mirror of
https://github.com/2martens/uni.git
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674 lines
18 KiB
TeX
674 lines
18 KiB
TeX
\documentclass[10pt,a4paper,oneside,ngerman,numbers=noenddot]{scrartcl}
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\usepackage[T1]{fontenc}
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\usepackage[utf8x]{inputenc}
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\usepackage[ngerman]{babel}
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\usepackage{amsmath}
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\usepackage{amsfonts}
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\usepackage{amssymb}
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\usepackage{paralist}
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\usepackage{gauss}
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\usepackage{pgfplots}
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\usepackage[locale=DE,exponent-product=\cdot,detect-all]{siunitx}
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\usepackage{tikz}
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\usetikzlibrary{automata,matrix,fadings,calc,positioning,decorations.pathreplacing,arrows,decorations.markings,petri}
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\usepackage{polynom}
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\usepackage{multirow}
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\usepackage[german]{fancyref}
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\usepackage{morefloats}
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\polyset{style=C, div=:,vars=x}
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\pgfplotsset{compat=1.8}
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\pagenumbering{arabic}
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% ensures that paragraphs are separated by empty lines
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\parskip 12pt plus 1pt minus 1pt
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\parindent 0pt
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% define how the sections are rendered
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\def\thesection{8.\arabic{section})}
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\def\thesubsection{\arabic{subsection}.}
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\def\thesubsubsection{(\alph{subsubsection})}
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% some matrix magic
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\makeatletter
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\renewcommand*\env@matrix[1][*\c@MaxMatrixCols c]{%
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\hskip -\arraycolsep
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\let\@ifnextchar\new@ifnextchar
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\array{#1}}
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\makeatother
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\tikzset{
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place/.style={
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circle,
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thick,
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draw=black,
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fill=white,
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minimum size=6mm,
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font=\bfseries
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},
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transitionH/.style={
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rectangle,
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thick,
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draw=black,
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fill=white,
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minimum width=8mm,
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inner ysep=4pt,
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font=\bfseries
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},
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transitionV/.style={
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rectangle,
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thick,
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fill=black,
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minimum height=8mm,
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inner xsep=2pt
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}
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}
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\begin{document}
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\author{Benjamin Kuffel, Jim Martens\\Gruppe 6}
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\title{Hausaufgaben zum 8. Dezember}
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\maketitle
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\setcounter{section}{2}
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\section{} %8.3
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\subsection{}
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Die Prozesse sind auf den Abbildungen von \fref{fig:831-1} bis \fref{fig:831-18} zu sehen.
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\begin{figure}
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\begin{tikzpicture}[node distance=1cm]
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\node[place] (b1) {b1};
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\end{tikzpicture}
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\caption{Prozess 1 für 8.3.1}
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\label{fig:831-1}
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\end{figure}
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\begin{figure}
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\begin{tikzpicture}[node distance=1cm]
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\node[place] (b1) {b1};
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\node[transitionH] (a) [right=of b1] {a};
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\node[place] (b2) [right=of a] {b2};
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\node[place] (b3) [below=0.25 of b2] {b3};
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\node[place] (b4) [above=0.5 of b2] {b4};
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\node[place] (b5) [below=0.5 of b3] {b5};
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\path[->] (b1) edge (a)
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(a) edge (b2)
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(a) edge (b3)
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(a) edge (b4)
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(a) edge (b5);
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\end{tikzpicture}
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\caption{Prozess 2 für 8.3.1}
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\label{fig:831-2}
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\end{figure}
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\begin{figure}
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\begin{tikzpicture}[node distance=1cm]
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\node[place] (b1) {b1};
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\node[transitionH] (a) [right=of b1] {a};
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\node[place] (b2) [right=of a] {b2};
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\node[place] (b3) [below=0.25 of b2] {b3};
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\node[place] (b4) [above=of b2] {b4};
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\node[place] (b5) [below=of b3] {b5};
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\node[transitionH] (b) [above right=0.5 and 1 of b2] {b};
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\node[place] (b6) [right=of b] {b6};
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\path[->] (b1) edge (a)
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(a) edge (b2)
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(a) edge (b3)
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(a) edge (b4)
