diff --git a/fgi2/Blatt12/Aufgabenblatt12.tex b/fgi2/Blatt12/Aufgabenblatt12.tex index e51badc..3a7ce8d 100644 --- a/fgi2/Blatt12/Aufgabenblatt12.tex +++ b/fgi2/Blatt12/Aufgabenblatt12.tex @@ -146,6 +146,50 @@ 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 \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 \end{document}