diff --git a/fgi2/Blatt8/Aufgabenblatt8.tex b/fgi2/Blatt8/Aufgabenblatt8.tex index bb2f0b9..50eadcc 100644 --- a/fgi2/Blatt8/Aufgabenblatt8.tex +++ b/fgi2/Blatt8/Aufgabenblatt8.tex @@ -14,6 +14,7 @@ \usepackage{polynom} \usepackage{multirow} \usepackage[german]{fancyref} +\usepackage{morefloats} \polyset{style=C, div=:,vars=x} \pgfplotsset{compat=1.8} \pagenumbering{arabic} @@ -195,20 +196,21 @@ \node[place] (b3) [below=0.25 of b2] {b3}; \node[place] (b4) [above=of b2] {b4}; \node[place] (b5) [below=of b3] {b5}; - \node[transitionH] (b) [above right=0.5 and 1 of b2] {b}; - \node[place] (b6) [right=of b] {b6}; - \node[transitionH] (d) [right=of b6] {d}; - \node[place] (b7) [right=of d] {b7}; + \node[transitionH] (c) [right=of b3] {c}; + \node[place] (b6) [right=of c] {b6}; + \node[transitionH] (b) [right=of b2] {b}; + \node[place] (b7) [right=of b] {b7}; \path[->] (b1) edge (a) (a) edge (b2) (a) edge (b3) (a) edge (b4) (a) edge (b5) - (b2) edge (b) + (b2) edge (c) + (b5) edge (c) + (c) edge (b6) (b4) edge (b) - (b) edge (b6) - (b6) edge (d) - (d) edge (b7); + (b3) edge (b) + (b) edge (b7); \end{tikzpicture} \caption{Prozess 7 für 8.3.1} \label{fig:831-7} @@ -222,20 +224,21 @@ \node[place] (b3) [below=0.25 of b2] {b3}; \node[place] (b4) [above=of b2] {b4}; \node[place] (b5) [below=of b3] {b5}; - \node[transitionH] (b) [right=of b2] {b}; - \node[place] (b6) [right=of b] {b6}; - \node[transitionH] (d) [right=of b6] {d}; - \node[place] (b7) [right=of d] {b7}; + \node[transitionH] (c) [below right=0.5 and 1 of b3] {c}; + \node[place] (b6) [right=of c] {b6}; + \node[transitionH] (b) [above right=0.5 and 1 of b2] {b}; + \node[place] (b7) [right=of b] {b7}; \path[->] (b1) edge (a) (a) edge (b2) (a) edge (b3) (a) edge (b4) (a) edge (b5) - (b3) edge (b) + (b3) edge (c) + (b5) edge (c) + (c) edge (b6) (b4) edge (b) - (b) edge (b6) - (b6) edge (d) - (d) edge (b7); + (b2) edge (b) + (b) edge (b7); \end{tikzpicture} \caption{Prozess 8 für 8.3.1} \label{fig:831-8} @@ -249,8 +252,8 @@ \node[place] (b3) [below=0.25 of b2] {b3}; \node[place] (b4) [above=of b2] {b4}; \node[place] (b5) [below=of b3] {b5}; - \node[transitionH] (c) [below right=0.5 and 1 of b3] {c}; - \node[place] (b6) [right=of c] {b6}; + \node[transitionH] (b) [above right=0.5 and 1 of b2] {b}; + \node[place] (b6) [right=of b] {b6}; \node[transitionH] (d) [right=of b6] {d}; \node[place] (b7) [right=of d] {b7}; \path[->] (b1) edge (a) @@ -258,9 +261,9 @@ (a) edge (b3) (a) edge (b4) (a) edge (b5) - (b3) edge (c) - (b5) edge (c) - (c) edge (b6) + (b2) edge (b) + (b4) edge (b) + (b) edge (b6) (b6) edge (d) (d) edge (b7); \end{tikzpicture} @@ -276,8 +279,8 @@ \node[place] (b3) [below=0.25 of b2] {b3}; \node[place] (b4) [above=of b2] {b4}; \node[place] (b5) [below=of b3] {b5}; - \node[transitionH] (c) [right=of b3] {c}; - \node[place] (b6) [right=of c] {b6}; + \node[transitionH] (b) [right=of b2] {b}; + \node[place] (b6) [right=of b] {b6}; \node[transitionH] (d) [right=of