Commit 758e6c92 authored by Florian Kothmeier's avatar Florian Kothmeier

Add Automatenminimierung

parent 03b866de
\section{Automatenminimierung \hfill 6 Punkte}
Gegeben sei folgender Automat:
\begin{center}
\begin{tikzpicture}
\tikzstyle{vertex}=[circle,draw=black,minimum size=17pt,inner sep=0pt]
\tikzset{edge/.style = {->,> = latex'}}
\node[vertex] (q0) at (0,6) {$q_0$};
\node[vertex, accepting] (q1) at (0,0) {$q_1$};
\node[vertex, accepting] (q2) at (-2,4) {$q_2$};
\node[vertex, accepting] (q3) at (0,4) {$q_3$};
\node[vertex, accepting] (q4) at (3.5,3) {$q_4$};
\node[vertex, accepting] (q5) at (2,2) {$q_5$};
\node[vertex] (q6) at (0,2) {$q_6$};
\node[vertex, accepting] (q7) at (-2,2) {$q_7$};
\node[vertex, accepting] (q8) at (2,5) {$q_8$};
\node[vertex, accepting] (q9) at (-3.5,3) {$q_9$};
\path[edge] (q0) edge node [midway, above right] {0} (q8);
\path[edge] (q0) edge node [midway, above left] {1} (q2);
\path[edge] (q1) edge node [midway, below right] {0|1} (q5);
\path[edge] (q2) edge node [midway, above] {0} (q3);
\path[edge] (q2) edge node [midway, left] {1} (q7);
\path[edge] (q3) edge[bend left=20] node [midway, above right] {0} (q5);
\path[edge] (q3) edge node [midway, left] {1} (q0);
\path[edge] (q4) edge node [midway, above right] {0} (q8);
\path[edge] (q4) edge node [midway, above] {1} (q5);
\path[edge] (q5) edge[bend left=20] node [midway, above] {0} (q3);
\path[edge] (q5) edge node [midway, above] {1} (q6);
\path[edge] (q6) edge [loop below] node [midway, below] {0} (q6);
\path[edge] (q6) edge node [midway, left] {1} (q3);
\path[edge] (q7) edge node [midway, below] {0} (q1);
\path[edge] (q7) edge node [midway, above] {1} (q6);
\path[edge] (q8) edge node [midway, right] {0|1} (q5);
\path[edge] (q9) edge node [midway, above] {0} (q7);
\path[edge] (q9) edge node [midway, below] {1} (q2);
\end{tikzpicture}
\end{center}
Minimieren sie den Automaten und zeichnen sie den resultierenden minimalen Automaten.
\ No newline at end of file
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