-31 0 V
+-5810 73 R
+63 0 V
+5778 0 R
+-63 0 V
+-5886 0 R
+(1000) Rshow
+1080 2926 M
+31 0 V
+5810 0 R
+-31 0 V
+1080 3224 M
+31 0 V
+5810 0 R
+-31 0 V
+1080 3377 M
+31 0 V
+5810 0 R
+-31 0 V
+-5810 73 R
+63 0 V
+5778 0 R
+-63 0 V
+-5886 0 R
+(10000) Rshow
+1080 3675 M
+31 0 V
+5810 0 R
+-31 0 V
+1080 3974 M
+31 0 V
+5810 0 R
+-31 0 V
+1080 4127 M
+31 0 V
+5810 0 R
+-31 0 V
+-5810 72 R
+63 0 V
+5778 0 R
+-63 0 V
+-5886 0 R
+(100000) Rshow
+1080 4425 M
+31 0 V
+5810 0 R
+-31 0 V
+1080 4723 M
+31 0 V
+5810 0 R
+-31 0 V
+1080 4876 M
+31 0 V
+5810 0 R
+-31 0 V
+-5810 73 R
+63 0 V
+5778 0 R
+-63 0 V
+-5886 0 R
+(1e+06) Rshow
+1479 451 M
+0 31 V
+0 4467 R
+0 -31 V
+2042 451 M
+0 31 V
+0 4467 R
+0 -31 V
+2441 451 M
+0 31 V
+0 4467 R
+0 -31 V
+2751 451 M
+0 31 V
+0 4467 R
+0 -31 V
+3004 451 M
+0 31 V
+0 4467 R
+0 -31 V
+3217 451 M
+0 31 V
+0 4467 R
+0 -31 V
+3403 451 M
+0 31 V
+0 4467 R
+0 -31 V
+3566 451 M
+0 31 V
+0 4467 R
+0 -31 V
+3712 451 M
+0 63 V
+0 4435 R
+0 -63 V
+0 -4615 R
+(1) Cshow
+4674 451 M
+0 31 V
+0 4467 R
+0 -31 V
+5237 451 M
+0 31 V
+0 4467 R
+0 -31 V
+5636 451 M
+0 31 V
+0 4467 R
+0 -31 V
+5945 451 M
+0 31 V
+0 4467 R
+0 -31 V
+6198 451 M
+0 31 V
+0 4467 R
+0 -31 V
+6412 451 M
+0 31 V
+0 4467 R
+0 -31 V
+6598 451 M
+0 31 V
+0 4467 R
+0 -31 V
+6761 451 M
+0 31 V
+0 4467 R
+0 -31 V
+6907 451 M
+0 63 V
+0 4435 R
+0 -63 V
+0 -4615 R
+(10) Cshow
+1080 451 M
+5841 0 V
+0 4498 V
+-5841 0 V
+0 -4498 V
+180 2700 M
+currentpoint gsave translate 90 rotate 0 0 M
+(CPU-time \(msec\) / Number of States \(input+output\)) Cshow
+grestore
+4000 91 M
+(Deterministic Density) Cshow
+LT0
+6318 4706 M
+(fsa) Rshow
+6534 4706 D
+1479 1070 D
+2042 1558 D
+2441 1950 D
+2751 2617 D
+3004 2859 D
+3217 3229 D
+3403 3308 D
+3566 3601 D
+3712 3914 D
+3845 4026 D
+3965 4198 D
+4076 4274 D
+4179 4434 D
+4364 4541 D
+5369 4438 D
+5636 3841 D
+5945 3431 D
+6412 2687 D
+6907 2481 D
+LT1
+6318 4526 M
+(fsm) Rshow
+6534 4526 A
+1479 1070 A
+2042 1426 A
+2441 1558 A
+2751 2151 A
+3004 2418 A
+3217 2849 A
+3403 2950 A
+3566 3316 A
+3712 3676 A
+3845 3813 A
+3965 3982 A
+4076 4049 A
+4179 4262 A
+4364 4332 A
+5369 4329 A
+5636 3756 A
+5945 3371 A
+6412 2693 A
+6907 2499 A
+LT2
+6318 4346 M
+(states) Rshow
+6534 4346 B
+1479 1624 B
+2042 2067 B
+2441 2350 B
+2751 2865 B
+3004 3043 B
+3217 3348 B
+3403 3412 B
+3566 3624 B
+3712 3893 B
+3845 3981 B
+3965 4106 B
+4076 4154 B
+4179 4314 B
+4364 4359 B
+5369 4018 B
+5636 3372 B
+5945 2909 B
+6412 2125 B
+6907 1905 B
+stroke
+grestore
+end
+showpage
+
+%%EndDocument
+
+ endTexFig
+ 330 3871 a Fd(Figure)f(5)330 3954 y Fo(Deterministic)g(transition)h
+(density)f(versus)g(CPU-time)g(in)h(msec.)f(The)h(input)g(automata)h
+(have)g(25)330 4037 y(states,)f(15)g(symbols,)e(and)i(no)g
+Fa(\017)p Fo(-moves.)f Fc(fsa)h Fo(r)o(epr)o(esents)d(the)k(CPU-time)e
+(r)o(equir)o(ed)e(by)j(our)f(FSA6)330 4120 y(implementation;)h
+Fc(fsm)g Fo(r)o(epr)o(esents)d(the)j(CPU-time)g(r)o(equir)o(ed)d(by)i
+(A)-6 b(T&T's)19 b(FSM)f(library;)f Fc(states)330 4203
+y Fo(r)o(epr)o(esents)g(the)i(sum)f(of)h(the)g(number)g(of)f(states)h
+(of)f(the)i(input)f(and)g(output)g(automata.)p Black
+Black 3288 5944 a Fv(9)p Black eop
+%%Page: 10 10
+10 9 bop Black 330 91 a Fo(van)20 b(Noor)o(d)1145 b(Epsilon)17
+b(Moves)h(in)h(Subset)g(Constr)o(uction)p Black 629 357
+a Fv(tion)k(time,)f(and)g(the)h(maximum)g(number)f(of)h(states,)e(at)h
+(an)h(appr)o(oximate)629 457 y(deterministic)c(density)g(of)f(2.)g
+(Most)h(of)f(the)h(ar)o(ea)d(under)i(the)h(curve)f(occurs)629
+556 y(within)k(0.5)e(and)h(2.5)f(deterministic)i(density\227this)g(is)g
+(the)f(ar)o(ea)f(in)h(which)629 656 y(subset)g(constr)o(uction)h(is)f
+(expensive.)629 789 y Fs(Conjecture.)d Fv(For)i(a)g(given)h(NF)-6
+b(A,)19 b(we)h(can)g(compute)h(the)f(expected)f(num-)629
+888 y(bers)g(of)g(states)g(and)g(transitions)i(in)f(the)f(corr)o
+(esponding)g(DF)-6 b(A,)19 b(pr)o(oduced)629 988 y(by)g(subset)g
+(constr)o(uction,)h(fr)o(om)f(the)g(deterministic)g(density)g(of)g(the)
+g(NF)-6 b(A.)629 1088 y(In)18 b(addition,)g(this)h(functional)f(r)o
+(elationship)g(gives)h(rise)f(to)g(a)g(Poisson-like)629
+1187 y(curve)i(with)i(its)f(peak)f(appr)o(oximately)f(at)i(a)f
+(deterministic)h(density)g(of)g(2.)479 1370 y(A)h(number)h(of)f
+(automata)f(wer)o(e)g(generated)g(randomly)-9 b(,)22
+b(accor)o(ding)g(to)g(the)h(number)f(of)330 1469 y(states,)32
+b(symbols,)g(and)g(transition)h(density)-9 b(.)32 b(For)g(the)g
+(\002rst)g(experiment,)g(automata)f(wer)o(e)330 1569
+y(generated)i(consisting)j(of)e(15)f(symbols,)i(25)e(states,)g(and)h
+(various)g(densities)g(\(and)f(no)i Ft(\017)p Fv(-)330
+1669 y(moves\).)22 b(The)f(r)o(esults)g(ar)o(e)g(summarised)g(in)h
+(\002gur)o(e)g(5.)e(CPU-time)i(was)f(measur)o(ed)f(on)j(a)e(HP)330
+1768 y(9000/785)c(machine)j(r)o(unning)h(HP-UX)f(10.20.)d(Note)j(that)g
+(our)g(timings)h(do)f(not)g(include)g(the)330 1868 y(start-up)g(of)h
+(the)g(Pr)o(olog)g(engine,)g(nor)g(the)g(time)g(r)o(equir)o(ed)e(for)i
+(garbage)e(collection.)479 1968 y(In)26 b(or)o(der)d(to)j(establish)f
+(that)f(the)h(dif)o(fer)o(ences)e(we)i(obtain)g(later)f(ar)o(e)g
+(genuinely)h(due)g(to)330 2067 y(dif)o(fer)o(ences)30
+b(in)k(the)e(underlying)i(algorithm,)f(and)f(not)i(due)e(to)h
+(`accidental')f(implemen-)330 2167 y(tation)h(details,)g(we)g(have)f
+(compar)o(ed)g(our)h(implementation)h(with)g(the)f(determiniser)g(of)
+330 2267 y(A)-6 b(T&T's)30 b(FSM)f(utilities)i(\(Mohri,)f(Per)o(eira,)f
+(and)h(Riley)-9 b(,)31 b(1998\).)d(For)i(automata)g(without)i
+Ft(\017)p Fv(-)330 2366 y(moves)19 b(we)f(establish)g(that)g(FSM)f
+(normally)i(is)f(faster:)f(for)h(automata)f(with)i(very)e(small)i
+(tran-)330 2466 y(sition)24 b(densities)g(FSM)f(is)g(up)g(to)h(four)f
+(times)h(as)f(fast,)f(for)h(automata)g(with)h(lar)o(ger)e(densities)330
+2565 y(the)f(r)o(esults)f(ar)o(e)g(similar)-6 b(.)479
+2665 y(A)27 b(new)g(concept)g(called)g Fu(absolute)g(jump)f(density)h
+Fv(is)g(intr)o(oduced)g(to)g(specify)g(the)g(num-)330
+2765 y(ber)h(of)g Ft(\017)p Fv(-moves.)g(It)g(is)h(de\002ned)e(as)h
+(the)h(number)f(of)g Ft(\017)p Fv(-moves)g(divided)g(by)g(the)g(squar)o
+(e)g(of)330 2864 y(the)c(number)h(of)f(states)g(\(i.e.,)f(the)h(pr)o
+(obability)g(that)g(an)g Ft(\017)p Fv(-move)g(exists)g(for)g(a)g(given)
+g(pair)g(of)330 2964 y(states\).)i(Furthermor)o(e,)h
+Fu(deterministic)g(jump)g(density)f Fv(is)i(the)f(number)h(of)f
+Ft(\017)p Fv(-moves)g(divided)330 3064 y(by)d(the)g(number)g(of)g
+(states)g(\(i.e.,)f(the)h(average)e(number)i(of)g Ft(\017)p
+Fv(-moves)g(which)h(leave)e(a)h(given)330 3163 y(state\).)j(In)i(or)o
+(der)e(to)i(measur)o(e)e(the)i(dif)o(fer)o(ences)d(between)i(the)g(thr)
+o(ee)g(implementations,)h(a)330 3263 y(number)g(of)f(automata)g(has)h
+(been)f(generated)f(consisting)k(of)d(15)g(states)g(and)g(15)g
+(symbols,)330 3362 y(using)33 b(various)f(transition)h(densities)g
+(between)f(0.01)e(and)i(0.3)f(\(for)g(lar)o(ger)g(densities)i(the)330
+3462 y(automata)d(tend)g(to)h(collapse)f(to)h(an)f(automaton)h(for)g
+Fj(\006)2184 3432 y Fl(\003)2222 3462 y Fv(\).)e(For)i(each)f(of)h
+(these)f(transition)330 3562 y(densities,)19 b(deterministic)h(jump)g
+(densities)g(wer)o(e)e(chosen)i(in)g(the)f(range)g(0)g(to)h(2.5)e
+(\(again,)g(for)330 3661 y(lar)o(ger)f(values)g(the)h(automata)f(tend)h
+(to)g(collapse\).)f(In)h(\002gur)o(es)g(6)f(to)36 b(9)17
+b(the)h(outcomes)h(of)f(these)330 3761 y(experiments)j(ar)o(e)g
+(summarised)g(by)h(listing)h(the)f(average)e(amount)i(of)f(CPU-time)g
+(r)o(equir)o(ed)330 3861 y(per)k(deterministic)g(jump)h(density)f
+(\(for)g(each)f(of)h(the)g(algorithms\),)h(using)g(automata)e(with)330
+3960 y(15,)16 b(20,)h(25)g(and)g(100)f(states)h(r)o(espectively)-9
+b(.)17 b(Thus,)g(every)h(dot)f(r)o(epr)o(esents)g(the)g(average)f(for)i
+(de-)330 4060 y(terminising)k(a)d(number)i(of)f(dif)o(fer)o(ent)e
+(input)j(automata)f(with)h(various)f(absolute)g(transition)330
+4159 y(densities)h(and)f(the)h(same)g(deterministic)g(jump)g(density)-9
+b(.)479 4259 y(The)18 b(striking)g(aspect)e(of)i(these)f(experiments)g
+(is)g(that)h(the)f(integrated)g Fu(per)g(subset)h Fv(and)f
+Fu(per)330 4359 y(state)h Fv(variants)f(ar)o(e)g(much)i(mor)o(e)f(ef)o
+(\002cient)f(for)h(lar)o(ger)f(deterministic)h(jump)h(density)-9
