Example automaton graph.
1.1 --- a/paper/src/paper.tex Fri Jul 15 18:22:30 2011 +0200
1.2 +++ b/paper/src/paper.tex Fri Jul 15 19:15:52 2011 +0200
1.3 @@ -184,20 +184,28 @@
1.4 Given all legal computations of an automaton, we have defined the acceptance condition. A computation is accepting, if it passes through an accepting state infinitely times. Since the set of states $S$ is finite, there must be a state $s \in S$, which occurs infinitely often within an infinite run; but it is not necessary, that $s$ is an accepting state; notice that $F$ can be an empty set.
1.5
1.6 \subsection{Example}
1.7 -Let $\A_1 = (\Sigma, S, S_0, \Delta, F)$ be an automaton.
1.8 +Let $\A_1 = (\Sigma, S, S_0, \Delta, F)$ be an automaton with $\Sigma = \{a, b\}$, $S = \{q_0, q_1, q_2\},$ $S_0 = \{q_0\}$ and $\Delta = \{\}, F = \{q_2\}$.
1.9
1.10 -\begin{tikzpicture}[shorten >=1pt,node distance=2cm,auto]
1.11 -\draw[help lines] (0,0) grid (3,2);
1.12 -\node[state,initial] (q_0) {$q_0$};
1.13 +\begin{tikzpicture}[shorten >=0pt, node distance=2cm, auto, semithick, >=stealth
1.14 + %every state/.style={fill, draw=none, gray, text=white},
1.15 + ,accepting/.style={fill, gray!50!black, text=white}
1.16 + %initial/.style ={gray, text=white}]%, thick]
1.17 + ]
1.18 +%\draw[help lines] (0,0) grid (3,2);
1.19 +\node[state,initial, initial text=] (q_0) {$q_0$};
1.20 \node[state] (q_1) [above right of= q_0] {$q_1$};
1.21 \node[state] (q_2) [below right of= q_0] {$q_2$};
1.22 \node[state,accepting](q_3) [below right of= q_1] {$q_3$};
1.23 -\path[->] (q_0) edge node {0} (q_1)
1.24 -edge node [swap] {1} (q_2)
1.25 -(q_1) edge node {1} (q_3)
1.26 -edge [loop above] node {0} ()
1.27 -(q_2) edge node [swap] {0} (q_3)
1.28 -edge [loop below] node {1} ();
1.29 +\path[->]
1.30 +(q_0) edge node {$a$} (q_1)
1.31 + edge node [swap] {$b$} (q_2)
1.32 +(q_1) edge node {$b$} (q_3)
1.33 + edge [loop above] node {$a$} ()
1.34 +(q_2) edge node [swap] {$a$} (q_1)
1.35 + edge [loop below] node {$b$} ()
1.36 +(q_3) %edge node {$a$} (q_1)
1.37 + edge node {$b$} (q_2);
1.38 +\draw[->] (q_3) .. controls +(up:1cm) and +(right:1cm) .. node[above] {$a$} (q_1);
1.39 \end{tikzpicture}
1.40
1.41 \subsection{Generalised B\"uchi automata}