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FGI2: Arbeitsblatt 2 fertiggestellt

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Jim Martens
2014-10-24 09:00:57 +02:00
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fgi2/Blatt2/Aufgabenblatt2.tex
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@ -137,4 +137,45 @@
&\Rightarrow & W \cdot U \text{ ist eine \(\omega\)-reguläre Menge}
\end{alignat*}
\subsection{} % 4.
\begin{figure}
\begin{tikzpicture}[node distance=2cm]
\node[state,initial] (p0) {\(p_{0}\)};
\node[state] (p1) [right=of p0] {\(p_{1}\)};
\node[state] (p2) [below=of p1] {\(p_{2}\)};
\node[state] (p3) [left=of p2] {\(p_{3}\)};
\node[state] (q0) [below=of p3] {\(q_{0}\)};
\node[state,accepting] (q1) [below=of q0] {\(q_{1}\)};
\node[state] (q2) [right=of q1] {\(q_{2}\)};
\node[state] (q3) [right=of q0] {\(q_{3}\)};
\node[state] (q4) [right=of q3] {\(q_{4}\)};
\node[state,accepting] (q6) [right=of q4] {\(q_{6}\)};
\node[state,accepting] (q5) [below=of q4] {\(q_{5}\)};
\node[state] (q7) [below=of q1] {\(q_{7}\)};
\path[->] (q0) edge node [above] {\(b\)} (q3)
(q0) edge node [left] {\(a\)} (q1)
(q1) edge[bend left] node [above] {\(b\)} (q2)
(q2) edge[loop below] node [below] {\(a\)} (q2)
(q2) edge[bend left] node [below] {\(c\)} (q1)
(q3) edge node [above] {\(c\)} (q4)
(q4) edge node [right] {\(a\)} (q5)
(q5) edge node [below left] {\(b\)} (q3)
(q4) edge node [above] {\(e\)} (q6)
(q6) edge[bend right] node [above] {\(b\)} (q3)
(q1) edge node [left] {\(a\)} (q7)
(q7) edge node [below right] {\(b\)} (q2)
(p0) edge[loop above] node [above] {\(f\)} (p0)
(p2) edge[loop right] node [right] {\(e\)} (p2)
(p3) edge[loop left] node [left] {\(e,f\)} (p3)
(p0) edge[bend left] node [above] {\(e\)} (p1)
(p1) edge[bend left] node [below] {\(f\)} (p0)
(p1) edge node [right] {\(e\)} (p2)
(p2) edge node [above] {\(f\)} (p3)
(p3) edge node [above right] {\(b\)} (q3)
(p3) edge[bend right] node [left] {\(a\)} (q1);
\end{tikzpicture}
\caption{Durch Konkatenation von \(A\) und \(A_{2.3.}\) entstandener Automat.}
\label{fig:2}
\end{figure}
Auf \fref{fig:2} ist der mithilfe des Verfahrens konstruierte Automat zu sehen.
\end{document}