+b(.)18 b(The)g Fu(per)330 4458 y(graph)525 4428 y Fi(t)579
+4458 y Fv(is)27 b(typically)g(the)g(fastest)f(algorithm)h(of)f(the)h
+(non-integrated)g(versions.)g(However)-6 b(,)330 4558
+y(in)26 b(these)g(experiments)g(all)g(states)f(in)i(the)e(input)i(ar)o
+(e)d(co-accessible)h(by)h(constr)o(uction;)h(and)330
+4658 y(mor)o(eover)-6 b(,)26 b(all)g(states)h(in)g(the)g(input)g(ar)o
+(e)f(\002nal)h(states.)f(Ther)o(efor)o(e,)f(the)i(advantages)e(of)i
+(the)330 4757 y Fu(per)21 b(graph)652 4727 y Fi(t;c)750
+4757 y Fv(algorithm)g(could)g(not)h(be)e(observed)g(her)o(e.)479
+4857 y(The)30 b(turning)g(point)h(is)e(ar)o(ound)g(a)g(deterministic)h
+(jump)g(density)g(of)f(ar)o(ound)g(0.8:)f(for)330 4956
+y(smaller)f(densities)g(the)f Fu(per)h(graph)1448 4926
+y Fi(t)1503 4956 y Fv(is)g(typically)g(slightly)h(faster;)d(for)h(lar)o
+(ger)g(densities)h(the)330 5056 y Fu(per)19 b(state)g
+Fv(algorithm)g(is)g(much)h(faster)-6 b(.)17 b(For)j(densities)f(beyond)
+g(1.5,)e(the)i Fu(per)g(subset)h Fv(algorithm)330 5156
+y(tends)25 b(to)g(perform)g(better)f(than)h(the)g Fu(per)g(state)f
+Fv(algorithm.)i(Inter)o(estingly)-9 b(,)24 b(this)i(generalisa-)330
+5255 y(tion)i(is)g(supported)f(by)h(the)g(experiments)f(on)h(automata)f
+(which)h(wer)o(e)f(generated)f(by)i(ap-)330 5355 y(pr)o(oximation)k
+(techniques)g(\(although)h(the)e(r)o(esults)h(for)f(randomly)h
+(generated)f(automata)330 5455 y(ar)o(e)19 b(mor)o(e)i(consistent)h
+(than)f(the)g(r)o(esults)f(for)h(`r)o(eal')e(examples\).)p
+Black 3247 5944 a(10)p Black eop
+%%Page: 11 11
+11 10 bop Black 330 91 a Fo(van)20 b(Noor)o(d)1145 b(Epsilon)17
+b(Moves)h(in)h(Subset)g(Constr)o(uction)p Black Black
+330 413 a
+ 23681433 16577003 3289088 3289088 26970521 19866091 startTexFig
+ 330 413 a
+%%BeginDocument: 15n.ps
+/gnudict 40 dict def
+gnudict begin
+/Color false def
+/Solid true def
+/gnulinewidth 5.000 def
+/vshift -60 def
+/dl {10 mul} def
+/hpt 31.5 def
+/vpt 31.5 def
+/M {moveto} bind def
+/L {lineto} bind def
+/R {rmoveto} bind def
+/V {rlineto} bind def
+/vpt2 vpt 2 mul def
+/hpt2 hpt 2 mul def
+/Lshow { currentpoint stroke M
+  0 vshift R show } def
+/Rshow { currentpoint stroke M
+  dup stringwidth pop neg vshift R show } def
+/Cshow { currentpoint stroke M
+  dup stringwidth pop -2 div vshift R show } def
+/DL { Color {setrgbcolor Solid {pop []} if 0 setdash }
+ {pop pop pop Solid {pop []} if 0 setdash} ifelse } def
+/BL { stroke gnulinewidth 2 mul setlinewidth } def
+/AL { stroke gnulinewidth 2 div setlinewidth } def
+/PL { stroke gnulinewidth setlinewidth } def
+/LTb { BL [] 0 0 0 DL } def
+/LTa { AL [1 dl 2 dl] 0 setdash 0 0 0 setrgbcolor } def
+/LT0 { PL [] 0 1 0 DL } def
+/LT1 { PL [4 dl 2 dl] 0 0 1 DL } def
+/LT2 { PL [2 dl 3 dl] 1 0 0 DL } def
+/LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def
+/LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def
+/LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def
+/LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def
+/LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def
+/LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def
+/P { stroke [] 0 setdash
+  currentlinewidth 2 div sub M
+  0 currentlinewidth V stroke } def
+/D { stroke [] 0 setdash 2 copy vpt add M
+  hpt neg vpt neg V hpt vpt neg V
+  hpt vpt V hpt neg vpt V closepath stroke
+  P } def
+/A { stroke [] 0 setdash vpt sub M 0 vpt2 V
+  currentpoint stroke M
+  hpt neg vpt neg R hpt2 0 V stroke
+  } def
+/B { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M
+  0 vpt2 neg V hpt2 0 V 0 vpt2 V
+  hpt2 neg 0 V closepath stroke
+  P } def
+/C { stroke [] 0 setdash exch hpt sub exch vpt add M
+  hpt2 vpt2 neg V currentpoint stroke M
+  hpt2 neg 0 R hpt2 vpt2 V stroke } def
+/T { stroke [] 0 setdash 2 copy vpt 1.12 mul add M
+  hpt neg vpt -1.62 mul V
+  hpt 2 mul 0 V
+  hpt neg vpt 1.62 mul V closepath stroke
+  P  } def
+/S { 2 copy A C} def
+end
+gnudict begin
+gsave
+50 50 translate
+0.050 0.050 scale
+0 setgray
+/Palatino-Roman findfont 180 scalefont setfont
+newpath
+LTa
+1080 451 M
+0 4498 V
+LTb
+1080 451 M
+63 0 V
+5778 0 R
+-63 0 V
+972 451 M
+(10) Rshow
+1080 902 M
+31 0 V
+5810 0 R
+-31 0 V
+1080 1166 M
+31 0 V
+5810 0 R
+-31 0 V
+1080 1354 M
+31 0 V
+5810 0 R
+-31 0 V
+1080 1499 M
+31 0 V
+5810 0 R
+-31 0 V
+1080 1618 M
+31 0 V
+5810 0 R
+-31 0 V
+1080 1718 M
+31 0 V
+5810 0 R
+-31 0 V
+-5810 87 R
+31 0 V
+5810 0 R
+-31 0 V
+-5810 77 R
+31 0 V
+5810 0 R
+-31 0 V
+-5810 68 R
+63 0 V
+5778 0 R
+-63 0 V
+-5886 0 R
+(100) Rshow
+1080 2402 M
+31 0 V
+5810 0 R
+-31 0 V
+1080 2666 M
+31 0 V
+5810 0 R
+-31 0 V
+1080 2853 M
+31 0 V
+5810 0 R
+-31 0 V
+1080 2998 M
+31 0 V
+5810 0 R
+-31 0 V
+1080 3117 M
+31 0 V
+5810 0 R
+-31 0 V
+1080 3217 M
+31 0 V
+5810 0 R
+-31 0 V
+-5810 87 R
+31 0 V
+5810 0 R
+-31 0 V
+-5810 77 R
+31 0 V
+5810 0 R
+-31 0 V
+-5810 69 R
+63 0 V
+5778 0 R
+-63 0 V
+-5886 0 R
+(1000) Rshow
+1080 3901 M
+31 0 V
+5810 0 R
+-31 0 V
+1080 4165 M
+31 0 V
+5810 0 R
+-31 0 V
+1080 4352 M
+31 0 V
+5810 0 R
+-31 0 V
+1080 4498 M
+31 0 V
+5810 0 R
+-31 0 V
+1080 4616 M
+31 0 V
+5810 0 R
+-31 0 V
+1080 4717 M
+31 0 V
+5810 0 R
+-31 0 V
+-5810 87 R
+31 0 V
+5810 0 R
+-31 0 V
+-5810 76 R
+31 0 V
+5810 0 R
+-31 0 V
+-5810 69 R
+63 0 V
+5778 0 R
+-63 0 V
+-5886 0 R
+(10000) Rshow
+1080 451 M
+0 63 V
+0 4435 R
+0 -63 V
+0 -4615 R
+(0) Cshow
+2087 451 M
+0 63 V
+0 4435 R
+0 -63 V
+0 -4615 R
+(0.5) Cshow
+3094 451 M
+0 63 V
+0 4435 R
+0 -63 V
+0 -4615 R
+(1) Cshow
+4101 451 M
+0 63 V
+0 4435 R
+0 -63 V
+0 -4615 R
+(1.5) Cshow
+5108 451 M
+0 63 V
+0 4435 R
+0 -63 V
+0 -4615 R
+(2) Cshow
+6115 451 M
+0 63 V
+0 4435 R
+0 -63 V
+0 -4615 R
+(2.5) Cshow
+1080 451 M
+5841 0 V
+0 4498 V
+-5841 0 V
+0 -4498 V
+180 2700 M
+currentpoint gsave translate 90 rotate 0 0 M
+(Mean CPU-time \(msec\)) Cshow
+grestore
+4000 91 M
+(#Jumps/#States) Cshow
+LT0
+6318 4706 M
+(per_graph\(t\)) Rshow
+6426 4706 M
+324 0 V
+1483 4047 M
+403 -642 V
+402 -251 V
+403 -554 V
+403 -290 V
+403 -369 V
+403 -96 V
+403 -279 V
+402 -212 V
+403 0 V
+403 171 V
+403 -26 V
+403 -333 V
+403 300 V
+6534 4706 D
+1483 4047 D
+1886 3405 D
+2288 3154 D
+2691 2600 D
+3094 2310 D
+3497 1941 D
+3900 1845 D
+4303 1566 D
+4705 1354 D
+5108 1354 D
+5511 1525 D
+5914 1499 D
+6317 1166 D
+6720 1466 D
+LT1
+6318 4526 M
+(per_graph\(s\)) Rshow
+6426 4526 M
+324 0 V
+1483 4241 M
+403 -505 V
+402 -144 V
+403 -432 V
+403 -243 V
+403 -368 V
+403 -33 V
+403 -372 V
+402 -151 V
+403 -215 V
+403 246 V
+403 117 V
+403 73 V
+403 -248 V
+6534 4526 A
+1483 4241 A
+1886 3736 A
+2288 3592 A
+2691 3160 A
+3094 2917 A
+3497 2549 A
+3900 2516 A
+4303 2144 A
+4705 1993 A
+5108 1778 A
+5511 2024 A
+5914 2141 A
+6317 2214 A
+6720 1966 A
+LT2
+6318 4346 M
+(per_graph\(s,a\)) Rshow
+6426 4346 M
+324 0 V
+1483 4237 M
+403 -497 V
+402 -145 V
+403 -421 V
+403 -224 V
+403 -307 V
+403 -13 V
+403 -218 V
+402 -97 V
+403 -194 V
+403 388 V
+403 -82 V
+403 6 V
+403 67 V
+6534 4346 B
+1483 4237 B
+1886 3740 B
+2288 3595 B
+2691 3174 B
+3094 2950 B
+3497 2643 B
+3900 2630 B
+4303 2412 B
+4705 2315 B
+5108 2121 B
+5511 2509 B
+5914 2427 B
+6317 2433 B
+6720 2500 B
+LT3
+6318 4166 M
+(per_graph\(t,c\)) Rshow
+6426 4166 M
+324 0 V
+1483 4048 M
+403 -635 V
+402 -246 V
+403 -518 V
+403 -233 V
+403 -295 V
+403 -40 V
+403 -111 V
+402 -88 V
+403 -134 V
+403 252 V
+403 12 V
+403 -130 V
+403 145 V
+6534 4166 C
+1483 4048 C
+1886 3413 C
+2288 3167 C
+2691 2649 C
+3094 2416 C
+3497 2121 C
+3900 2081 C
+4303 1970 C
+4705 1882 C
+5108 1748 C
+5511 2000 C
+5914 2012 C
+6317 1882 C
+6720 2027 C
+LT4
+6318 3986 M
+(per_subset) Rshow
+6426 3986 M
+324 0 V
+1483 4169 M
+403 -659 V
+402 -271 V
+403 -577 V
+403 -330 V
+403 -424 V
+403 -142 V
+403 -507 V
+4705 955 L
+403 -53 V
+5511 757 L
+403 264 V
+403 145 V
+6720 715 L
+6534 3986 T
+1483 4169 T
+1886 3510 T
+2288 3239 T
+2691 2662 T
+3094 2332 T
+3497 1908 T
+3900 1766 T
+4303 1259 T
+4705 955 T
+5108 902 T
+5511 757 T
+5914 1021 T
+6317 1166 T
+6720 715 T
+LT5
+6318 3806 M
+(per_state) Rshow
+6426 3806 M
+324 0 V
+1483 4157 M
+403 -663 V
+402 -279 V
+403 -596 V
+403 -311 V
+403 -451 V
+403 -135 V
+403 -508 V
+4705 845 L
+403 157 V
+5511 670 L
+403 294 V
+403 -62 V
+6720 715 L
+6534 3806 S
+1483 4157 S
+1886 3494 S
+2288 3215 S
+2691 2619 S
+3094 2308 S