b6] {d}; \node[place] (b7) [right=of d] {b7}; \path[->] (b1) edge (a) @@ -285,9 +288,9 @@ (a) edge (b3) (a) edge (b4) (a) edge (b5) - (b2) edge (c) - (b5) edge (c) - (c) edge (b6) + (b3) edge (b) + (b4) edge (b) + (b) edge (b6) (b6) edge (d) (d) edge (b7); \end{tikzpicture} @@ -303,30 +306,84 @@ \node[place] (b3) [below=0.25 of b2] {b3}; \node[place] (b4) [above=of b2] {b4}; \node[place] (b5) [below=of b3] {b5}; - \node[transitionH] (b) [above right=0.5 and 1 of b2] {b}; - \node[place] (b6) [right=of b] {b6}; + \node[transitionH] (c) [below right=0.5 and 1 of b3] {c}; + \node[place] (b6) [right=of c] {b6}; \node[transitionH] (d) [right=of b6] {d}; \node[place] (b7) [right=of d] {b7}; - \node[transitionH] (c) [below right=0.5 and 1 of b3] {c}; - \node[place] (b8) [right=of c] {b8}; \path[->] (b1) edge (a) (a) edge (b2) (a) edge (b3) (a) edge (b4) (a) edge (b5) - (b2) edge (b) - (b4) edge (b) - (b) edge (b6) - (b6) edge (d) - (d) edge (b7) (b3) edge (c) (b5) edge (c) - (c) edge (b8); + (c) edge (b6) + (b6) edge (d) + (d) edge (b7); \end{tikzpicture} \caption{Prozess 11 für 8.3.1} \label{fig:831-11} \end{figure} + \begin{figure} + \begin{tikzpicture}[node distance=1cm] + \node[place] (b1) {b1}; + \node[transitionH] (a) [right=of b1] {a}; + \node[place] (b2) [right=of a] {b2}; + \node[place] (b3) [below=0.25 of b2] {b3}; + \node[place] (b4) [above=of b2] {b4}; + \node[place] (b5) [below=of b3] {b5}; + \node[transitionH] (c) [right=of b3] {c}; + \node[place] (b6) [right=of c] {b6}; + \node[transitionH] (d) [right=of b6] {d}; + \node[place] (b7) [right=of d] {b7}; + \path[->] (b1) edge (a) + (a) edge (b2) + (a) edge (b3) + (a) edge (b4) + (a) edge (b5) + (b2) edge (c) + (b5) edge (c) + (c) edge (b6) + (b6) edge (d) + (d) edge (b7); + \end{tikzpicture} + \caption{Prozess 12 für 8.3.1} + \label{fig:831-12} + \end{figure} + + \begin{figure} + \begin{tikzpicture}[node distance=1cm] + \node[place] (b1) {b1}; + \node[transitionH] (a) [right=of b1] {a}; + \node[place] (b2) [right=of a] {b2}; + \node[place] (b3) [below=0.25 of b2] {b3}; + \node[place] (b4) [above=of b2] {b4}; + \node[place] (b5) [below=of b3] {b5}; + \node[transitionH] (b) [above right=0.5 and 1 of b2] {b}; + \node[place] (b6) [right=of b] {b6}; + \node[transitionH] (d) [right=of b6] {d}; + \node[place] (b7) [right=of d] {b7}; + \node[transitionH] (c) [below right=0.5 and 1 of b3] {c}; + \node[place] (b8) [right=of c] {b8}; + \path[->] (b1) edge (a) + (a) edge (b2) + (a) edge (b3) + (a) edge (b4) + (a) edge (b5) + (b2) edge (b) + (b4) edge (b) + (b) edge (b6) + (b6) edge (d) + (d) edge (b7) + (b3) edge (c) + (b5) edge (c) + (c) edge (b8); + \end{tikzpicture} + \caption{Prozess 13 für 8.3.1} + \label{fig:831-13} + \end{figure} + \begin{figure} \begin{tikzpicture}[node distance=1cm] \node[place] (b1) {b1}; @@ -355,70 +412,6 @@ (b5) edge (c) (c) edge (b8); \end{tikzpicture} - \caption{Prozess 12 für 8.3.1} - \label{fig:831-12} - \end{figure} - - \begin{figure} - \begin{tikzpicture}[node