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(a) edge (b5)
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(b2) edge (b)
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(b4) edge (b)
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(b) edge (b6);
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\end{tikzpicture}
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\caption{Prozess 3 für 8.3.1}
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\label{fig:831-3}
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\end{figure}
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\begin{figure}
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\begin{tikzpicture}[node distance=1cm]
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\node[place] (b1) {b1};
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\node[transitionH] (a) [right=of b1] {a};
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\node[place] (b2) [right=of a] {b2};
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\node[place] (b3) [below=0.25 of b2] {b3};
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\node[place] (b4) [above=of b2] {b4};
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\node[place] (b5) [below=of b3] {b5};
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\node[transitionH] (b) [right=of b2] {b};
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\node[place] (b6) [right=of b] {b6};
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\path[->] (b1) edge (a)
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(a) edge (b2)
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(a) edge (b3)
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(a) edge (b4)
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(a) edge (b5)
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(b3) edge (b)
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(b4) edge (b)
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(b) edge (b6);
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\end{tikzpicture}
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\caption{Prozess 4 für 8.3.1}
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\label{fig:831-4}
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\end{figure}
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\begin{figure}
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\begin{tikzpicture}[node distance=1cm]
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\node[place] (b1) {b1};
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\node[transitionH] (a) [right=of b1] {a};
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\node[place] (b2) [right=of a] {b2};
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\node[place] (b3) [below=0.25 of b2] {b3};
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\node[place] (b4) [above=of b2] {b4};
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\node[place] (b5) [below=of b3] {b5};
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\node[transitionH] (c) [below right=0.5 and 1 of b3] {c};
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\node[place] (b6) [right=of c] {b6};
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\path[->] (b1) edge (a)
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(a) edge (b2)
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(a) edge (b3)
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(a) edge (b4)
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(a) edge (b5)
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(b3) edge (c)
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(b5) edge (c)
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(c) edge (b6);
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\end{tikzpicture}
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\caption{Prozess 5 für 8.3.1}
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\label{fig:831-5}
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\end{figure}
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\begin{figure}
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\begin{tikzpicture}[node distance=1cm]
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\node[place] (b1) {b1};
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\node[transitionH] (a) [right=of b1] {a};
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\node[place] (b2) [right=of a] {b2};
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\node[place] (b3) [below=0.25 of b2] {b3};
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\node[place] (b4) [above=of b2] {b4};
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\node[place] (b5) [below=of b3] {b5};
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\node[transitionH] (c) [right=of b3] {c};
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\node[place] (b6) [right=of c] {b6};
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\path[->] (b1) edge (a)
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(a) edge (b2)
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(a) edge (b3)
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(a) edge (b4)
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(a) edge (b5)
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(b2) edge (c)
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(b5) edge (c)
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(c) edge (b6);
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\end{tikzpicture}
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\caption{Prozess 6 für 8.3.1}
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\label{fig:831-6}
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\end{figure}
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\begin{figure}
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\begin{tikzpicture}[node distance=1cm]
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\node[place] (b1) {b1};
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\node[transitionH] (a) [right=of b1] {a};
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\node[place] (b2) [right=of a] {b2};
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\node[place] (b3) [below=0.25 of b2] {b3};
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\node[place] (b4) [above=of b2] {b4};
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\node[place] (b5) [below=of b3] {b5};
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\node[transitionH] (c) [right=of b3] {c};
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\node[place] (b6) [right=of c] {b6};
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\node[transitionH] (b) [right=of b2] {b};
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\node[place] (b7) [right=of b] {b7};
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\path[->] (b1) edge (a)
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(a) edge (b2)
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(a) edge (b3)
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(a) edge (b4)
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(a) edge (b5)
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(b2) edge (c)
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(b5) edge (c)
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(c) edge (b6)
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(b4) edge (b)
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(b3) edge (b)
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(b) edge (b7);
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\end{tikzpicture}
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\caption{Prozess 7 für 8.3.1}
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\label{fig:831-7}
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\end{figure}
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\begin{figure}
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\begin{tikzpicture}[node distance=1cm]
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\node[place] (b1) {b1};
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\node[transitionH] (a) [right=of b1] {a};
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\node[place] (b2) [right=of a] {b2};
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\node[place] (b3) [below=0.25 of b2] {b3};
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\node[place] (b4) [above=of b2] {b4};