+3497 1857 S
+3900 1722 S
+4303 1214 S
+4705 845 S
+5108 1002 S
+5511 670 S
+5914 964 S
+6317 902 S
+6720 715 S
+LT6
+6318 3626 M
+(fsm) Rshow
+6426 3626 M
+324 0 V
+1483 3879 M
+403 -448 V
+402 -101 V
+403 -387 V
+403 -188 V
+403 -320 V
+403 -7 V
+403 -448 V
+402 -135 V
+403 -127 V
+403 54 V
+403 252 V
+403 232 V
+403 -612 V
+stroke
+grestore
+end
+showpage
+
+%%EndDocument
+
+ endTexFig
+ 330 2596 a Fd(Figure)f(6)330 2679 y Fo(A)-7 b(verage)18
+b(amount)i(of)e(CPU-time)h(versus)f(jump)h(density)f(for)f(each)j(of)e
+(the)i(algorithms,)d(and)i(FSM.)330 2762 y(Input)h(automata)g(have)g
+(15)f(states.)f(Absolute)h(transition)g(densities:)f(0.01-0.3.)p
+Black Black 330 3128 a
+ 23681433 16577003 3289088 3289088 26970521 19866091 startTexFig
+ 330 3128 a
+%%BeginDocument: 20n.ps
+/gnudict 40 dict def
+gnudict begin
+/Color false def
+/Solid true def
+/gnulinewidth 5.000 def
+/vshift -60 def
+/dl {10 mul} def
+/hpt 31.5 def
+/vpt 31.5 def
+/M {moveto} bind def
+/L {lineto} bind def
+/R {rmoveto} bind def
+/V {rlineto} bind def
+/vpt2 vpt 2 mul def
+/hpt2 hpt 2 mul def
+/Lshow { currentpoint stroke M
+  0 vshift R show } def
+/Rshow { currentpoint stroke M
+  dup stringwidth pop neg vshift R show } def
+/Cshow { currentpoint stroke M
+  dup stringwidth pop -2 div vshift R show } def
+/DL { Color {setrgbcolor Solid {pop []} if 0 setdash }
+ {pop pop pop Solid {pop []} if 0 setdash} ifelse } def
+/BL { stroke gnulinewidth 2 mul setlinewidth } def
+/AL { stroke gnulinewidth 2 div setlinewidth } def
+/PL { stroke gnulinewidth setlinewidth } def
+/LTb { BL [] 0 0 0 DL } def
+/LTa { AL [1 dl 2 dl] 0 setdash 0 0 0 setrgbcolor } def
+/LT0 { PL [] 0 1 0 DL } def
+/LT1 { PL [4 dl 2 dl] 0 0 1 DL } def
+/LT2 { PL [2 dl 3 dl] 1 0 0 DL } def
+/LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def
+/LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def
+/LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def
+/LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def
+/LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def
+/LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def
+/P { stroke [] 0 setdash
+  currentlinewidth 2 div sub M
+  0 currentlinewidth V stroke } def
+/D { stroke [] 0 setdash 2 copy vpt add M
+  hpt neg vpt neg V hpt vpt neg V
+  hpt vpt V hpt neg vpt V closepath stroke
+  P } def
+/A { stroke [] 0 setdash vpt sub M 0 vpt2 V
+  currentpoint stroke M
+  hpt neg vpt neg R hpt2 0 V stroke
+  } def
+/B { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M
+  0 vpt2 neg V hpt2 0 V 0 vpt2 V
+  hpt2 neg 0 V closepath stroke
+  P } def
+/C { stroke [] 0 setdash exch hpt sub exch vpt add M
+  hpt2 vpt2 neg V currentpoint stroke M
+  hpt2 neg 0 R hpt2 vpt2 V stroke } def
+/T { stroke [] 0 setdash 2 copy vpt 1.12 mul add M
+  hpt neg vpt -1.62 mul V
+  hpt 2 mul 0 V
+  hpt neg vpt 1.62 mul V closepath stroke
+  P  } def
+/S { 2 copy A C} def
+end
+gnudict begin
+gsave
+50 50 translate
+0.050 0.050 scale
+0 setgray
+/Palatino-Roman findfont 180 scalefont setfont
+newpath
+LTa
+1080 451 M
+0 4498 V
+LTb
+1080 451 M
+63 0 V
+5778 0 R
+-63 0 V
+972 451 M
+(10) Rshow
+1080 902 M
+31 0 V
+5810 0 R
+-31 0 V
+1080 1166 M
+31 0 V
+5810 0 R
+-31 0 V
+1080 1354 M
+31 0 V
+5810 0 R
+-31 0 V
+1080 1499 M
+31 0 V
+5810 0 R
+-31 0 V
+1080 1618 M
+31 0 V
+5810 0 R
+-31 0 V
+1080 1718 M
+31 0 V
+5810 0 R
+-31 0 V
+-5810 87 R
+31 0 V
+5810 0 R
+-31 0 V
+-5810 77 R
+31 0 V
+5810 0 R
+-31 0 V
+-5810 68 R
+63 0 V
+5778 0 R
+-63 0 V
+-5886 0 R
+(100) Rshow
+1080 2402 M
+31 0 V
+5810 0 R
+-31 0 V
+1080 2666 M
+31 0 V
+5810 0 R
+-31 0 V
+1080 2853 M
+31 0 V
+5810 0 R
+-31 0 V
+1080 2998 M
+31 0 V
+5810 0 R
+-31 0 V
+1080 3117 M
+31 0 V
+5810 0 R
+-31 0 V
+1080 3217 M
+31 0 V
+5810 0 R
+-31 0 V
+-5810 87 R
+31 0 V
+5810 0 R
+-31 0 V
+-5810 77 R
+31 0 V
+5810 0 R
+-31 0 V
+-5810 69 R
+63 0 V
+5778 0 R
+-63 0 V
+-5886 0 R
+(1000) Rshow
+1080 3901 M
+31 0 V
+5810 0 R
+-31 0 V
+1080 4165 M
+31 0 V
+5810 0 R
+-31 0 V
+1080 4352 M
+31 0 V
+5810 0 R
+-31 0 V
+1080 4498 M
+31 0 V
+5810 0 R
+-31 0 V
+1080 4616 M
+31 0 V
+5810 0 R
+-31 0 V
+1080 4717 M
+31 0 V
+5810 0 R
+-31 0 V
+-5810 87 R
+31 0 V
+5810 0 R
+-31 0 V
+-5810 76 R
+31 0 V
+5810 0 R
+-31 0 V
+-5810 69 R
+63 0 V
+5778 0 R
+-63 0 V
+-5886 0 R
+(10000) Rshow
+1080 451 M
+0 63 V
+0 4435 R
+0 -63 V
+0 -4615 R
+(0) Cshow
+2087 451 M
+0 63 V
+0 4435 R
+0 -63 V
+0 -4615 R
+(0.5) Cshow
+3094 451 M
+0 63 V
+0 4435 R
+0 -63 V
+0 -4615 R
+(1) Cshow
+4101 451 M
+0 63 V
+0 4435 R
+0 -63 V
+0 -4615 R
+(1.5) Cshow
+5108 451 M
+0 63 V
+0 4435 R
+0 -63 V
+0 -4615 R
+(2) Cshow
+6115 451 M
+0 63 V
+0 4435 R
+0 -63 V
+0 -4615 R
+(2.5) Cshow
+1080 451 M
+5841 0 V
+0 4498 V
+-5841 0 V
+0 -4498 V
+180 2700 M
+currentpoint gsave translate 90 rotate 0 0 M
+(Mean CPU-time \(msec\)) Cshow
+grestore
+4000 91 M
+(#Jumps/#States) Cshow
+LT0
+6318 4706 M
+(per_graph\(t\)) Rshow
+6426 4706 M
+324 0 V
+1483 4654 M
+403 -225 V
+402 -601 V
+403 -329 V
+403 -698 V
+403 -215 V
+403 -314 V
+403 -197 V
+402 -197 V
+403 143 V
+403 -104 V
+403 -169 V
+403 -78 V
+403 187 V
+6534 4706 D
+1483 4654 D
+1886 4429 D
+2288 3828 D
+2691 3499 D
+3094 2801 D
+3497 2586 D
+3900 2272 D
+4303 2075 D
+4705 1878 D
+5108 2021 D
+5511 1917 D
+5914 1748 D
+6317 1670 D
+6720 1857 D
+LT1
+6318 4526 M
+(per_graph\(s\)) Rshow
+6426 4526 M
+324 0 V
+1483 4822 M
+403 -82 V
+402 -466 V
+403 -276 V
+403 -652 V
+403 -215 V
+403 -273 V
+403 -207 V
+402 -155 V
+403 161 V
+403 -123 V
+403 13 V
+403 -162 V
+403 171 V
+6534 4526 A
+1483 4822 A
+1886 4740 A
+2288 4274 A
+2691 3998 A
+3094 3346 A
+3497 3131 A
+3900 2858 A
+4303 2651 A
+4705 2496 A
+5108 2657 A
+5511 2534 A
+5914 2547 A
+6317 2385 A
+6720 2556 A
+LT2
+6318 4346 M
+(per_graph\(s,a\)) Rshow
+6426 4346 M
+324 0 V
+1483 4817 M
+403 -77 V
+402 -463 V
+403 -278 V
+403 -594 V
+403 -212 V
+403 -197 V
+403 -115 V
+402 46 V
+403 61 V
+403 37 V
+403 -14 V
+403 -438 V
+403 493 V
+6534 4346 B
+1483 4817 B
+1886 4740 B
+2288 4277 B
+2691 3999 B
+3094 3405 B
+3497 3193 B
+3900 2996 B
+4303 2881 B
+4705 2927 B
+5108 2988 B
+5511 3025 B
+5914 3011 B
+6317 2573 B
+6720 3066 B
+LT3
+6318 4166 M
+(per_graph\(t,c\)) Rshow
+6426 4166 M
+324 0 V
+1483 4661 M
+403 -221 V
+402 -595 V
+403 -329 V
+403 -604 V
+403 -168 V
+403 -230 V
+403 -53 V
+402 -28 V
+403 55 V
+403 10 V
+403 4 V
+403 -288 V
+403 283 V
+6534 4166 C
+1483 4661 C
+1886 4440 C
+2288 3845 C
+2691 3516 C
+3094 2912 C
+3497 2744 C
+3900 2514 C
+4303 2461 C
+4705 2433 C
+5108 2488 C
+5511 2498 C
+5914 2502 C
+6317 2214 C
+6720 2497 C
+LT4
+6318 3986 M
+(per_subset) Rshow
+6426 3986 M
+324 0 V
+1483 4760 M
+403 -273 V
+402 -627 V
+403 -339 V
+403 -737 V
+403 -294 V
+403 -358 V
+403 -280 V
+402 -397 V
+403 249 V
+403 -274 V
+403 -340 V
+403 76 V
+403 -76 V
+6534 3986 T
+1483 4760 T
+1886 4487 T
+2288 3860 T
+2691 3521 T
+3094 2784 T
+3497 2490 T
+3900 2132 T
+4303 1852 T
+4705 1455 T
+5108 1704 T
+5511 1430 T
+5914 1090 T
+6317 1166 T
+6720 1090 T
+LT5
+6318 3806 M
+(per_state) Rshow
+6426 3806 M
+324 0 V
+1483 4756 M
+403 -275 V
+402 -652 V
+403 -347 V
+403 -752 V
+403 -246 V
+403 -377 V
+403 -268 V
+402 -340 V
+403 171 V
+403 -254 V
+403 -326 V
+403 177 V
+403 58 V
+6534 3806 S
+1483 4756 S
+1886 4481 S
+2288 3829 S
+2691 3482 S
+3094 2730 S
+3497 2484 S
+3900 2107 S
+4303 1839 S
+4705 1499 S
+5108 1670 S
+5511 1416 S
+5914 1090 S
+6317 1267 S
+6720 1325 S
+LT6
+6318 3626 M
+(fsm) Rshow
+6426 3626 M
+324 0 V
+1483 4510 M
+403 21 V
+402 -411 V
+403 -282 V
+403 -577 V
+403 -156 V
+403 -236 V
+403 -269 V
+402 -188 V
+403 206 V
+403 -213 V
+403 -37 V
+403 0 V
+403 -29 V
+stroke
+grestore
+end
+showpage
+
+%%EndDocument
+
+ endTexFig
+ 330 5311 a Fd(Figure)g(7)330 5394 y Fo(A)-7 b(verage)18
+b(amount)i(of)e(CPU-time)h(versus)f(jump)h(density)f(for)f(each)j(of)e
+(the)i(algorithms,)d(and)i(FSM.)330 5477 y(Input)h(automata)g(have)g
+(20)f(states.)f(Absolute)h(transition)g(densities:)f(0.01-0.3.)p
+Black Black 3252 5944 a Fv(1)-5 b(1)p Black eop
+%%Page: 12 12
+12 11 bop Black 330 91 a Fo(van)20 b(Noor)o(d)1145 b(Epsilon)17
+b(Moves)h(in)h(Subset)g(Constr)o(uction)p Black Black
+330 413 a
+ 23681433 16577003 3289088 3289088 26970521 19866091 startTexFig
+ 330 413 a
+%%BeginDocument: 25n.ps
