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FGI2: 12.3.5 bearbeitet

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Signed-off-by: Jim Martens <github@2martens.de>
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Jim Martens
2015-01-14 18:54:39 +01:00
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fgi2/Blatt12/Aufgabenblatt12.tex
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@ -146,6 +146,50 @@
bb + a \overset{a}{\rightarrow} \sqrt{} \;&&\; (T^{\sqrt{}}_{+L}), y = a, v = a, x = bb \\ bb + a \overset{a}{\rightarrow} \sqrt{} \;&&\; (T^{\sqrt{}}_{+L}), y = a, v = a, x = bb \\
(bb + a) \cdot b \overset{a}{\rightarrow} b \;&&\; (T^{\sqrt{}}), x = (bb + a), v = a, y = b (bb + a) \cdot b \overset{a}{\rightarrow} b \;&&\; (T^{\sqrt{}}), x = (bb + a), v = a, y = b
\end{alignat*} \end{alignat*}
\subsection{}
Der Prozessgraph für \(t_5\) ist auf \fref{fig:t5-graph} sichtbar. Der Prozessgraph für \(t_6\) ist auf \fref{fig:t6-graph} sichtbar.
Die Knoten \(f\) in beiden Graphen, \((c + d)f\) in beiden Graphen, sowie \(cf + df\) im Graph von \(t_5\) und die beiden Wurzelknoten sind jeweils bisimilar.
\begin{figure}
\begin{tikzpicture}[node distance=1cm]
\node (t5-start) {\(b(cf + df) + a(c + d)f\)};
% left side
\node (t5-b-left) [below left=of t5-start] {\(cf + df\)};
\node (t5-finish-left) [below=of t5-b-left] {\(\sqrt{}\)};
% right side
\node (t5-a-right) [below right=of t5-start] {\((c + d)f\)};
\node (t5-f-right) [below=of t5-a-right] {\(f\)};
\node (t5-finish-right) [below=of t5-f-right] {\(\sqrt{}\)};
\path[->] (t5-start) edge node[above left] {b} (t5-b-left)
(t5-b-left) edge[bend right] node[left] {cf} (t5-finish-left)
(t5-b-left) edge[bend left] node[right] {df} (t5-finish-left)
(t5-start) edge node[above right] {a} (t5-a-right)
(t5-a-right) edge[bend right] node[left] {c} (t5-f-right)
(t5-a-right) edge[bend left] node[right] {d} (t5-f-right)
(t5-f-right) edge node[right] {f} (t5-finish-right);
\end{tikzpicture}
\caption{Prozessgraph für \(t_5\)}
\label{fig:t5-graph}
\end{figure}
\begin{figure}
\begin{tikzpicture}[node distance=1cm]
\node (t6-start) {\((a + b)(c + d)f\)};
\node (t6-c-plus-d-f) [below=of t6-start] {\((c + d)f\)};
\node (t6-f) [below=of t6-c-plus-d-f] {\(f\)};
\node (t6-finish) [below=of t6-f] {\(\sqrt{}\)};
\path[->] (t6-start) edge[bend right] node[left] {a} (t6-c-plus-d-f)
(t6-start) edge[bend left] node[right] {b} (t6-c-plus-d-f)
(t6-c-plus-d-f) edge[bend right] node[left] {c} (t6-f)
(t6-c-plus-d-f) edge[bend left] node[right] {d} (t6-f)
(t6-f) edge node[right] {f} (t6-finish);
\end{tikzpicture}
\caption{Prozessgraph für \(t_6\)}
\label{fig:t6-graph}
\end{figure}
\section{} %12.4 \section{} %12.4
\end{document} \end{document}