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\node[place] (b5) [below=of b3] {b5};
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\node[transitionH] (c) [below right=0.5 and 1 of b3] {c};
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\node[place] (b6) [right=of c] {b6};
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\node[transitionH] (b) [above right=0.5 and 1 of b2] {b};
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\node[place] (b7) [right=of b] {b7};
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\path[->] (b1) edge (a)
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(a) edge (b2)
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(a) edge (b3)
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(a) edge (b4)
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(a) edge (b5)
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(b3) edge (c)
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(b5) edge (c)
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(c) edge (b6)
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(b4) edge (b)
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(b2) edge (b)
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(b) edge (b7);
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\end{tikzpicture}
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\caption{Prozess 8 für 8.3.1}
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\label{fig:831-8}
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\end{figure}
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\begin{figure}
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\begin{tikzpicture}[node distance=1cm]
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\node[place] (b1) {b1};
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\node[transitionH] (a) [right=of b1] {a};
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\node[place] (b2) [right=of a] {b2};
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\node[place] (b3) [below=0.25 of b2] {b3};
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\node[place] (b4) [above=of b2] {b4};
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\node[place] (b5) [below=of b3] {b5};
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\node[transitionH] (b) [above right=0.5 and 1 of b2] {b};
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\node[place] (b6) [right=of b] {b6};
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\node[transitionH] (d) [right=of b6] {d};
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\node[place] (b7) [right=of d] {b7};
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\path[->] (b1) edge (a)
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(a) edge (b2)
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(a) edge (b3)
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(a) edge (b4)
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(a) edge (b5)
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(b2) edge (b)
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(b4) edge (b)
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(b) edge (b6)
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(b6) edge (d)
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(d) edge (b7);
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\end{tikzpicture}
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\caption{Prozess 9 für 8.3.1}
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\label{fig:831-9}
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\end{figure}
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\begin{figure}
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\begin{tikzpicture}[node distance=1cm]
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\node[place] (b1) {b1};
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\node[transitionH] (a) [right=of b1] {a};
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\node[place] (b2) [right=of a] {b2};
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\node[place] (b3) [below=0.25 of b2] {b3};
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\node[place] (b4) [above=of b2] {b4};
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\node[place] (b5) [below=of b3] {b5};
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\node[transitionH] (b) [right=of b2] {b};
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\node[place] (b6) [right=of b] {b6};
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\node[transitionH] (d) [right=of b6] {d};
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\node[place] (b7) [right=of d] {b7};
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\path[->] (b1) edge (a)
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(a) edge (b2)
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(a) edge (b3)
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(a) edge (b4)
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(a) edge (b5)
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(b3) edge (b)
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(b4) edge (b)
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(b) edge (b6)
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(b6) edge (d)
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(d) edge (b7);
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\end{tikzpicture}
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\caption{Prozess 10 für 8.3.1}
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\label{fig:831-10}
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\end{figure}
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\begin{figure}
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\begin{tikzpicture}[node distance=1cm]
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\node[place] (b1) {b1};
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\node[transitionH] (a) [right=of b1] {a};
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\node[place] (b2) [right=of a] {b2};
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\node[place] (b3) [below=0.25 of b2] {b3};
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\node[place] (b4) [above=of b2] {b4};
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\node[place] (b5) [below=of b3] {b5};
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\node[transitionH] (c) [below right=0.5 and 1 of b3] {c};
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\node[place] (b6) [right=of c] {b6};
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\node[transitionH] (d) [right=of b6] {d};
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\node[place] (b7) [right=of d] {b7};
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\path[->] (b1) edge (a)
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(a) edge (b2)
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(a) edge (b3)
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(a) edge (b4)
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(a) edge (b5)
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(b3) edge (c)
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(b5) edge (c)
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(c) edge (b6)
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(b6) edge (d)
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(d) edge (b7);
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\end{tikzpicture}
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\caption{Prozess 11 für 8.3.1}
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\label{fig:831-11}
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\end{figure}
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\begin{figure}
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\begin{tikzpicture}[node distance=1cm]
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\node[place] (b1) {b1};
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\node[transitionH] (a) [right=of b1] {a};
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\node[place] (b2) [right=of a] {b2};
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\node[place] (b3) [below=0.25 of b2] {b3};
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\node[place] (b4) [above=of b2] {b4};
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\node[place] (b5) [below=of b3] {b5};
