lasalle/2024/automata: lecture 8

_tikz/gnfa.tex

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+\documentclass[tikz,convert={outfile=\jobname.svg}]{standalone}
+\usetikzlibrary{automata, arrows.meta, positioning}
+\begin{document} 
+\begin{tikzpicture}[
+    thick,
+    node distance={25mm},
+    auto
+]
+
+\node[state, initial, initial text = {}] (q1) {$q_1$}; 
+\node[state, accepting] (q3) [below=4cm, right of=q1] {$q_3$};
+\node[state, accepting] (q2) [above=4cm, right of=q3] {$q_2$}; 
+
+\path[->]
+    (q1) edge [loop above]  node {$a$} (q1)
+    (q1) edge [bend left]  node {$a^{*}b^{*}$} (q2)
+    (q1) edge [bend right]  node [swap, left=0.8cm, above] {$a\cup b$} (q3)
+    (q2) edge [loop right]  node {$ab$} (q2)
+    (q2) edge [bend left]  node [swap] {$b$} (q1)
+    (q2) edge [bend left]  node [right=0.6cm, above] {$aab$} (q3)
+    ;
+
+\end{tikzpicture} 
+\end{document}

_tikz/gnfa_convenient.tex

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+\documentclass[tikz,convert={outfile=\jobname.svg}]{standalone}
+\usepackage{amssymb}
+\usetikzlibrary{automata, arrows.meta, positioning}
+\begin{document} 
+\begin{tikzpicture}[
+    thick,
+    node distance={25mm},
+    auto
+]
+
+\node[state, initial, initial text = {}] (q1) {$q_1$}; 
+\node[state] (qn) [right of=q1] {$q_n$}; 
+\node[state] (q3) [below=4cm, right of=qn] {$q_3$};
+\node[state] (q2) [above=4cm, right of=q3] {$q_2$}; 
+\node[state, accepting] (q4) [below=2cm, right of=q2] {$q_4$};
+
+\path[->]
+    (q1) edge node {$\varepsilon$} (qn)
+    (qn) edge [loop above]  node {$a$} (qn)
+    (qn) edge [bend left]  node {$a^{*}b^{*}$} (q2)
+    (qn) edge [bend right]  node [swap, left=0.8cm, above] {$a\cup b$} (q3)
+    (q2) edge [loop above]  node {$ab$} (q2)
+    (q2) edge [bend left]  node [swap] {$b$} (qn)
+    (q2) edge [bend left]  node [right=0.6cm, above] {$aab$} (q3)
+    (q3) edge []  node [] {$\varnothing$} (q2)
+    (q3) edge []  node [swap] {$\varnothing$} (qn)
+    (q2) edge [bend left]  node [swap] {$\varepsilon$} (q4)
+    (q3) edge [bend right]  node [swap] {$\varepsilon$} (q4)
+    ;
+
+\end{tikzpicture} 
+\end{document}

_tikz/gnfa_kstate.tex

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+\documentclass[tikz,convert={outfile=\jobname.svg}]{standalone}
+\usetikzlibrary{automata, arrows.meta, positioning}
+\begin{document} 
+\begin{tikzpicture}[
+    thick,
+    node distance={25mm},
+    auto
+]
+
+\node[state] (qi) {$q_i$}; 
+\node[state] (x) [above right of =qi] {$x$}; 
+\node[state] (qj) [below right of=x] {$q_j$}; 
+
+\path[->]
+    (qi) edge []  node {$r_1$} (x)
+    (qi) edge []  node {$r_4$} (qj)
+    (x) edge [loop right]  node {$r_2$} (x)
+    (x) edge []  node {$r_3$} (qj)
+    ;
+
+\end{tikzpicture} 
+\end{document}

_tikz/gnfa_kstate_reduced.tex

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+\documentclass[tikz,convert={outfile=\jobname.svg}]{standalone}
+\usetikzlibrary{automata, arrows.meta, positioning}
+\begin{document} 
+\begin{tikzpicture}[
+    thick,
+    node distance={25mm},
+    auto
+]
+
+\node[state] (qi) {$q_i$}; 
+\node[state] (qj) [right=4cm] {$q_j$}; 
+
+\path[->]
+    (qi) edge []  node {$r_1(r_2)^*r_3 \cup r_4$} (qj)
+    ;
+
+\end{tikzpicture} 
+\end{document}