+/gnudict 40 dict def
+gnudict begin
+/Color false def
+/Solid true def
+/gnulinewidth 5.000 def
+/vshift -60 def
+/dl {10 mul} def
+/hpt 31.5 def
+/vpt 31.5 def
+/M {moveto} bind def
+/L {lineto} bind def
+/R {rmoveto} bind def
+/V {rlineto} bind def
+/vpt2 vpt 2 mul def
+/hpt2 hpt 2 mul def
+/Lshow { currentpoint stroke M
+  0 vshift R show } def
+/Rshow { currentpoint stroke M
+  dup stringwidth pop neg vshift R show } def
+/Cshow { currentpoint stroke M
+  dup stringwidth pop -2 div vshift R show } def
+/DL { Color {setrgbcolor Solid {pop []} if 0 setdash }
+ {pop pop pop Solid {pop []} if 0 setdash} ifelse } def
+/BL { stroke gnulinewidth 2 mul setlinewidth } def
+/AL { stroke gnulinewidth 2 div setlinewidth } def
+/PL { stroke gnulinewidth setlinewidth } def
+/LTb { BL [] 0 0 0 DL } def
+/LTa { AL [1 dl 2 dl] 0 setdash 0 0 0 setrgbcolor } def
+/LT0 { PL [] 0 1 0 DL } def
+/LT1 { PL [4 dl 2 dl] 0 0 1 DL } def
+/LT2 { PL [2 dl 3 dl] 1 0 0 DL } def
+/LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def
+/LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def
+/LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def
+/LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def
+/LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def
+/LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def
+/P { stroke [] 0 setdash
+  currentlinewidth 2 div sub M
+  0 currentlinewidth V stroke } def
+/D { stroke [] 0 setdash 2 copy vpt add M
+  hpt neg vpt neg V hpt vpt neg V
+  hpt vpt V hpt neg vpt V closepath stroke
+  P } def
+/A { stroke [] 0 setdash vpt sub M 0 vpt2 V
+  currentpoint stroke M
+  hpt neg vpt neg R hpt2 0 V stroke
+  } def
+/B { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M
+  0 vpt2 neg V hpt2 0 V 0 vpt2 V
+  hpt2 neg 0 V closepath stroke
+  P } def
+/C { stroke [] 0 setdash exch hpt sub exch vpt add M
+  hpt2 vpt2 neg V currentpoint stroke M
+  hpt2 neg 0 R hpt2 vpt2 V stroke } def
+/T { stroke [] 0 setdash 2 copy vpt 1.12 mul add M
+  hpt neg vpt -1.62 mul V
+  hpt 2 mul 0 V
+  hpt neg vpt 1.62 mul V closepath stroke
+  P  } def
+/S { 2 copy A C} def
+end
+gnudict begin
+gsave
+50 50 translate
+0.050 0.050 scale
+0 setgray
+/Palatino-Roman findfont 180 scalefont setfont
+newpath
+LTa
+1080 451 M
+0 4498 V
+LTb
+1080 451 M
+63 0 V
+5778 0 R
+-63 0 V
+972 451 M
+(10) Rshow
+1080 790 M
+31 0 V
+5810 0 R
+-31 0 V
+1080 988 M
+31 0 V
+5810 0 R
+-31 0 V
+1080 1128 M
+31 0 V
+5810 0 R
+-31 0 V
+1080 1237 M
+31 0 V
+5810 0 R
+-31 0 V
+-5810 89 R
+31 0 V
+5810 0 R
+-31 0 V
+-5810 75 R
+31 0 V
+5810 0 R
+-31 0 V
+-5810 66 R
+31 0 V
+5810 0 R
+-31 0 V
+-5810 57 R
+31 0 V
+5810 0 R
+-31 0 V
+-5810 52 R
+63 0 V
+5778 0 R
+-63 0 V
+-5886 0 R
+(100) Rshow
+1080 1914 M
+31 0 V
+5810 0 R
+-31 0 V
+1080 2112 M
+31 0 V
+5810 0 R
+-31 0 V
+1080 2253 M
+31 0 V
+5810 0 R
+-31 0 V
+1080 2361 M
+31 0 V
+5810 0 R
+-31 0 V
+-5810 90 R
+31 0 V
+5810 0 R
+-31 0 V
+-5810 75 R
+31 0 V
+5810 0 R
+-31 0 V
+-5810 65 R
+31 0 V
+5810 0 R
+-31 0 V
+-5810 58 R
+31 0 V
+5810 0 R
+-31 0 V
+-5810 51 R
+63 0 V
+5778 0 R
+-63 0 V
+-5886 0 R
+(1000) Rshow
+1080 3039 M
+31 0 V
+5810 0 R
+-31 0 V
+1080 3237 M
+31 0 V
+5810 0 R
+-31 0 V
+1080 3377 M
+31 0 V
+5810 0 R
+-31 0 V
+1080 3486 M
+31 0 V
+5810 0 R
+-31 0 V
+-5810 89 R
+31 0 V
+5810 0 R
+-31 0 V
+-5810 75 R
+31 0 V
+5810 0 R
+-31 0 V
+-5810 66 R
+31 0 V
+5810 0 R
+-31 0 V
+-5810 57 R
+31 0 V
+5810 0 R
+-31 0 V
+-5810 52 R
+63 0 V
+5778 0 R
+-63 0 V
+-5886 0 R
+(10000) Rshow
+1080 4163 M
+31 0 V
+5810 0 R
+-31 0 V
+1080 4361 M
+31 0 V
+5810 0 R
+-31 0 V
+1080 4502 M
+31 0 V
+5810 0 R
+-31 0 V
+1080 4610 M
+31 0 V
+5810 0 R
+-31 0 V
+-5810 90 R
+31 0 V
+5810 0 R
+-31 0 V
+-5810 75 R
+31 0 V
+5810 0 R
+-31 0 V
+-5810 65 R
+31 0 V
+5810 0 R
+-31 0 V
+-5810 58 R
+31 0 V
+5810 0 R
+-31 0 V
+-5810 51 R
+63 0 V
+5778 0 R
+-63 0 V
+-5886 0 R
+(100000) Rshow
+1080 451 M
+0 63 V
+0 4435 R
+0 -63 V
+0 -4615 R
+(0) Cshow
+2087 451 M
+0 63 V
+0 4435 R
+0 -63 V
+0 -4615 R
+(0.5) Cshow
+3094 451 M
+0 63 V
+0 4435 R
+0 -63 V
+0 -4615 R
+(1) Cshow
+4101 451 M
+0 63 V
+0 4435 R
+0 -63 V
+0 -4615 R
+(1.5) Cshow
+5108 451 M
+0 63 V
+0 4435 R
+0 -63 V
+0 -4615 R
+(2) Cshow
+6115 451 M
+0 63 V
+0 4435 R
+0 -63 V
+0 -4615 R
+(2.5) Cshow
+1080 451 M
+5841 0 V
+0 4498 V
+-5841 0 V
+0 -4498 V
+180 2700 M
+currentpoint gsave translate 90 rotate 0 0 M
+(Mean CPU-time \(msec\)) Cshow
+grestore
+4000 91 M
+(#Jumps/#States) Cshow
+LT0
+6318 4706 M
+(per_graph\(t\)) Rshow
+6426 4706 M
+324 0 V
+1483 4180 M
+403 -175 V
+402 -587 V
+403 -454 V
+403 -359 V
+403 -363 V
+403 -319 V
+403 -68 V
+402 -108 V
+403 -59 V
+403 -32 V
+403 17 V
+403 9 V
+403 77 V
+6534 4706 D
+1483 4180 D
+1886 4005 D
+2288 3418 D
+2691 2964 D
+3094 2605 D
+3497 2242 D
+3900 1923 D
+4303 1855 D
+4705 1747 D
+5108 1688 D
+5511 1656 D
+5914 1673 D
+6317 1682 D
+6720 1759 D
+LT1
+6318 4526 M
+(per_graph\(s\)) Rshow
+6426 4526 M
+324 0 V
+1483 4351 M
+403 -94 V
+402 -526 V
+403 -351 V
+403 -345 V
+403 -346 V
+403 -376 V
+403 -29 V
+402 -24 V
+403 -50 V
+403 -27 V
+403 31 V
+403 -1 V
+403 73 V
+6534 4526 A
+1483 4351 A
+1886 4257 A
+2288 3731 A
+2691 3380 A
+3094 3035 A
+3497 2689 A
+3900 2313 A
+4303 2284 A
+4705 2260 A
+5108 2210 A
+5511 2183 A
+5914 2214 A
+6317 2213 A
+6720 2286 A
+LT2
+6318 4346 M
+(per_graph\(s,a\)) Rshow
+6426 4346 M
+324 0 V
+-5267 6 R
+403 -95 V
+402 -523 V
+403 -347 V
+403 -333 V
+403 -307 V
+403 -269 V
+403 35 V
+402 14 V
+403 34 V
+403 -13 V
+403 57 V
+403 13 V
+403 115 V
+6534 4346 B
+1483 4352 B
+1886 4257 B
+2288 3734 B
+2691 3387 B
+3094 3054 B
+3497 2747 B
+3900 2478 B
+4303 2513 B
+4705 2527 B
+5108 2561 B
+5511 2548 B
+5914 2605 B
+6317 2618 B
+6720 2733 B
+LT3
+6318 4166 M
+(per_graph\(t,c\)) Rshow
+6426 4166 M
+324 0 V
+-5267 14 R
+403 -175 V
+402 -580 V
+403 -436 V
+403 -335 V
+403 -287 V
+403 -199 V
+403 4 V
+402 -37 V
+403 2 V
+403 -15 V
+403 29 V
+403 -21 V
+403 108 V
+6534 4166 C
+1483 4180 C
+1886 4005 C
+2288 3425 C
+2691 2989 C
+3094 2654 C
+3497 2367 C
+3900 2168 C
+4303 2172 C
+4705 2135 C
+5108 2137 C
+5511 2122 C
+5914 2151 C
+6317 2130 C
+6720 2238 C
+LT4
+6318 3986 M
+(per_subset) Rshow
+6426 3986 M
+324 0 V
+1483 4211 M
+403 -166 V
+402 -612 V
+403 -477 V
+403 -402 V
+403 -406 V
+403 -417 V
+403 -90 V
+402 -210 V
+403 -137 V
+403 -135 V
+403 23 V
+403 -37 V
+403 63 V
+6534 3986 T
+1483 4211 T
+1886 4045 T
+2288 3433 T
+2691 2956 T
+3094 2554 T
+3497 2148 T
+3900 1731 T
+4303 1641 T
+4705 1431 T
+5108 1294 T
+5511 1159 T
+5914 1182 T
+6317 1145 T
+6720 1208 T
+LT5
+6318 3806 M
+(per_state) Rshow
+6426 3806 M
+324 0 V
+1483 4208 M
+403 -175 V
+402 -614 V
+403 -486 V
+403 -401 V
+403 -398 V
+403 -408 V
+403 -90 V
+402 -166 V
+403 -119 V
+403 -105 V
+403 22 V
+403 22 V
+403 12 V
+6534 3806 S
+1483 4208 S
+1886 4033 S
+2288 3419 S
+2691 2933 S
+3094 2532 S
+3497 2134 S
+3900 1726 S
+4303 1636 S
+4705 1470 S
+5108 1351 S
+5511 1246 S
+5914 1268 S
+6317 1290 S
+6720 1302 S
+LT6
+6318 3626 M
+(fsm) Rshow
+6426 3626 M
+324 0 V
+1483 4200 M
+403 -116 V
+402 -501 V
+403 -296 V
+403 -307 V
+403 -301 V
+403 -366 V
+403 -4 V
+402 -34 V
+403 -163 V
+403 -59 V
+403 46 V
+403 -87 V
+403 22 V
+stroke
+grestore
+end
+showpage
+
+%%EndDocument
+
+ endTexFig
+ 330 2596 a Fd(Figure)f(8)330 2679 y Fo(A)-7 b(verage)17
+b(amount)i(of)f(CPU-time)g(versus)f(deterministic)g(jump)h(density)f
+(for)g(each)i(of)f(the)g(algorithms,)330 2762 y(and)h(FSM.)f(Input)i
+(automata)g(have)g(25)f(states.)f(Absolute)h(transition)g(densities:)f
+(0.01-0.3.)p Black Black 330 3128 a
+ 23681433 16577003 3289088 3289088 26970521 19866091 startTexFig
+ 330 3128 a
+%%BeginDocument: 100n.ps
+/gnudict 40 dict def
+gnudict begin
+/Color false def
+/Solid true def
+/gnulinewidth 5.000 def
+/vshift -60 def
+/dl {10 mul} def
+/hpt 31.5 def
+/vpt 31.5 def
+/M {moveto} bind def
+/L {lineto} bind def
+/R {rmoveto} bind def
+/V {rlineto} bind def
+/vpt2 vpt 2 mul def
+/hpt2 hpt 2 mul def
+/Lshow { currentpoint stroke M
+  0 vshift R show } def
+/Rshow { currentpoint stroke M
+  dup stringwidth pop neg vshift R show } def
+/Cshow { currentpoint stroke M
+  dup stringwidth pop -2 div vshift R show } def
+/DL { Color {setrgbcolor Solid {pop []} if 0 setdash }
+ {pop pop pop Solid {pop []} if 0 setdash} ifelse } def