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\node[transitionH] (c) [right=of b3] {c};
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\node[place] (b6) [right=of c] {b6};
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\node[transitionH] (d) [right=of b6] {d};
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\node[place] (b7) [right=of d] {b7};
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\path[->] (b1) edge (a)
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(a) edge (b2)
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(a) edge (b3)
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(a) edge (b4)
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(a) edge (b5)
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(b2) edge (c)
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(b5) edge (c)
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(c) edge (b6)
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(b6) edge (d)
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(d) edge (b7);
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\end{tikzpicture}
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\caption{Prozess 12 für 8.3.1}
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\label{fig:831-12}
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\end{figure}
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\begin{figure}
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\begin{tikzpicture}[node distance=1cm]
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\node[place] (b1) {b1};
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\node[transitionH] (a) [right=of b1] {a};
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\node[place] (b2) [right=of a] {b2};
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\node[place] (b3) [below=0.25 of b2] {b3};
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\node[place] (b4) [above=of b2] {b4};
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\node[place] (b5) [below=of b3] {b5};
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\node[transitionH] (b) [above right=0.5 and 1 of b2] {b};
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\node[place] (b6) [right=of b] {b6};
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\node[transitionH] (d) [right=of b6] {d};
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\node[place] (b7) [right=of d] {b7};
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\node[transitionH] (c) [below right=0.5 and 1 of b3] {c};
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\node[place] (b8) [right=of c] {b8};
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\path[->] (b1) edge (a)
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(a) edge (b2)
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(a) edge (b3)
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(a) edge (b4)
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(a) edge (b5)
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(b2) edge (b)
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(b4) edge (b)
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(b) edge (b6)
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(b6) edge (d)
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(d) edge (b7)
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(b3) edge (c)
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(b5) edge (c)
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(c) edge (b8);
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\end{tikzpicture}
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\caption{Prozess 13 für 8.3.1}
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\label{fig:831-13}
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\end{figure}
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\begin{figure}
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\begin{tikzpicture}[node distance=1cm]
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\node[place] (b1) {b1};
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\node[transitionH] (a) [right=of b1] {a};
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\node[place] (b2) [right=of a] {b2};
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\node[place] (b3) [below=0.25 of b2] {b3};
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\node[place] (b4) [above=of b2] {b4};
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\node[place] (b5) [below=of b3] {b5};
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\node[transitionH] (b) [right=of b2] {b};
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\node[place] (b6) [right=of b] {b6};
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\node[transitionH] (d) [right=of b6] {d};
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\node[place] (b7) [right=of d] {b7};
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\node[transitionH] (c) [right=of b3] {c};
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\node[place] (b8) [right=of c] {b8};
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\path[->] (b1) edge (a)
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(a) edge (b2)
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(a) edge (b3)
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(a) edge (b4)
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(a) edge (b5)
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(b3) edge (b)
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(b4) edge (b)
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(b) edge (b6)
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(b6) edge (d)
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(d) edge (b7)
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(b2) edge (c)
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(b5) edge (c)
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(c) edge (b8);
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\end{tikzpicture}
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\caption{Prozess 14 für 8.3.1}
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\label{fig:831-14}
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\end{figure}
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|
|
\begin{figure}
|
|
\begin{tikzpicture}[node distance=1cm]
|
|
\node[place] (b1) {b1};
|
|
\node[transitionH] (a) [right=of b1] {a};
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|
\node[place] (b2) [right=of a] {b2};
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|
\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 15 für 8.3.1}
|
|
\label{fig:831-15}
|
|
\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 16 für 8.3.1}
|
|
\label{fig:831-16}
|
|
\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};
|
|
\node[transitionH] (d2) [right=of b8] {d};
|
|
\node[place] (b9) [right=of d2] {b9};
|
|
\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);
|
|
\end{tikzpicture}
|
|
\caption{Prozess 17 für 8.3.1}
|
|
\label{fig:831-17}
|
|
\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) [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) [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)
|
|
(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);
|
|
\end{tikzpicture}
|
|
\caption{Prozess 18 für 8.3.1}
|
|
\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
|
|
\subsection{}
|
|
Diese Transitionen sind nebenläufig, können also unabhängig voneinander schalten.
|
|
\subsection{}
|
|
Diese Stellen sind Teil eines Stellenschnittes, einer erreichbaren Markierung.
|
|
\subsection{}
|
|
Jeder Prozess ist ein Kausalnetz mit einem Abbildungspaar, welches die Bedingungen auf Stellen und die Ereignisse auf Transitionen abbildet. Das zu einem Prozess gehörende Kausalnetz ist vorgängerendlich. Es gibt jedoch auch Kausalnetze, die nicht vorgängerendlich und damit nicht Bestandteil von Prozessen sind.
|
|
|
|
Der strukturelle Unterschied besteht darin, dass Kausalnetze aus Bedingungen und Ereignissen bestehen, wohingegen Prozesse ein Kausalnetz referenzieren und eine Abbildung von Bedingungen und Ereignissen auf Plätze und Transitionen enthalten. Naiv gesehen könnte man sagen, dass Kausalnetze weniger umfassen als Prozesse.
|
|
|
|
Rein zahlenmäßig ist das Verhältnis jedoch umgekehrt, wie bereits mit der Vorgängerendlichkeit beschrieben.
|
|
\subsection{}
|
|
%TODO
|
|
\end{document}
|