distance=1cm] - \node[place] (b1) {b1}; - \node[transitionH] (a) [right=of b1] {a}; - \node[place] (b2) [right=of a] {b2}; - \node[place] (b3) [below=0.25 of b2] {b3}; - \node[place] (b4) [above=of b2] {b4}; - \node[place] (b5) [below=of b3] {b5}; - \node[transitionH] (c) [below right=0.5 and 1 of b3] {c}; - \node[place] (b6) [right=of c] {b6}; - \node[transitionH] (d) [right=of b6] {d}; - \node[place] (b7) [right=of d] {b7}; - \node[transitionH] (b) [above right=0.5 and 1 of b2] {b}; - \node[place] (b8) [right=of b] {b8}; - \path[->] (b1) edge (a) - (a) edge (b2) - (a) edge (b3) - (a) edge (b4) - (a) edge (b5) - (b3) edge (c) - (b5) edge (c) - (c) edge (b6) - (b6) edge (d) - (d) edge (b7) - (b2) edge (b) - (b4) edge (b) - (b) edge (b8); - \end{tikzpicture} - \caption{Prozess 13 für 8.3.1} - \label{fig:831-13} - \end{figure} - - \begin{figure} - \begin{tikzpicture}[node distance=1cm] - \node[place] (b1) {b1}; - \node[transitionH] (a) [right=of b1] {a}; - \node[place] (b2) [right=of a] {b2}; - \node[place] (b3) [below=0.25 of b2] {b3}; - \node[place] (b4) [above=of b2] {b4}; - \node[place] (b5) [below=of b3] {b5}; - \node[transitionH] (c) [right=of b3] {c}; - \node[place] (b6) [right=of c] {b6}; - \node[transitionH] (d) [right=of b6] {d}; - \node[place] (b7) [right=of d] {b7}; - \node[transitionH] (b) [right=of b2] {b}; - \node[place] (b8) [right=of b] {b8}; - \path[->] (b1) edge (a) - (a) edge (b2) - (a) edge (b3) - (a) edge (b4) - (a) edge (b5) - (b2) edge (c) - (b5) edge (c) - (c) edge (b6) - (b6) edge (d) - (d) edge (b7) - (b3) edge (b) - (b4) edge (b) - (b) edge (b8); - \end{tikzpicture} \caption{Prozess 14 für 8.3.1} \label{fig:831-14} \end{figure} @@ -431,29 +424,25 @@ \node[place] (b3) [below=0.25 of b2] {b3}; \node[place] (b4) [above=of b2] {b4}; \node[place] (b5) [below=of b3] {b5}; - \node[transitionH] (b) [above right=0.5 and 1 of b2] {b}; - \node[place] (b6) [right=of b] {b6}; + \node[transitionH] (c) [below right=0.5 and 1 of b3] {c}; + \node[place] (b6) [right=of c] {b6}; \node[transitionH] (d) [right=of b6] {d}; \node[place] (b7) [right=of d] {b7}; - \node[transitionH] (c) [below right=0.5 and 1 of b3] {c}; - \node[place] (b8) [right=of c] {b8}; - \node[transitionH] (d2) [right=of b8] {d}; - \node[place] (b9) [right=of d2] {b9}; + \node[transitionH] (b) [above right=0.5 and 1 of b2] {b}; + \node[place] (b8) [right=of b] {b8}; \path[->] (b1) edge (a) (a) edge (b2) (a) edge (b3) (a) edge (b4) (a) edge (b5) - (b2) edge (b) - (b4) edge (b) - (b) edge (b6) - (b6) edge (d) - (d) edge (b7) (b3) edge (c) (b5) edge (c) - (c) edge (b8) - (b8) edge (d2) - (d2) edge (b9); + (c) edge (b6) + (b6) edge (d) + (d) edge (b7) + (b2) edge (b) + (b4) edge (b) + (b) edge (b8); \end{tikzpicture} \caption{Prozess 15 für 8.3.1} \label{fig:831-15} @@ -467,29 +456,25 @@ \node[place] (b3) [below=0.25 of b2] {b3}; \node[place] (b4) [above=of b2] {b4}; \node[place] (b5) [below=of