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mirror of https://github.com/2martens/uni.git synced 2026-05-07 03:46:25 +02:00

FGI2: 8.3 abgeschlossen

This commit is contained in:
Jim Martens
2014-12-03 11:04:02 +01:00
parent 00861df453
commit a3ce6e397a

View File

@ -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}