From 8451c8146bc301135d72c7a41f091ff429bf7dfb Mon Sep 17 00:00:00 2001 From: Patrick Simianer Date: Sun, 15 Jun 2014 04:21:04 +0200 Subject: cleanup --- resources/literature/04-regulaere-ausdruecke.pdf | Bin 150900 -> 0 bytes resources/literature/compactdfa.pdf | Bin 259747 -> 0 bytes resources/literature/epsilonmoves.pdf | Bin 925842 -> 0 bytes resources/literature/fsmnlp.ps | 6674 ---------------------- 4 files changed, 6674 deletions(-) delete mode 100644 resources/literature/04-regulaere-ausdruecke.pdf delete mode 100644 resources/literature/compactdfa.pdf delete mode 100644 resources/literature/epsilonmoves.pdf delete mode 100644 resources/literature/fsmnlp.ps (limited to 'resources/literature') diff --git a/resources/literature/04-regulaere-ausdruecke.pdf b/resources/literature/04-regulaere-ausdruecke.pdf deleted file mode 100644 index fe4e985..0000000 Binary files a/resources/literature/04-regulaere-ausdruecke.pdf and /dev/null differ diff --git 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.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. 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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 - 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All Rights Reserved. - -11 dict begin -/FontInfo 7 dict dup begin -/version (1.100) readonly def -/Notice (Copyright (C) 1997 American Mathematical Society. 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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 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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 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