+/BL { stroke gnulinewidth 2 mul setlinewidth } def
+/AL { stroke gnulinewidth 2 div setlinewidth } def
+/PL { stroke gnulinewidth setlinewidth } def
+/LTb { BL [] 0 0 0 DL } def
+/LTa { AL [1 dl 2 dl] 0 setdash 0 0 0 setrgbcolor } def
+/LT0 { PL [] 0 1 0 DL } def
+/LT1 { PL [4 dl 2 dl] 0 0 1 DL } def
+/LT2 { PL [2 dl 3 dl] 1 0 0 DL } def
+/LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def
+/LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def
+/LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def
+/LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def
+/LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def
+/LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def
+/P { stroke [] 0 setdash
+  currentlinewidth 2 div sub M
+  0 currentlinewidth V stroke } def
+/D { stroke [] 0 setdash 2 copy vpt add M
+  hpt neg vpt neg V hpt vpt neg V
+  hpt vpt V hpt neg vpt V closepath stroke
+  P } def
+/A { stroke [] 0 setdash vpt sub M 0 vpt2 V
+  currentpoint stroke M
+  hpt neg vpt neg R hpt2 0 V stroke
+  } def
+/B { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M
+  0 vpt2 neg V hpt2 0 V 0 vpt2 V
+  hpt2 neg 0 V closepath stroke
+  P } def
+/C { stroke [] 0 setdash exch hpt sub exch vpt add M
+  hpt2 vpt2 neg V currentpoint stroke M
+  hpt2 neg 0 R hpt2 vpt2 V stroke } def
+/T { stroke [] 0 setdash 2 copy vpt 1.12 mul add M
+  hpt neg vpt -1.62 mul V
+  hpt 2 mul 0 V
+  hpt neg vpt 1.62 mul V closepath stroke
+  P  } def
+/S { 2 copy A C} def
+end
+gnudict begin
+gsave
+50 50 translate
+0.050 0.050 scale
+0 setgray
+/Palatino-Roman findfont 180 scalefont setfont
+newpath
+LTa
+1080 451 M
+0 4498 V
+LTb
+1080 451 M
+63 0 V
+5778 0 R
+-63 0 V
+972 451 M
+(100) Rshow
+1080 902 M
+31 0 V
+5810 0 R
+-31 0 V
+1080 1166 M
+31 0 V
+5810 0 R
+-31 0 V
+1080 1354 M
+31 0 V
+5810 0 R
+-31 0 V
+1080 1499 M
+31 0 V
+5810 0 R
+-31 0 V
+1080 1618 M
+31 0 V
+5810 0 R
+-31 0 V
+1080 1718 M
+31 0 V
+5810 0 R
+-31 0 V
+-5810 87 R
+31 0 V
+5810 0 R
+-31 0 V
+-5810 77 R
+31 0 V
+5810 0 R
+-31 0 V
+-5810 68 R
+63 0 V
+5778 0 R
+-63 0 V
+-5886 0 R
+(1000) Rshow
+1080 2402 M
+31 0 V
+5810 0 R
+-31 0 V
+1080 2666 M
+31 0 V
+5810 0 R
+-31 0 V
+1080 2853 M
+31 0 V
+5810 0 R
+-31 0 V
+1080 2998 M
+31 0 V
+5810 0 R
+-31 0 V
+1080 3117 M
+31 0 V
+5810 0 R
+-31 0 V
+1080 3217 M
+31 0 V
+5810 0 R
+-31 0 V
+-5810 87 R
+31 0 V
+5810 0 R
+-31 0 V
+-5810 77 R
+31 0 V
+5810 0 R
+-31 0 V
+-5810 69 R
+63 0 V
+5778 0 R
+-63 0 V
+-5886 0 R
+(10000) Rshow
+1080 3901 M
+31 0 V
+5810 0 R
+-31 0 V
+1080 4165 M
+31 0 V
+5810 0 R
+-31 0 V
+1080 4352 M
+31 0 V
+5810 0 R
+-31 0 V
+1080 4498 M
+31 0 V
+5810 0 R
+-31 0 V
+1080 4616 M
+31 0 V
+5810 0 R
+-31 0 V
+1080 4717 M
+31 0 V
+5810 0 R
+-31 0 V
+-5810 87 R
+31 0 V
+5810 0 R
+-31 0 V
+-5810 76 R
+31 0 V
+5810 0 R
+-31 0 V
+-5810 69 R
+63 0 V
+5778 0 R
+-63 0 V
+-5886 0 R
+(100000) Rshow
+1080 451 M
+0 63 V
+0 4435 R
+0 -63 V
+0 -4615 R
+(0) Cshow
+2087 451 M
+0 63 V
+0 4435 R
+0 -63 V
+0 -4615 R
+(0.5) Cshow
+3094 451 M
+0 63 V
+0 4435 R
+0 -63 V
+0 -4615 R
+(1) Cshow
+4101 451 M
+0 63 V
+0 4435 R
+0 -63 V
+0 -4615 R
+(1.5) Cshow
+5108 451 M
+0 63 V
+0 4435 R
+0 -63 V
+0 -4615 R
+(2) Cshow
+6115 451 M
+0 63 V
+0 4435 R
+0 -63 V
+0 -4615 R
+(2.5) Cshow
+1080 451 M
+5841 0 V
+0 4498 V
+-5841 0 V
+0 -4498 V
+180 2700 M
+currentpoint gsave translate 90 rotate 0 0 M
+(Mean CPU-time \(msec\)) Cshow
+grestore
+4000 91 M
+(#Jumps/#States) Cshow
+LT0
+6318 4706 M
+(per_graph\(t\)) Rshow
+6426 4706 M
+324 0 V
+1483 1826 M
+403 888 V
+402 958 V
+403 -82 V
+403 80 V
+403 -400 V
+403 -466 V
+403 -663 V
+402 -104 V
+403 -65 V
+403 -45 V
+403 -110 V
+403 80 V
+403 -28 V
+201 -18 V
+6534 4706 D
+1483 1826 D
+1886 2714 D
+2288 3672 D
+2691 3590 D
+3094 3670 D
+3497 3270 D
+3900 2804 D
+4303 2141 D
+4705 2037 D
+5108 1972 D
+5511 1927 D
+5914 1817 D
+6317 1897 D
+6720 1869 D
+LT1
+6318 4526 M
+(per_graph\(s\)) Rshow
+6426 4526 M
+324 0 V
+1483 1801 M
+403 837 V
+402 891 V
+403 -130 V
+403 49 V
+403 -324 V
+403 -390 V
+403 -509 V
+402 0 V
+403 15 V
+403 -85 V
+403 -121 V
+403 125 V
+403 20 V
+201 -49 V
+6534 4526 A
+1483 1801 A
+1886 2638 A
+2288 3529 A
+2691 3399 A
+3094 3448 A
+3497 3124 A
+3900 2734 A
+4303 2225 A
+4705 2225 A
+5108 2240 A
+5511 2155 A
+5914 2034 A
+6317 2159 A
+6720 2179 A
+LT2
+6318 4346 M
+(per_graph\(s,a\)) Rshow
+6426 4346 M
+324 0 V
+1483 1811 M
+403 826 V
+402 890 V
+403 -129 V
+403 45 V
+403 -325 V
+403 -364 V
+403 -452 V
+402 23 V
+403 30 V
+403 -58 V
+403 -111 V
+403 156 V
+403 -2 V
+201 -40 V
+6534 4346 B
+1483 1811 B
+1886 2637 B
+2288 3527 B
+2691 3398 B
+3094 3443 B
+3497 3118 B
+3900 2754 B
+4303 2302 B
+4705 2325 B
+5108 2355 B
+5511 2297 B
+5914 2186 B
+6317 2342 B
+6720 2340 B
+LT3
+6318 4166 M
+(per_graph\(t,c\)) Rshow
+6426 4166 M
+324 0 V
+1483 1838 M
+403 884 V
+402 953 V
+403 -85 V
+403 78 V
+403 -381 V
+403 -430 V
+403 -528 V
+402 -20 V
+403 -15 V
+403 8 V
+403 -83 V
+403 138 V
+403 -37 V
+201 -22 V
+6534 4166 C
+1483 1838 C
+1886 2722 C
+2288 3675 C
+2691 3590 C
+3094 3668 C
+3497 3287 C
+3900 2857 C
+4303 2329 C
+4705 2309 C
+5108 2294 C
+5511 2302 C
+5914 2219 C
+6317 2357 C
+6720 2320 C
+LT4
+6318 3986 M
+(per_subset) Rshow
+6426 3986 M
+324 0 V
+1483 2037 M
+403 854 V
+402 885 V
+403 -162 V
+403 -27 V
+403 -529 V
+403 -624 V
+403 -898 V
+402 -203 V
+403 -118 V
+403 -196 V
+5914 752 L
+403 14 V
+6720 640 L
+201 -90 V
+6534 3986 T
+1483 2037 T
+1886 2891 T
+2288 3776 T
+2691 3614 T
+3094 3587 T
+3497 3058 T
+3900 2434 T
+4303 1536 T
+4705 1333 T
+5108 1215 T
+5511 1019 T
+5914 752 T
+6317 766 T
+6720 640 T
+LT5
+6318 3806 M
+(per_state) Rshow
+6426 3806 M
+324 0 V
+1483 2024 M
+403 828 V
+402 864 V
+403 -185 V
+403 -64 V
+403 -544 V
+403 -584 V
+403 -748 V
+402 -93 V
+403 -53 V
+403 -131 V
+403 -141 V
+403 95 V
+403 -29 V
+201 -42 V
+6534 3806 S
+1483 2024 S
+1886 2852 S
+2288 3716 S
+2691 3531 S
+3094 3467 S
+3497 2923 S
+3900 2339 S
+4303 1591 S
+4705 1498 S
+5108 1445 S
+5511 1314 S
+5914 1173 S
+6317 1268 S
+6720 1239 S
+LT6
+6318 3626 M
+(fsm) Rshow
+6426 3626 M
+324 0 V
+1483 869 M
+403 1219 V
+402 976 V
+403 -128 V
+403 161 V
+403 -161 V
+403 -187 V
+403 -428 V
+402 -6 V
+403 19 V
+403 -215 V
+403 -298 V
+403 128 V
+403 46 V
+201 -205 V
+stroke
+grestore
+end
+showpage
+
+%%EndDocument
+
+ endTexFig
+ 330 5311 a Fd(Figure)g(9)330 5394 y Fo(A)-7 b(verage)17
+b(amount)i(of)f(CPU-time)g(versus)f(deterministic)g(jump)h(density)f
+(for)g(each)i(of)f(the)g(algorithms,)330 5477 y(and)h(FSM.)f(Input)i
+(automata)g(have)g(100)f(states.)g(Absolute)f(transition)i(densities:)d
+(0.001-0.0035.)p Black Black 3247 5944 a Fv(12)p Black
+eop
+%%Page: 13 13
+13 12 bop Black 330 91 a Fo(van)20 b(Noor)o(d)1145 b(Epsilon)17
+b(Moves)h(in)h(Subset)g(Constr)o(uction)p Black 330 357
+a Fu(Comparison)30 b(with)g(the)g(FSM)h(library)36 b
+Fv(W)-8 b(e)31 b(also)g(pr)o(ovide)e(the)i(r)o(esults)f(for)h(A)-6
+b(T&T's)29 b(FSM)h(li-)330 457 y(brary)23 b(again.)g(FSM)g(is)h
+(designed)g(to)g(tr)o(eat)f(weighted)h(automata)f(for)h(very)f(general)
+g(weight)330 556 y(sets.)g(The)f(initial)i(implementation)g(of)e(the)h
+(library)f(consisted)i(of)e(an)h(on-the-\003y)g(computa-)330
+656 y(tion)j(of)e(the)h(epsilon-closur)o(es)g(combined)g(with)h
+(determinisation.)f(This)g(was)g(abandoned)330 756 y(for)d(two)g(r)o
+(easons:)f(it)i(could)f(not)g(be)g(generalised)f(to)h(the)g(case)g(of)g
+(general)f(weight)i(sets,)e(and)330 855 y(it)g(was)g(not)h(outputting)g
+(the)f(intermediate)g(epsilon-r)o(emoved)f(machine)i(\(which)f(might)h
+(be)330 955 y(of)f(inter)o(est)h(in)g(itself\).)e(In)i(the)g(curr)o
+(ent)e(version)i Ft(\017)p Fv(-moves)g(must)g(be)f(r)o(emoved)g(befor)o
+(e)f(deter)o(-)330 1054 y(minisation)f(is)g(possible.)f(This)g
+(mechanism)h(thus)g(is)f(comparable)f(to)h(our)g Fu(per)g(graph)f
+Fv(variant.)330 1154 y(Appar)o(ently)-9 b(,)22 b(FSM)g(employs)i(an)f
+(algorithm)h(equivalent)g(to)g(our)f Fu(per)h(graph)2799
+1124 y Fi(s;a)2888 1154 y Fv(.)g(The)f(r)o(esult-)330
+1254 y(ing)31 b(determinised)f(machines)h(ar)o(e)d(generally)i(lar)o
+(ger)f(than)i(the)f(machines)h(pr)o(oduced)e(by)330 1353
+y(our)c(integrated)f(variants)g(and)g(the)g(variants)g(which)i
+(incorporate)e Ft(\017)p Fv(-moves)g(on)h(the)g(tar)o(get)330
