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diff --git a/presentation/g.tex b/presentation/g.tex new file mode 100644 index 0000000..8b32c8e --- /dev/null +++ b/presentation/g.tex @@ -0,0 +1,267 @@ +% g.tex +% Patrick Simianer <p@simianer.de> +% 2010-05-24 +\documentclass{scrartcl} + +\usepackage[utf8]{inputenc} +\usepackage[T1]{fontenc} +\usepackage[ngerman]{babel} +\usepackage{lmodern} + +\usepackage{tikz} +\usetikzlibrary{arrows,automata} + + +\begin{document} + + +$a*$\\ + +\begin{tikzpicture}[shorten >=1pt,node distance=3cm,>=stealth',thick] + \tikzstyle{every state}=[draw=blue!50,very thick,fill=blue!20] + + \node[state,initial] (A) {$\{2, 3\}$}; + \node[state,accepting] (B) [below of=A] {$\{0, 1, 3\}$}; + + \path[->] (A) edge node {$\ \ \ \ a$} (B) + (B) edge [loop below] node {$a$} (); +\end{tikzpicture} + +\begin{tikzpicture}[shorten >=1pt,node distance=3cm,>=stealth',thick] + \tikzstyle{every state}=[draw=blue!50,very thick,fill=blue!20] + + \node[state,initial] (s2) {$2$}; + \node[state,accepting] (s3) [right of=s2] {$3$}; + \node[state] (s0) [below left of=s2] {$0$}; + \node[state] (s1) [below left of=s3] {$1$}; + + +\path[->] (s2) edge node {$\epsilon$} (s3) + (s2) edge node {$a$} (s0) + (s0) edge [bend right] node {$\epsilon$} (s1) + (s1) edge [bend right] node {$a$} (s0) + (s1) edge node {$\epsilon$} (s3); + +\end{tikzpicture} + + + +\begin{tikzpicture}[shorten >=1pt,node distance=3cm,>=stealth',thick] + \tikzstyle{every state}=[draw=blue!50,very thick,fill=blue!20] + + \node[state,initial] (s2) {$2$}; + \node[state] (s0) [right of=s2] {$0$}; + \node[state] (s1) [right of=s0] {$1$}; + \node[state,accepting] (s3) [right of=s1] {$3$}; + + +\path[->] (s2) edge [bend right] node {$\epsilon$} (s3) + (s2) edge node {$\epsilon$} (s0) + (s0) edge node {$a$} (s1) + (s1) edge [bend right] node {$\epsilon$} (s0) + (s1) edge node {$\epsilon$} (s3); +\end{tikzpicture} + + +$(a|b)*$\\ + +\begin{tikzpicture}[shorten >=1pt,node distance=2cm,>=stealth',thick] + \tikzstyle{every state}=[draw=blue!50,very thick,fill=blue!20] + + \node[state,initial] (s6) {$6$}; + \node[state] (s4) [right of=s6] {$4$}; + \node[state] (s0) [above right of=s4] {$0$}; + \node[state] (s2) [below right of=s4] {$2$}; + \node[state] (s1) [right of=s0] {$1$}; + \node[state] (s3) [right of=s2] {$3$}; + \node[state] (s5) [below right of=s1] {$5$}; + \node[state,accepting] (s7) [right of=s5] {$7$}; + +\path[->] (s6) edge node {$\epsilon$} (s4) + (s4) edge node {$\epsilon$} (s0) + (s4) edge node {$\epsilon$} (s2) + (s0) edge node {$a$} (s1) + (s2) edge node {$b$} (s3) + (s1) edge node {$\epsilon$} (s5) + (s3) edge node {$\epsilon$} (s5) + (s5) edge node {$\epsilon$} (s4) + (s5) edge node {$\epsilon$} (s7) + (s6) edge [bend right] node {$\epsilon$} (s7); +\end{tikzpicture} + + +\begin{tikzpicture}[shorten >=1pt,node distance=4cm,>=stealth',thick] + \tikzstyle{every state}=[draw=blue!50,very thick,fill=blue!20] + + \node[state,initial] (A) {$\{6,7,4,0,2\}$}; + \node[state] (B) [below left of=A] {$\{1,5,7,4,0,2\}$}; + \node[state,accepting] (C) [below right of=A] {$\{3,5,7,4,0,2\}$}; + + +\path[->] (A) edge node {$a$} (B) + (A) edge node {$b$} (C) + (B) edge [loop below] node {$a$} (B) + (C) edge [loop below] node {$b$} (C) + (B) edge [bend right] node {$b$} (C) + (C) edge [bend right] node {$a$} (B); +\end{tikzpicture} + +$a*b|b*a$\\ + +\begin{tikzpicture}[shorten >=1pt,node distance=3cm,>=stealth',thick] + \tikzstyle{every state}=[draw=blue!50,very thick,fill=blue!20] + + \node[state,initial] (s12) {$12$}; + + \node[state] (s2) [above right of=s12] {$2$}; + \node[state] (s3) [right of=s2] {$3$}; + \node[state] (s0) [above of=s2] {$0$}; + \node[state] (s1) [above of=s3] {$1$}; + \node[state] (s4) [right of=s3] {$4$}; + \node[state] (s5) [right of=s4] {$5$}; + + \node[state] (s8) [below right of=s12] {$8$}; + \node[state] (s6) [below of=s8] {$6$}; + \node[state] (s7) [right of=s6] {$7$}; + \node[state] (s9) [right