diff --git a/fgi2/Blatt8/Aufgabenblatt8.tex b/fgi2/Blatt8/Aufgabenblatt8.tex new file mode 100644 index 0000000..bb2f0b9 --- /dev/null +++ b/fgi2/Blatt8/Aufgabenblatt8.tex @@ -0,0 +1,572 @@ +\documentclass[10pt,a4paper,oneside,ngerman,numbers=noenddot]{scrartcl} +\usepackage[T1]{fontenc} +\usepackage[utf8x]{inputenc} +\usepackage[ngerman]{babel} +\usepackage{amsmath} +\usepackage{amsfonts} +\usepackage{amssymb} +\usepackage{paralist} +\usepackage{gauss} +\usepackage{pgfplots} +\usepackage[locale=DE,exponent-product=\cdot,detect-all]{siunitx} +\usepackage{tikz} +\usetikzlibrary{automata,matrix,fadings,calc,positioning,decorations.pathreplacing,arrows,decorations.markings,petri} +\usepackage{polynom} +\usepackage{multirow} +\usepackage[german]{fancyref} +\polyset{style=C, div=:,vars=x} +\pgfplotsset{compat=1.8} +\pagenumbering{arabic} +% ensures that paragraphs are separated by empty lines +\parskip 12pt plus 1pt minus 1pt +\parindent 0pt +% define how the sections are rendered +\def\thesection{8.\arabic{section})} +\def\thesubsection{\arabic{subsection}.} +\def\thesubsubsection{(\alph{subsubsection})} +% some matrix magic +\makeatletter +\renewcommand*\env@matrix[1][*\c@MaxMatrixCols c]{% + \hskip -\arraycolsep + \let\@ifnextchar\new@ifnextchar + \array{#1}} +\makeatother + +\tikzset{ + place/.style={ + circle, + thick, + draw=black, + fill=white, + minimum size=6mm, + font=\bfseries + }, + transitionH/.style={ + rectangle, + thick, + draw=black, + fill=white, + minimum width=8mm, + inner ysep=4pt, + font=\bfseries + }, + transitionV/.style={ + rectangle, + thick, + fill=black, + minimum height=8mm, + inner xsep=2pt + } +} + +\begin{document} +\author{Benjamin Kuffel, Jim Martens\\Gruppe 6} +\title{Hausaufgaben zum 8. Dezember} +\maketitle + +\setcounter{section}{2} +\section{} %8.3 + \subsection{} + Die Prozesse sind auf den Abbildungen von \fref{fig:831-1} bis \fref{fig:831-18} zu sehen. + \begin{figure} + \begin{tikzpicture}[node distance=1cm] + \node[place] (b1) {b1}; + \end{tikzpicture} + \caption{Prozess 1 für 8.3.1} + \label{fig:831-1} + \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=0.5 of b2] {b4}; + \node[place] (b5) [below=0.5 of b3] {b5}; + + \path[->] (b1) edge (a) + (a) edge (b2) + (a) edge (b3) + (a) edge (b4) + (a) edge (b5); + \end{tikzpicture} + \caption{Prozess 2 für 8.3.1} + \label{fig:831-2} + \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}; + \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); + \end{tikzpicture} + \caption{Prozess 3 für 8.3.1} + \label{fig:831-3} + \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}; + \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); + \end{tikzpicture} + \caption{Prozess 4 für 8.3.1} + \label{fig:831-4} + \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}; + \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); + \end{tikzpicture} + \caption{Prozess 5 für 8.3.1} + \label{fig:831-5} + \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}; + \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); + \end{tikzpicture} + \caption{Prozess 6 für 8.3.1} + \label{fig:831-6} + \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}; + \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); + \end{tikzpicture} + \caption{Prozess 7 für 8.3.1} + \label{fig:831-7} + \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}; + \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); + \end{tikzpicture} + \caption{Prozess 8 für 8.3.1} + \label{fig:831-8} + \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}; + \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); + \end{tikzpicture} + \caption{Prozess 9 für 8.3.1} + \label{fig:831-9} + \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 10 für 8.3.1} + \label{fig:831-10} + \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 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] (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}; + \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); + \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} + + \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 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] (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 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] (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}; + \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 (c) + (b5) edge (c) + (c) edge (b6) + (b6) edge (d) + (d) edge (b7) + (b2) edge (b) + (b4) edge (b) + (b) 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] (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}; + \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 (c) + (b5) edge (c) + (c) edge (b6) + (b6) edge (d) + (d) edge (b7) + (b3) edge (b) + (b4) edge (b) + (b) edge (b8) + (b8) edge (d2) + (d2) edge (b9); + \end{tikzpicture} + \caption{Prozess 18 für 8.3.1} + \label{fig:831-18} + \end{figure} + +\section{} %8.4 +\section{} %8.5 +\end{document}