+1453 y(side)c(of)f(transitions.)i(The)f(timings)h(below)f(ar)o(e)e
+(obtained)i(for)f(the)h(pipe)1083 1631 y Fb(fsmrmepsilon)47
+b(|)j(fsmdeterminize)330 1808 y Fv(This)20 b(is)g(somewhat)g(unfair)f
+(since)h(this)g(includes)g(the)g(time)f(to)h(write)g(and)f(r)o(ead)f
+(the)h(interme-)330 1908 y(diate)24 b(machine.)h(Even)g(so,)h(it)f(is)g
+(inter)o(esting)h(to)f(note)h(that)f(the)g(FSM)g(library)f(is)i(a)e
+(constant)330 2008 y(factor)c(faster)f(than)i(our)g Fu(per)f(graph)1442
+1978 y Fi(s;a)1532 2008 y Fv(;)g(for)h(lar)o(ger)e(numbers)i(of)f
+(jumps)h(the)g Fu(per)g(state)f Fv(and)g Fu(per)330 2107
+y(subset)i Fv(variants)e(consistently)i(beat)e(the)h(FSM)f(library)-9
+b(.)330 2307 y Fu(Experiment:)28 b(Automata)f(generated)h(by)h(appr)o
+(oximation)d(algorithms)35 b Fv(The)29 b(automata)f(used)h(in)330
+2406 y(the)20 b(pr)o(evious)g(experiments)h(wer)o(e)e(randomly)i
+(generated.)e(However)-6 b(,)19 b(it)i(may)f(well)h(be)f(that)330
+2506 y(in)d(practice)f(the)g(automata)g(that)h(ar)o(e)e(to)i(be)g(tr)o
+(eated)d(by)j(the)g(algorithm)g(have)f(typical)h(pr)o(oper)o(-)330
+2605 y(ties)k(which)h(wer)o(e)e(not)i(r)o(e\003ected)e(in)h(this)h
+(test)f(data.)f(For)h(this)h(r)o(eason)f(r)o(esults)g(ar)o(e)e(pr)o
+(esented)330 2705 y(for)f(a)g(number)h(of)f(automata)g(that)g(wer)o(e)f
+(generated)h(using)h(appr)o(oximation)f(techniques)h(for)330
+2805 y(context-fr)o(ee)29 b(grammars.)g(In)i(particular)-6
+b(,)28 b(automata)i(have)f(been)h(used)g(which)h(wer)o(e)e(cr)o(e-)330
+2904 y(ated)18 b(by)g(Neder)o(hof,)g(using)h(the)g(technique)g
+(described)f(in)h(Neder)o(hof)e(\(1997\).)f(In)j(addition,)f(a)330
+3004 y(small)g(number)g(of)f(automata)g(have)g(been)h(used)f(which)i
+(wer)o(e)d(cr)o(eated)g(using)i(the)g(technique)330 3104
+y(of)f(Per)o(eira)e(and)h(W)-6 b(right)17 b(\(1997\))d(\(as)h
+(implemented)i(by)g(Neder)o(hof\).)e(W)-8 b(e)16 b(have)h(r)o
+(estricted)e(our)330 3203 y(attention)21 b(to)h(automata)e(with)h(at)f
+(least)h(1000)e(states)h(in)i(the)e(input.)479 3303 y(The)k(automata)f
+(typically)h(contain)g(lots)h(of)e(jumps.)i(Mor)o(eover)-6
+b(,)22 b(the)i(number)g(of)f(states)330 3402 y(of)16
+b(the)g(r)o(esulting)g(automaton)g(is)h(often)f Fu(smaller)g
+Fv(than)g(the)g(number)g(of)g(states)g(in)g(the)g(input)h(au-)330
+3502 y(tomaton.)j(Results)g(ar)o(e)e(given)h(in)h(the)f(tables)g(1)g
+(and)g(2.)f(One)i(of)f(the)g(most)h(striking)h(examples)330
+3602 y(is)f(the)h Fu(ygrim)e Fv(automaton)h(consisting)i(of)e(3382)e
+(states)i(and)g(9124)e(jumps.)j(For)f(this)h(example,)330
+3701 y(the)i Fu(per)g(graph)f Fv(implementations)j(ran)d(out)i(of)f
+(memory)h(\(after)d(a)i(long)h(time\),)f(wher)o(eas)f(the)330
+3801 y(implementation)h(of)e(the)g Fu(per)h(subset)h
+Fv(algorithm)f(pr)o(oduced)e(the)h(determinised)h(automaton)330
+3901 y(\(containing)28 b(only)g(9)f(states\))f(within)j(a)d(single)i
+(CPU-second.)e(The)h(FSM)g(implementation)330 4000 y(took)f(much)g
+(longer)g(for)f(this)h(example)e(\(wher)o(eas)g(for)h(many)g(of)h(the)f
+(other)h(examples)e(it)i(is)330 4100 y(faster)d(than)h(our)g
+(implementations\).)h(Note)f(that)f(this)i(example)e(has)h(the)g
+(highest)h(number)330 4199 y(of)20 b(jumps)h(per)e(number)h(of)g
+(states)g(ratio.)f(This)h(con\002rms)h(the)f(observation)h(that)e(the)h
+Fu(per)g(sub-)330 4299 y(set)h Fv(algorithm)h(performs)e(better)g(on)i
+(inputs)f(with)h(a)e(high)i(deterministic)f(jump)g(density)-9
+b(.)330 4498 y Fs(5)20 b(Conclusion)330 4698 y Fv(W)-8
+b(e)25 b(have)f(discussed)h(a)g(number)g(of)g(variants)f(of)h(the)g
+(subset-constr)o(uction)i(algorithm)e(for)330 4797 y(determinising)31
+b(\002nite)f(automata)f(containing)j Ft(\017)p Fv(-moves.)d(The)h
+(experiments)g(support)g(the)330 4897 y(following)22
+b(conclusions:)p Black 571 5075 a Fk(\017)p Black 16
+w Fv(The)f(integrated)f(variants)g Fu(per)h(subset)h
+Fv(and)e Fu(per)h(state)f Fv(work)i(much)f(better)f(for)629
+5174 y(automata)g(containing)i(a)e(lar)o(ge)g(number)h(of)g
+Ft(\017)p Fv(-moves.)f(The)h Fu(per)f(subset)i Fv(variant)629
+5274 y(tends)f(to)g(impr)o(ove)f(upon)i(the)f Fu(per)f(state)h
+Fv(algorithm)g(if)g(the)g(number)g(of)g Ft(\017)p Fv(-moves)629
+5373 y(incr)o(eases)f(even)g(further)-6 b(.)p Black 571
+5538 a Fk(\017)p Black 16 w Fv(W)e(e)21 b(have)f(identi\002ed)h(four)f
+(dif)o(fer)o(ent)f(variants)h(of)h(the)g Fu(per)g(graph)e
+Fv(algorithm.)i(In)629 5637 y(our)g(experiments,)f(the)h
+Fu(per)g(graph)1730 5607 y Fi(t)1779 5637 y Fv(is)g(the)g(algorithm)g
+(of)g(choice)g(for)g(automata)p Black 3247 5944 a(13)p
+Black eop
+%%Page: 14 14
+14 13 bop Black 330 91 a Fo(van)20 b(Noor)o(d)1145 b(Epsilon)17
+b(Moves)h(in)h(Subset)g(Constr)o(uction)p Black Black
+380 705 2900 4 v 378 805 4 100 v 772 805 V 772 805 V
+1193 775 a Fv(Input)p 1814 805 V 1814 805 V 1017 w(Output)p
+3278 805 V 380 808 2900 4 v 378 908 4 100 v 537 878 a(Id)p
+772 908 V 207 w(#states)p 1119 908 V 99 w(#trans)p 1445
+908 V 99 w(#jumps)p 1814 908 V 1814 908 V 659 w(#states)p
+3278 908 V 1815 911 1465 4 v 378 1007 4 100 v 772 1007
+V 1119 1007 V 1445 1007 V 1814 1007 V 1918 977 a Fo(per)e(graph)2243
+946 y Fg(s)p 2325 1007 V 2376 977 a Fo(per)h(graph)2702
+946 y Fg(t)p 2778 1007 V 2829 977 a Fo(per)g(graph)3155
+946 y Fg(t;c)p 3278 1007 V 378 1107 V 772 1107 V 1119
+1107 V 1445 1107 V 1814 1107 V 1865 1077 a Fo(per)g(graph)2191
+1045 y Fg(s;a)p 2325 1107 V 2391 1077 a Fo(per)g(subset)p
+2778 1107 V 3278 1107 V 378 1207 V 772 1207 V 1119 1207
+V 1445 1207 V 1814 1207 V 2106 1177 a Fu(FSM)p 2325 1207
+V 171 w Fo(per)g(state)p 2778 1207 V 3278 1207 V 380
+1210 2900 4 v 378 1310 4 100 v 512 1280 a Fv(g14)p 772
+1310 V 262 w(1048)p 1119 1310 V 200 w(403)p 1445 1310
+V 201 w(1272)p 1814 1310 V 385 w(137)p 2325 1310 V 327
+w(137)p 2778 1310 V 374 w(131)p 3278 1310 V 378 1409
+V 446 1379 a(ovis4.n)p 772 1409 V 196 w(1424)p 1119 1409
+V 158 w(2210)p 1445 1409 V 243 w(517)p 1814 1409 V 385
+w(164)p 2325 1409 V 327 w(133)p 2778 1409 V 374 w(107)p
+3278 1409 V 378 1509 V 512 1479 a(g13)p 772 1509 V 262
+w(1441)p 1119 1509 V 158 w(1006)p 1445 1509 V 201 w(1272)p
+1814 1509 V 385 w(337)p 2325 1509 V 327 w(337)p 2778
+1509 V 374 w(329)p 3278 1509 V 378 1608 V 476 1579 a(r)o(ene2)p
+772 1608 V 226 w(1800)p 1119 1608 V 158 w(2597)p 1445
+1608 V 284 w(96)p 1814 1608 V 386 w(846)p 2325 1608 V
+327 w(844)p 2778 1608 V 374 w(844)p 3278 1608 V 378 1708
+V 445 1678 a(ovis9.p)p 772 1708 V 195 w(1868)p 1119 1708
+V 158 w(2791)p 1445 1708 V 201 w(2688)p 1814 1708 V 344
+w(2478)p 2325 1708 V 285 w(2478)p 2778 1708 V 332 w(1386)p
+3278 1708 V 378 1808 V 466 1778 a(ygrim)p 772 1808 V
+216 w(3382)p 1119 1808 V 158 w(5422)p 1445 1808 V 201
+w(9124)p 1814 1808 V 468 w(9)p 2325 1808 V 411 w(9)p
+2778 1808 V 458 w(9)p 3278 1808 V 378 1907 V 430 1877
+a(ygrim.p)p 772 1907 V 140 w(48062)p 1119 1907 V 116
+w(63704)p 1445 1907 V 117 w(109296)p 1814 1907 V 384
+w(702)p 2325 1907 V 327 w(702)p 2778 1907 V 374 w(702)p
+3278 1907 V 378 2007 V 461 1977 a(java19)p 772 2007 V
+168 w(54369)p 1119 2007 V 116 w(28333)p 1445 2007 V 159
+w(51018)p 1814 2007 V 343 w(1971)p 2325 2007 V 285 w(1971)p
+2778 2007 V 332 w(1855)p 3278 2007 V 378 2107 V 461 2077
+a(java16)p 772 2107 V 168 w(64210)p 1119 2107 V 116 w(43935)p
+1445 2107 V 159 w(41305)p 1814 2107 V 343 w(3186)p 2325
+2107 V 285 w(3186)p 2778 2107 V 332 w(3078)p 3278 2107
+V 378 2206 V 460 2176 a(zovis3)p 772 2206 V 168 w(88156)p
+1119 2206 V 116 w(78895)p 1445 2206 V 159 w(68093)p 1814
+2206 V 343 w(5174)p 2325 2206 V 285 w(5154)p 2778 2206
+V 332 w(4182)p 3278 2206 V 378 2306 V 460 2276 a(zovis2)p
+772 2306 V 168 w(89832)p 1119 2306 V 116 w(80400)p 1445
+2306 V 159 w(69377)p 1814 2306 V 343 w(6561)p 2325 2306
+V 285 w(6541)p 2778 2306 V 332 w(5309)p 3278 2306 V 380
+2309 2900 4 v 330 2371 a Fd(T)-8 b(able)18 b(1)330 2454
+y Fo(The)h(automata)h(generated)e(by)h(appr)o(oximation)e(algorithms.)h
+(The)h(table)g(lists)f(the)h(number)g(of)f(states,)330
+2537 y(transitions)h(and)g(jumps)g(of)f(the)i(input)f(automaton,)h(and)
+f(the)g(number)g(of)f(states)h(of)g(the)330 2629 y(determinised)e
+(machine)j(using)e(r)o(espectively)e(the)k Fc(efr)o(ee)1962
+2597 y Fg(s)1995 2629 y Fo(,)e Fc(efr)o(ee)2168 2597
+y Fg(t)2196 2629 y Fo(,)g(and)h(the)g Fc(efr)o(ee)2636