b3] {b5}; - \node[transitionH] (b) [right=of b2] {b}; - \node[place] (b6) [right=of b] {b6}; + \node[transitionH] (c) [right=of b3] {c}; + \node[place] (b6) [right=of c] {b6}; \node[transitionH] (d) [right=of b6] {d}; \node[place] (b7) [right=of d] {b7}; - \node[transitionH] (c) [right=of b3] {c}; - \node[place] (b8) [right=of c] {b8}; - \node[transitionH] (d2) [right=of b8] {d}; - \node[place] (b9) [right=of d2] {b9}; + \node[transitionH] (b) [right=of b2] {b}; + \node[place] (b8) [right=of b] {b8}; \path[->] (b1) edge (a) (a) edge (b2) (a) edge (b3) (a) edge (b4) (a) edge (b5) - (b3) edge (b) - (b4) edge (b) - (b) edge (b6) - (b6) edge (d) - (d) edge (b7) (b2) edge (c) (b5) edge (c) - (c) edge (b8) - (b8) edge (d2) - (d2) edge (b9); + (c) edge (b6) + (b6) edge (d) + (d) edge (b7) + (b3) edge (b) + (b4) edge (b) + (b) edge (b8); \end{tikzpicture} \caption{Prozess 16 für 8.3.1} \label{fig:831-16} @@ -503,12 +488,12 @@ \node[place] (b3) [below=0.25 of b2] {b3}; \node[place] (b4) [above=of b2] {b4}; \node[place] (b5) [below=of b3] {b5}; - \node[transitionH] (c) [below right=0.5 and 1 of b3] {c}; - \node[place] (b6) [right=of c] {b6}; + \node[transitionH] (b) [above right=0.5 and 1 of b2] {b}; + \node[place] (b6) [right=of b] {b6}; \node[transitionH] (d) [right=of b6] {d}; \node[place] (b7) [right=of d] {b7}; - \node[transitionH] (b) [above right=0.5 and 1 of b2] {b}; - \node[place] (b8) [right=of b] {b8}; + \node[transitionH] (c) [below right=0.5 and 1 of b3] {c}; + \node[place] (b8) [right=of c] {b8}; \node[transitionH] (d2) [right=of b8] {d}; \node[place] (b9) [right=of d2] {b9}; \path[->] (b1) edge (a) @@ -516,14 +501,14 @@ (a) edge (b3) (a) edge (b4) (a) edge (b5) - (b3) edge (c) - (b5) edge (c) - (c) edge (b6) - (b6) edge (d) - (d) edge (b7) (b2) edge (b) (b4) edge (b) - (b) edge (b8) + (b) edge (b6) + (b6) edge (d) + (d) edge (b7) + (b3) edge (c) + (b5) edge (c) + (c) edge (b8) (b8) edge (d2) (d2) edge (b9); \end{tikzpicture} @@ -539,12 +524,12 @@ \node[place] (b3) [below=0.25 of b2] {b3}; \node[place] (b4) [above=of b2] {b4}; \node[place] (b5) [below=of b3] {b5}; - \node[transitionH] (c) [right=of b3] {c}; - \node[place] (b6) [right=of c] {b6}; + \node[transitionH] (b) [right=of b2] {b}; + \node[place] (b6) [right=of b] {b6}; \node[transitionH] (d) [right=of b6] {d}; \node[place] (b7) [right=of d] {b7}; - \node[transitionH] (b) [right=of b2] {b}; - \node[place] (b8) [right=of b] {b8}; + \node[transitionH] (c) [right=of b3] {c}; + \node[place] (b8) [right=of c] {b8}; \node[transitionH] (d2) [right=of b8] {d}; \node[place] (b9) [right=of d2] {b9}; \path[->] (b1) edge (a) @@ -552,14 +537,14 @@ (a) edge (b3) (a) edge (b4) (a) edge (b5) - (b2) edge (c) - (b5) edge (c) - (c) edge (b6) - (b6) edge (d) - (d) edge (b7) (b3) edge (b) (b4) edge (b) - (b) edge (b8) + (b) edge (b6) + (b6) edge (d) + (d) edge (b7) + (b2) edge (c) + (b5) edge (c) + (c) edge (b8) (b8) edge (d2) (d2) edge (b9); \end{tikzpicture} @@ -567,6 +552,110 @@ \label{fig:831-18} \end{figure} + \subsection{} + Die \(<\)-Relation kann auf \fref{fig:832-l} gesehen werden. Die \(\lessdot \)-Relation kann auf \fref{fig:832-ld} gesehen werden. Die \textbf{li}-Relation kann auf \fref{fig:832-li} gesehen werden. Die \textbf{co}-Relation kann auf \fref{fig:832-co} gesehen werden. + \begin{figure} + \begin{tikzpicture}[node distance=2cm] + \node[place] (b1) {b1}; + \node[transitionH] (a) [right=of b1] {a}; + \node[place] (b3) [right=of a] {b3}; + \node[place] (b4) [below=of b3] {b4}; + \node[transitionH] (c) [below right=of b4] {c}; + \node[place] (b2) [left=3 of c] {b2}; + \node[place] (b5) [right=of c] {b5}; + + \path[->] (b1) edge (a) + (a) edge (b3) + (a) edge (b4) + (b4) edge (c) + (b2) edge (c) + (c) edge (b5) + (b1) edge[bend left] (b3) + (b1) edge[bend right] (b4) + (b1) edge[bend right] (c) + (b1) edge[bend left=90] (b5) + (a) edge[bend left] (c) + (a) edge (b5) + (b2) edge[bend right] (b5) + (b4) edge (b5); + \end{tikzpicture} + \caption{\(<\)-Relation} + \label{fig:832-l} + \end{figure} + \begin{figure} + \begin{tikzpicture}[node distance=1cm] + \node[place] (b1) {b1}; + \node[transitionH] (a) [right=of b1] {a}; + \node[place] (b3) [right=of a] {b3}; + \node[place] (b4) [below=of b3] {b4}; + \node[transitionH] (c) [below right=of b4] {c}; + \node[place] (b2) [left=3 of c] {b2}; + \node[place] (b5) [right=of c] {b5}; + + \path[->] (b1) edge (a) + (a) edge (b3) + (a) edge (b4) + (b4) edge (c) + (b2) edge (c) + (c) edge (b5); + \end{tikzpicture} + \caption{\(\lessdot \)-Relation} + \label{fig:832-ld} + \end{figure} + + \begin{figure} + \begin{tikzpicture}[node distance=2cm] + \node[place] (b1) {b1}; + \node[transitionH] (a) [right=of b1] {a}; + \node[place] (b3) [right=of a] {b3}; + \node[place] (b4) [below=of b3] {b4}; + \node[transitionH] (c) [below right=of b4] {c}; + \node[place] (b2) [left=3 of c] {b2}; + \node[place] (b5) [right=of c] {b5}; + + \path (b1) edge (a) + (a) edge (b3) + (a) edge (b4) + (b4) edge (c) + (b2) edge (c) + (c) edge (b5) + (b1) edge[bend left] (b3) + (b1) edge[bend right] (b4) + (b1) edge[bend right] (c) + (b1) edge[bend left=90] (b5) + (a) edge[bend left] (c) + (a) edge (b5) + (b2) edge[bend right] (b5) + (b4) edge (b5); + \end{tikzpicture} + \caption{\textbf{li}-Relation} + \label{fig:832-li} + \end{figure} + + \begin{figure} + \begin{tikzpicture}[node distance=1cm] + \node[place] (b1) {b1}; + \node[transitionH] (a) [right=of b1] {a}; + \node[place] (b3) [right=of a] {b3}; + \node[place] (b4) [below=of b3] {b4}; + \node[transitionH] (c) [below right=of b4] {c}; + \node[place] (b2) [left=3 of c] {b2}; + \node[place] (b5) [right=of c] {b5}; + + \path (b1) edge (b2) + (b3) edge (b5) + (b3) edge (b2) + (b2) edge (b4) + (a) edge (b2) + (b3) edge (b4) + (b3) edge (c); + \end{tikzpicture} + \caption{\textbf{co}-Relation} + \label{fig:832-co} + \end{figure} + + \subsection{} + P-Schnitt: b2, b4, b3 und T-Schnitt: a \section{} %8.4 \section{} %8.5 \end{document}