of=s8] {$9$}; + \node[state] (s10) [right of=s9] {$10$}; + \node[state] (s11) [right of=s10] {$11$}; + + \node[state,accepting] (s13) [below right of=s5] {$13$}; + +\path[->] +(s12) edge node {$\epsilon$} (s2) +(s2) edge node {$\epsilon$} (s0) +(s0) edge [bend right] node {$a$} (s1) +(s1) edge [bend right] node {$\epsilon$} (s0) +(s1) edge node {$\epsilon$} (s3) +(s2) edge node {$\epsilon$} (s3) +(s3) edge node {$\epsilon$} (s4) +(s4) edge node {$b$} (s5) +(s5) edge node {$\epsilon$} (s13) + +(s12) edge node {$\epsilon$} (s8) +(s8) edge node {$\epsilon$} (s6) +(s6) edge [bend right] node {$b$} (s7) +(s7) edge [bend right] node {$\epsilon$} (s6) +(s8) edge node {$\epsilon$} (s9) +(s7) edge node {$\epsilon$} (s9) +(s9) edge node {$\epsilon$} (s10) +(s10) edge node {$a$} (s11) +(s11) edge node {$\epsilon$} (s13); +\end{tikzpicture} + + +\begin{tikzpicture}[shorten >=1pt,node distance=5cm,>=stealth',thick] + \tikzstyle{every state}=[draw=blue!50,very thick,fill=blue!20] + + \node[state,initial] (A) {$\{12,2,0,3,4,8,6,9,10\}$}; + + \node[state,accepting] (B) [above right of=A] {$\{1, 3, 4, 0, 11, 13\}$}; + \node[state] (C) [right of=B] {$\{1, 3, 4, 0\}$}; + \node[state,accepting] (D) [right of=C] {$\{5, 13\}$}; + + \node[state,accepting] (E) [below right of=A] {$\{7,9,10,6,5,13\}$}; + \node[state,accepting] (F) [right of=E] {$\{7,9,10,6\}$}; + \node[state,accepting] (G) [right of=F] {$\{11,13\}$}; + + +\path[->] (A) edge node {$a$} (B) + (B) edge [bend left] node {$b$} (D) + (B) edge node {$a$} (C) + (C) edge [loop below] node {$a$} (C) + (C) edge node {$b$} (D) + + (A) edge node {$b$} (E) + (E) edge [bend right] node {$a$} (G) + + (E) edge node {$b$} (F) + (F) edge [loop above] node {$b$} (F) + (F) edge node {$a$} (G); +\end{tikzpicture} + + + +\begin{tikzpicture}[shorten >=1pt,node distance=3cm,>=stealth',thick] + \tikzstyle{every state}=[draw=blue!50,very thick,fill=blue!20] + + \node[state,initial] (A) {}; + \node[state,accepting] (B) [right of=A] {}; + + \path[->] (A) edge node {$a$} (B); +\end{tikzpicture}\\ + +\begin{tikzpicture}[shorten >=1pt,node distance=3cm,>=stealth',thick] + \tikzstyle{every state}=[draw=blue!50,very thick,fill=blue!20] + + \node[state,initial] (A) {}; + \node[state,accepting] (B) [right of=A] {}; + + \path[->] (A) edge node {$\epsilon$} (B); +\end{tikzpicture} + +$ab$\\ +\begin{tikzpicture}[shorten >=1pt,node distance=3cm,>=stealth',thick] + \tikzstyle{every state}=[draw=blue!50,very thick,fill=blue!20] + + \node[state,initial] (A) {}; + \node[state,accepting] (B) [right of=A] {}; + \node[state] (C) [right of=B] {}; + \node[state,accepting] (D) [right of=C] {}; + + \path[->] +(A) edge node {$a$} (B) +(B) edge node {$\epsilon$} (C) +(C) edge node {$b$} (D); +\end{tikzpicture} + + + +$(a|b)$\\ +\begin{tikzpicture}[shorten >=1pt,node distance=3cm,>=stealth',thick] + \tikzstyle{every state}=[draw=blue!50,very thick,fill=blue!20] + + \node[state,initial] (A) {}; + \node[state] (B) [above right of=A] {}; + \node[state] (C) [below right of=A] {}; + \node[state,accepting] (D) [right of=B] {}; + \node[state,accepting] (E) [right of=C] {}; + \node[state,accepting] (F) [above right of=E] {}; + +\path[->] (A) edge node {$\epsilon$} (B) +(A) edge node {$\epsilon$} (C) + +(B) edge node {$a$} (D) +(C) edge node {$b$} (E) + + +(D) edge node {$\epsilon$} (F) +(E) edge node {$\epsilon$} (F) +; +\end{tikzpicture} + + + + +$a*$\\ +\begin{tikzpicture}[shorten >=1pt,node distance=3cm,>=stealth',thick] + \tikzstyle{every state}=[draw=blue!50,very thick,fill=blue!20] + + \node[state,initial] (A) {}; + \node[state] (B) [right of=A] {}; + \node[state,accepting] (C) [right of=B] {}; + \node[state,accepting] (D) [right of=C] {}; + + \path[->] +(A) edge node {$\epsilon$} (B) +(B) edge node {$a$} (C) +(C) edge [bend right] node {$\epsilon$} (B) + +(C) edge node {$\epsilon$} (D) +(A) edge [bend right] node {$\epsilon$} (D); + +\end{tikzpicture} + + +\end{document} + |