1.1 --- a/paper/src/paper.tex	Fri Jul 15 19:15:52 2011 +0200
     1.2 +++ b/paper/src/paper.tex	Fri Jul 15 19:21:26 2011 +0200
     1.3 @@ -184,7 +184,7 @@
     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 with $\Sigma = \{a, b\}$, $S = \{q_0, q_1, q_2\},$ $S_0 = \{q_0\}$ and $\Delta = \{\}, F = \{q_2\}$.
     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 $\Delta = \{(q_0, a, q_1)\}, F = \{q_2\}$.
     1.9  
    1.10  \begin{tikzpicture}[shorten >=0pt, node distance=2cm, auto, semithick, >=stealth
    1.11      %every state/.style={fill, draw=none, gray, text=white},
    1.12 @@ -194,18 +194,18 @@
    1.13  %\draw[help lines] (0,0) grid (3,2);
    1.14  \node[state,initial, initial text=] (q_0) {$q_0$};
    1.15  \node[state] (q_1) [above right of= q_0] {$q_1$};
    1.16 -\node[state] (q_2) [below right of= q_0] {$q_2$};
    1.17 -\node[state,accepting](q_3) [below right of= q_1] {$q_3$};
    1.18 +%\node[state] (q_2) [below right of= q_0] {$q_2$};
    1.19 +\node[state,accepting](q_2) [below right of= q_1] {$q_2$};
    1.20  \path[->] 
    1.21  (q_0) edge node {$a$} (q_1)
    1.22 -  edge node [swap] {$b$} (q_2)
    1.23 -(q_1) edge node {$b$} (q_3)
    1.24 +  edge [loop above] node {$b$} ()
    1.25 +(q_1) edge node {$b$} (q_2)
    1.26    edge [loop above] node {$a$} ()
    1.27 -(q_2) edge node [swap] {$a$} (q_1)
    1.28 -  edge [loop below] node {$b$} ()
    1.29 -(q_3) %edge node {$a$} (q_1)
    1.30 -  edge node {$b$} (q_2);
    1.31 -\draw[->] (q_3) .. controls +(up:1cm) and +(right:1cm) .. node[above] {$a$} (q_1);
    1.32 +%(q_2) edge node [swap] {$a$} (q_1)
    1.33 +%  edge [loop below] node {$b$} ()
    1.34 +(q_2) %edge node {$a$} (q_1)
    1.35 +  edge node {$b$} (q_0);
    1.36 +\draw[->] (q_2) .. controls +(up:1cm) and +(right:1cm) .. node[above] {$a$} (q_1);
    1.37  \end{tikzpicture}
    1.38  
    1.39  \subsection{Generalised B\"uchi automata}