+2597 y Fg(t;c)2729 2629 y Fo(variants.)p Black Black
+468 3575 2725 4 v 466 3675 4 100 v 859 3675 V 859 3675
+V 1750 3645 a Fv(CPU-time)h(\(sec\))p 3190 3675 V 861
+3678 2332 4 v 466 3775 4 100 v 859 3775 V 911 3745 a
+Fo(graph)1108 3713 y Fg(t)p 1183 3775 V 1235 3745 a Fo(graph)1432
+3713 y Fg(t;c)p 1555 3775 V 1606 3745 a Fo(graph)1803
+3713 y Fg(s)p 1884 3775 V 1936 3745 a Fo(graph)2133 3713
+y Fg(s;a)p 2267 3775 V 2318 3745 a Fo(subset)p 2576 3775
+V 133 w(state)p 2862 3775 V 158 w Fu(FSM)p 3190 3775
+V 468 3778 2725 4 v 466 3878 4 100 v 600 3848 a Fv(g14)p
+859 3878 V 302 w(0.4)p 1183 3878 V 266 w(0.4)p 1555 3878
+V 224 w(0.3)p 1884 3878 V 278 w(0.3)p 2267 3878 V 204
+w(0.4)p 2576 3878 V 182 w(0.2)p 2862 3878 V 222 w(0.1)p
+3190 3878 V 466 3977 V 533 3947 a(ovis4.n)p 859 3977
+V 237 w(0.9)p 1183 3977 V 266 w(1.1)p 1555 3977 V 224
+w(0.8)p 1884 3977 V 278 w(1.0)p 2267 3977 V 204 w(0.7)p
+2576 3977 V 182 w(0.6)p 2862 3977 V 222 w(0.6)p 3190
+3977 V 466 4077 V 600 4047 a(g13)p 859 4077 V 302 w(0.9)p
+1183 4077 V 266 w(0.8)p 1555 4077 V 224 w(0.6)p 1884
+4077 V 278 w(0.6)p 2267 4077 V 204 w(1.2)p 2576 4077
+V 182 w(0.7)p 2862 4077 V 222 w(0.2)p 3190 4077 V 466
+4177 V 564 4147 a(r)o(ene2)p 859 4177 V 266 w(0.2)p 1183
+4177 V 266 w(0.3)p 1555 4177 V 224 w(0.2)p 1884 4177
+V 278 w(0.2)p 2267 4177 V 204 w(0.2)p 2576 4177 V 182
+w(0.2)p 2862 4177 V 222 w(0.1)p 3190 4177 V 466 4276
+V 532 4246 a(ovis9.p)p 859 4276 V 194 w(36.6)p 1183 4276
+V 224 w(16.0)p 1555 4276 V 183 w(16.9)p 1884 4276 V 235
+w(17.0)p 2267 4276 V 163 w(25.2)p 2576 4276 V 139 w(20.8)p
+2862 4276 V 181 w(21.9)p 3190 4276 V 466 4376 V 553 4346
+a(ygrim)p 859 4376 V 333 w(-)p 1183 4376 V 343 w(-)p
+1555 4376 V 301 w(-)p 1884 4376 V 355 w(-)p 2267 4376
+V 205 w(0.9)p 2576 4376 V 140 w(21.0)p 2862 4376 V 139
+w(512.1)p 3190 4376 V 466 4475 V 518 4446 a(ygrim.p)p
+859 4475 V 297 w(-)p 1183 4475 V 343 w(-)p 1555 4475
+V 301 w(-)p 1884 4475 V 355 w(-)p 2267 4475 V 122 w(562.1)p
+2576 4475 V 257 w(-)p 2862 4475 V 99 w(4512.4)p 3190
+4475 V 466 4575 V 548 4545 a(java19)p 859 4575 V 208
+w(55.5)p 1183 4575 V 224 w(67.4)p 1555 4575 V 183 w(52.6)p
+1884 4575 V 235 w(45.0)p 2267 4575 V 163 w(25.8)p 2576
+4575 V 139 w(19.0)p 2862 4575 V 222 w(3.8)p 3190 4575
+V 466 4675 V 548 4645 a(java16)p 859 4675 V 208 w(30.0)p
+1183 4675 V 224 w(45.8)p 1555 4675 V 183 w(35.0)p 1884
+4675 V 235 w(29.9)p 2267 4675 V 167 w(1)-5 b(1.3)p 2576
+4675 V 140 w(12.1)p 2862 4675 V 222 w(3.0)p 3190 4675
+V 466 4774 V 547 4744 a(zovis3)p 859 4774 V 167 w(741.1)p
+1183 4774 V 182 w(557.5)p 1555 4774 V 299 w(-)p 1884
+4774 V 196 w(407.4)p 2267 4774 V 120 w(358.4)p 2576 4774
+V 98 w(302.5)p 2862 4774 V 138 w(325.6)p 3190 4774 V
+466 4874 V 547 4844 a(zovis2)p 859 4874 V 167 w(909.2)p
+1183 4874 V 182 w(627.2)p 1555 4874 V 299 w(-)p 1884
+4874 V 196 w(496.0)p 2267 4874 V 120 w(454.4)p 2576 4874
+V 98 w(369.4)p 2862 4874 V 138 w(392.1)p 3190 4874 V
+468 4877 2725 4 v 330 4939 a Fd(T)d(able)18 b(2)330 5022
+y Fo(Results)g(for)g(automata)i(generated)e(by)h(appr)o(oximation)e
+(algorithms.)h(The)h(dashes)f(in)h(the)g(table)330 5105
+y(indicate)g(that)h(the)g(corr)o(esponding)c(algorithm)i(ran)h(out)g
+(of)f(memory)g(\(after)g(a)h(long)f(period)g(of)g(time\))330
+5188 y(for)g(that)i(particular)f(example.)p Black Black
+3247 5944 a Fv(14)p Black eop
+%%Page: 15 15
+15 14 bop Black 330 91 a Fo(van)20 b(Noor)o(d)1145 b(Epsilon)17
+b(Moves)h(in)h(Subset)g(Constr)o(uction)p Black Black
+629 357 a Fv(containing)i(few)f Ft(\017)g Fv(moves,)h(because)e(it)h
+(is)h(faster)e(than)i(the)f(other)g(algorithms,)h(and)629
+457 y(because)f(it)h(pr)o(oduces)f(smaller)g(automata)g(than)h(the)g
+Fu(per)g(graph)2674 426 y Fi(s)2729 457 y Fv(and)f Fu(per)h(graph)3212
+426 y Fi(s;a)629 556 y Fv(variants.)p Black 571 722 a
+Fk(\017)p Black 16 w Fv(The)g Fu(per)f(graph)1110 692
+y Fi(t;c)1209 722 y Fv(variant)g(is)h(an)f(inter)o(esting)h
+(alternative)f(in)h(that)g(it)g(pr)o(oduces)f(the)629
+822 y(smallest)h(r)o(esults.)f(This)i(variant)e(should)h(be)g(used)f
+(if)h(the)g(input)g(automaton)g(is)629 922 y(expected)e(to)i(contain)h
+(many)f(non-co-accessible)f(states.)p Black 571 1088
+a Fk(\017)p Black 16 w Fv(Automata)g(pr)o(oduced)f(by)i(\002nite-state)
+g(appr)o(oximation)f(techniques)i(tend)f(to)629 1187
+y(contain)g(many)g Ft(\017)p Fv(-moves.)g(W)-8 b(e)21
+b(found)f(that)h(for)g(these)f(automata)h(the)f(dif)o(fer)o(ences)629
+1287 y(in)h(speed)f(between)h(the)g(various)f(algorithms)i(can)f(be)f
+(enormous.)i(The)e Fu(per)h(subset)629 1386 y Fv(and)f
+Fu(per)h(state)g Fv(algorithms)g(ar)o(e)f(good)h(candidates)f(for)g
+(this)i(application.)479 1569 y(W)-8 b(e)30 b(have)e(attempted)h(to)g
+(characterize)e(the)i(expected)f(ef)o(\002ciency)g(of)h(the)h(various)f
+(al-)330 1669 y(gorithms)f(in)f(terms)f(of)h(the)f(number)h(of)f(jumps)
+h(and)f(the)h(number)f(of)h(states)f(in)h(the)g(input)330
+1768 y(automaton.)17 b(It)f(is)g(quite)h(conceivable)f(that)g(other)h
+(simple)g(pr)o(operties)e(of)h(the)h(input)g(automa-)330
+1868 y(ton)25 b(can)g(be)f(used)g(even)h(mor)o(e)f(ef)o(fectively)f
+(for)h(this)i(purpose.)e(One)h(r)o(eviewer)e(suggests)j(to)330
+1968 y(use)21 b(the)g(number)f(of)h(str)o(ongly)g Ft(\017)p
+Fv(-connected)f(components)i(\(the)f(str)o(ongly)g(connected)g(com-)330
+2067 y(ponents)g(of)g(the)g(graph)f(of)h(all)f Ft(\017)p
+Fv(-moves\))g(for)h(this)g(purpose.)f(W)-8 b(e)21 b(leave)f(this)h(and)
+f(other)h(pos-)330 2167 y(sibilities)h(to)f(a)f(futur)o(e)g(occasion.)p
+Black 330 2367 a Fd(Acknowledgments)330 2467 y Fo(I)f(am)g(grateful)f
+(to)h(Mark-Jan)f(Neder)o(hof)f(for)330 2550 y(support,)h(and)h(for)f
+(pr)o(oviding)e(me)j(with)g(lots)g(of)330 2633 y(\(often)g(dr)o
+(eadful\))e(automata)j(generated)e(by)330 2716 y(his)h(\002nite-state)g
+(appr)o(oximation)f(tools.)g(The)330 2799 y(comments)h(of)f(the)i
+(anonymous)e(FSMNLP)330 2882 y(and)h(CL)f(r)o(eviewers)f(wer)o(e)h
+(extr)o(emely)e(useful.)330 3081 y Fd(References)p Black
+Black 330 3214 a Fo(Aho,)j(Alfr)o(ed)e(V)-10 b(.,)18
+b(Ravi)h(Sethi,)g(and)g(Jef)o(fr)o(ey)e(D.)405 3297 y(Ullman.)27
+b(1986.)h Fc(Compilers.)18 b(Principles,)405 3380 y(T)-8
+b(echniques)17 b(and)i(T)-8 b(ools)p Fo(.)26 b(Addison)18
+b(W)-7 b(esley)f(.)p Black Black 330 3480 a(Black,)18
+b(A.W)-7 b(.)26 b(1989.)i(Finite)18 b(state)i(machines)405
+3563 y(fr)o(om)d(featur)o(e)h(grammars.)26 b(In)19 b
+Fc(International)405 3646 y(W)o(orkshop)g(on)f(Parsing)h(T)-8
+b(echnologies)p Fo(,)18 b(pages)405 3729 y(277\226285,)j(Pittsbur)o
+(gh.)p Black Black 330 3829 a(Chomsky)-8 b(,)17 b(Noam.)27
+b(1963.)h(Formal)18 b(pr)o(operties)405 3912 y(of)g(grammars.)26
+b(In)19 b(R.)f(Duncan)i(Luce,)405 3995 y(Robert)e(R.)g(Bush,)h(and)g
+(Eugene)f(Galanter)-6 b(,)405 4078 y(editors,)17 b Fc(Handbook)i(of)f
+(Mathematical)405 4161 y(Psychology;)i(V)-6 b(olume)19
+b(II)p Fo(.)f(John)h(W)l(iley)-8 b(,)17 b(pages)405 4244
+y(323\226418.)p Black Black 330 4343 a(Chomsky)-8 b(,)17
+b(Noam.)27 b(1964.)h(On)19 b(the)g(notion)405 4426 y(`r)o(ule)e(of)h
+(grammar)6 b('.)25 b(In)19 b(Jerry)e(E.)g(Fodor)g(and)405
+4509 y(Jerr)o(old)f(J.)i(Katz,)i(editors,)d Fc(The)i(Structur)o(e)e(of)
+405 4592 y(Language;)h(Readings)h(in)f(the)h(Philosophy)g(of)405
+4675 y(Language)p Fo(.)f(Pr)o(entice)g(Hall,)h(pages)f(1)l(19\226136.)p
+Black Black 330 4775 a(Cormen,)g(Leiserson,)e(and)k(Rivest.)26
+b(1990.)405 4858 y Fc(Intr)o(oduction)17 b(to)i(Algorithms)p
+Fo(.)27 b(MIT)18 b(Pr)o(ess,)405 4941 y(Cambridge)f(Mass.)p
+Black Black 330 5041 a(Evans,)i(Edmund)f(Grimley)-8 b(.)25
+b(1997.)405 5124 y(Appr)o(oximating)17 b(context-fr)o(ee)h(grammars)405
+5207 y(with)h(a)g(\002nite-state)h(calculus.)27 b(In)19
+b Fc(35th)405 5290 y(Annual)e(Meeting)h(of)g(the)h(Association)g(for)
+405 5373 y(Computational)f(Linguistics)f(and)i(8th)405
+5456 y(Confer)o(ence)f(of)g(the)h(Eur)o(opean)f(Chapter)i(of)e(the)405
+5539 y(Association)g(for)h(Computational)f(Linguistics)p
+Fo(,)405 5622 y(pages)g(452\226459,)j(Madrid.)p Black
+Black 1930 2367 a(Ger)o(demann,)d(Dale)g(and)h(Gertjan)h(van)g(Noor)o
+(d.)2004 2450 y(1999.)28 b(T)-7 b(ransducers)18 b(fr)o(om)g(r)o(ewrite)
+f(r)o(ules)2004 2533 y(with)j(backr)o(efer)o(ences.)25
+b(In)19 b Fc(Ninth)f(Confer)o(ence)2004 2617 y(of)h(the)g(Eur)o(opean)f
+(Chapter)h(of)g(the)g(Association)2004 2700 y(for)g(Computational)f
+(Linguistics)p Fo(,)f(Ber)o(gen)2004 2783 y(Norway)-8
+b(.)p Black Black 1930 2882 a(Hopcr)o(oft,)17 b(John)j(E.)e(and)h(Jef)o
+(fr)o(ey)d(D.)i(Ullman.)2004 2965 y(1979.)28 b Fc(Intr)o(oduction)18
+b(to)h(Automata)f(Theory)m(,)2004 3048 y(Languages)h(and)g(Computation)
+p Fo(.)26 b(Addison)2004 3131 y(W)-7 b(esley)f(.)p Black
+Black 1930 3231 a(Johnson,)19 b(J.)f(Howar)o(d)g(and)h(Derick)e(W)-7
+b(ood.)2004 3314 y(1997.)28 b(Instr)o(uction)20 b(computation)g(in)f
+(subset)2004 3397 y(constr)o(uction.)28 b(In)19 b(Darr)o(ell)e
+(Raymond,)2004 3480 y(Derick)h(W)-7 b(ood,)17 b(and)i(Sheng)g(Y)-7
+b(u,)19 b(editors,)2004 3563 y Fc(Automata)g(Implementation)p
+Fo(.)f(Springer)2004 3646 y(V)-8 b(erlag,)17 b(pages)h(64\22671.)29
+b(Lectur)o(e)17 b(Notes)i(in)2004 3729 y(Computer)f(Science)h(1260.)p
+Black Black 1930 3829 a(Johnson,)g(Mark.)25 b(1998.)j(Finite-state)2004
+3912 y(appr)o(oximation)18 b(of)h(constraint-based)2004
+3995 y(grammars)f(using)g(left-corner)g(grammar)2004
+4078 y(transforms.)26 b(In)20 b Fc(COLING-ACL)d('98.)i(36th)2004
+4161 y(Annual)f(Meeting)f(of)i(the)g(Association)g(for)2004
+4244 y(Computational)f(Linguistics)g(and)h(17th)2004
+4327 y(International)f(Confer)o(ence)f(on)i(Computational)2004
+4410 y(Linguistics.)e(Pr)o(oceedings)i(of)g(the)g(Confer)o(ence)p
+Fo(,)2004 4493 y(Montr)o(eal.)p Black Black 1930 4592
+a(Leslie,)d(T)-7 b(ed.)26 b(1995.)i(Ef)o(\002cient)19
+b(appr)o(oaches)f(to)2004 4675 y(subset)h(constr)o(uction.)28
+b(Master)6 b('s)17 b(thesis,)2004 4758 y(Computer)h(Science,)h
+(University)f(of)2004 4842 y(W)-7 b(aterloo.)p Black
+Black 1930 4941 a(Miller)h(,)17 b(Geor)o(ge)f(and)k(Noam)f(Chomsky)-8
+b(.)25 b(1963.)2004 5024 y(Finitary)18 b(models)g(of)g(language)h
+(users.)25 b(In)2004 5107 y(R.)19 b(Luce,)f(R.)g(Bush,)g(and)h(E.)f
+(Galanter)-6 b(,)2004 5190 y(editors,)17 b Fc(Handbook)i(of)g
+(Mathematical)2004 5273 y(Psychology)m(.)i(V)-6 b(olume)18
+b(2.)h Fo(John)g(W)l(iley)-8 b(.)p Black Black 1930 5373
+a(Mohri,)17 b(Mehryar)-6 b(,)18 b(Fernando)g(C.N.)g(Per)o(eira,)2004
+5456 y(and)i(Michael)e(Riley)-8 b(.)25 b(1998.)j(A)19
+b(rational)2004 5539 y(design)f(for)g(a)h(weighted)f(\002nite-state)
+2004 5622 y(transducer)h(library)-8 b(.)25 b(In)19 b
+Fc(Automata)p Black 3247 5944 a Fv(15)p Black eop
+%%Page: 16 16
+16 15 bop Black 330 91 a Fo(van)20 b(Noor)o(d)1145 b(Epsilon)17
+b(Moves)h(in)h(Subset)g(Constr)o(uction)p Black 405 357
+a Fc(Implementation.)e(Second)i(International)405 440
+y(W)o(orkshop)g(on)f(Implementing)g(Automata,)405 523
+y(WIA)g('97)p Fo(.)h(Springer)e(V)-8 b(erlag.)25 b(Lectur)o(e)18
+b(Notes)405 606 y(in)h(Computer)f(Science)h(1436.)p Black
+Black 330 706 a(Neder)o(hof,)e(M.)h(J.)27 b(1997.)h(Regular)405
+789 y(appr)o(oximations)17 b(of)h(CFLs:)f(A)h(grammatical)405
+872 y(view)-7 b(.)26 b(In)20 b Fc(International)d(W)o(orkshop)i(on)405
+955 y(Parsing)f(T)-8 b(echnologies)p Fo(,)19 b(Massachusetts)405
+1038 y(Institute)g(of)g(T)-7 b(echnology)f(.)p Black
+Black 330 1137 a(Neder)o(hof,)17 b(Mark-Jan.)26 b(1998.)i(Context-fr)o
+(ee)405 1220 y(parsing)18 b(thr)o(ough)g(r)o(egular)f(appr)o
+(oximation.)405 1303 y(In)i Fc(Finite-state)e(Methods)i(in)f(Natural)
+405 1386 y(Language)g(Pr)o(ocessing)p Fo(,)g(pages)g(13\22624,)405
+1469 y(Ankara.)p Black Black 330 1569 a(van)i(Noor)o(d,)d(Gertjan.)27
+b(1997.)h(FSA)19 b(Utilities:)e(A)405 1652 y(toolbox)h(to)h(manipulate)
+g(\002nite-state)405 1735 y(automata.)28 b(In)19 b(Darr)o(ell)e
+(Raymond,)h(Derick)405 1818 y(W)-7 b(ood,)17 b(and)i(Sheng)h(Y)-7
+b(u,)18 b(editors,)f Fc(Automata)405 1901 y(Implementation)p
+Fo(.)g(Springer)h(V)-8 b(erlag,)17 b(pages)405 1984 y(87\226108.)28
+b(Lectur)o(e)18 b(Notes)h(in)f(Computer)405 2067 y(Science)h(1260.)p
+Black Black 330 2167 a(van)h(Noor)o(d,)d(Gertjan.)27
+b(1998.)h(The)19 b(tr)o(eatment)405 2250 y(of)f(epsilon)g(moves)g(in)h
+(subset)g(constr)o(uction.)405 2333 y(In)g Fc(Finite-state)e(Methods)i
+(in)f(Natural)405 2416 y(Language)g(Pr)o(ocessing)p Fo(,)g(Ankara.)405
+2499 y(cmp-lg/9804003.)p Black Black 330 2599 a(van)i(Noor)o(d,)d
+(Gertjan.)27 b(1999.)h(FSA6)19 b(r)o(efer)o(ence)405
+2682 y(manual.)27 b(The)19 b Fc(FSA)f(Utilities)g Fo(toolbox)g(is)405
+2765 y(available)h(fr)o(ee)e(of)i(char)o(ge)f(under)g(Gnu)405
+2848 y(General)g(Public)h(License)f(at)405 2931 y(http://www)-7
+b(.let.r)o(ug.nl/\230vannoor)o(d/Fsa/.)p Black Black
+330 3030 a(van)20 b(Noor)o(d,)d(Gertjan)i(and)g(Dale)g(Ger)o(demann.)
+405 3113 y(1999.)28 b(An)19 b(extendible)f(r)o(egular)f(expr)o(ession)
+405 3196 y(compiler)g(for)h(\002nite-state)i(appr)o(oaches)e(in)405
+3279 y(natural)h(language)g(pr)o(ocessing.)24 b(In)405
+3362 y(O.)18 b(Boldt,)f(H.)i(Juer)o(gensen,)e(and)405
+3445 y(L.)h(Robbins,)g(editors,)f Fc(W)o(orkshop)i(on)405
+3528 y(Implementing)f(Automata;)g(WIA99)405 3611 y(Pr)o(e-Pr)o
+(oceedings)p Fo(,)g(Potsdam)g(Germany)-8 b(.)p Black
+Black 330 3711 a(O'Keefe,)17 b(Richar)o(d)i(A.)26 b(1990.)i
+Fc(The)19 b(Craft)f(of)405 3794 y(Pr)o(olog)p Fo(.)26
+b(The)19 b(MIT)f(Pr)o(ess,)f(Cambridge)405 3877 y(Mass.)p
+Black Black 330 3977 a(Per)o(eira,)g(Fernando)h(C.)h(N.)f(and)h(R.)f
+(N.)h(W)-6 b(right.)405 4060 y(1991.)28 b(Finite-state)19
+b(appr)o(oximation)e(of)405 4143 y(phrase)h(str)o(uctur)o(e)g
+(grammars.)26 b(In)19 b Fc(29th)405 4226 y(Annual)e(Meeting)h(of)g(the)
+h(Association)g(for)405 4309 y(Computational)f(Linguistics)p
+Fo(,)f(Berkeley)-8 b(.)p Black Black 330 4408 a(Per)o(eira,)17
+b(Fernando)h(C.)h(N.)f(and)h(Rebecca)g(N.)405 4491 y(W)-6
+b(right.)26 b(1997.)i(Finite-state)405 4575 y(appr)o(oximation)18
+b(of)g(phrase-str)o(uctur)o(e)405 4658 y(grammars.)25
+b(In)20 b(Emmanuel)e(Roche)h(and)405 4741 y(Y)-7 b(ves)18
+b(Schabes,)i(editors,)c Fc(Finite-State)405 4824 y(Language)i(Pr)o
+(ocessing)p Fo(.)g(MIT)h(Pr)o(ess,)405 4907 y(Cambridge,)e(pages)h
+(149\226173.)p Black Black 330 5006 a(Rood,)g(C.M.)25
+b(1996.)j(Ef)o(\002cient)19 b(\002nite-state)405 5089
+y(appr)o(oximation)f(of)g(context)h(fr)o(ee)405 5172
+y(grammars.)25 b(In)20 b(A.)e(Kornai,)h(editor)-6 b(,)405
+5255 y Fc(Extended)19 b(Finite)e(State)h(Models)h(of)f(Language)p
+Fo(,)405 5338 y(Pr)o(oceedings)e(of)j(the)g(ECAI'96)g(workshop,)405
+5421 y(pages)f(58\22664,)i(Budapest)e(University)g(of)405
+5504 y(Economic)g(Sciences,)h(Hungary)-8 b(.)p Black
+3247 5944 a Fv(16)p Black eop
+%%Trailer
+end
+userdict /end-hook known{end-hook}if
+%%EOF
diff --git a/resources/regexprdemo.jar b/resources/regexprdemo.jar
deleted file mode 100644
index 4d4f2cc..0000000
Binary files a/resources/regexprdemo.jar and /dev/null differ
diff --git a/resources/sources/RegExSource.zip b/resources/sources/RegExSource.zip
new file mode 100644
index 0000000..6171e3d
Binary files /dev/null and b/resources/sources/RegExSource.zip differ
diff --git a/resources/sources/graphregexpr.jar b/resources/sources/graphregexpr.jar
new file mode 100644
index 0000000..99e8440
Binary files /dev/null and b/resources/sources/graphregexpr.jar differ
diff --git a/resources/sources/regexprdemo.jar b/resources/sources/regexprdemo.jar
new file mode 100644
index 0000000..4d4f2cc
Binary files /dev/null and b/resources/sources/regexprdemo.jar differ
diff --git a/stylesheets/RegexVis.css b/stylesheets/RegexVis.css
deleted file mode 100644
index e69de29..0000000
diff --git a/stylesheets/styles.css b/stylesheets/styles.css
new file mode 100644
index 0000000..cac897b
--- /dev/null
+++ b/stylesheets/styles.css
@@ -0,0 +1,42 @@
+body {
+	background-color: #fff;
+	font-family: Helvetica;
+	color: #000;
+}
+
+a { color: #000 }
+
+input {
+	vertical-align: bottom;
+	font-size: 1.1em;
+}
+input[type='button'] {
+	vertical-align:middle;
+	font-size: 1.25em;
+	
+}
+input[type='text'] { padding: 4px }
+
+div#wrapper {
+	margin-left: auto;
+	margin-right: auto;
+	width: 1024px;
+	height: 100%;
+}
+
+div#holder {
+	margin-left: auto;
+	margin-right: auto;
+}
+
+span#desc { display:none }
+
+.message {
+	font-weight: bold;
+	-moz-border-radius: 5px;
+	padding: 4px;
+	text-decoration: none;
+}
+.success { background-color: #CDEB8B }
+.failure { background-color: #B02B2C }
+.gray { background-color: #ccc }
-- 
cgit v1.2.3