diff -r b98a0a49c432 -r 6e7c3db9023d slides/slides04.tex
--- a/slides/slides04.tex	Fri Oct 11 14:51:11 2013 +0100
+++ b/slides/slides04.tex	Sat Oct 12 09:13:42 2013 +0100
@@ -100,6 +100,74 @@
 \end{frame}}
  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
 
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
+\begin{frame}<1-2>[c]
+
+\begin{center}
+\begin{tikzpicture}[>=stealth',very thick,auto,
+                             every state/.style={minimum size=0pt,inner sep=2pt,draw=blue!50,very thick,fill=blue!20},]
+\node[state,initial]  (q_0)  {$q_0$};
+\node[state] (q_1) [right=of q_0] {$q_1$};
+\node[state] (q_2) [below right=of q_0] {$q_2$};
+\node[state] (q_3) [right=of q_2] {$q_3$};
+\node[state, accepting] (q_4) [right=of q_1] {$q_4$};
+\path[->] (q_0) edge node [above]  {\alert{$a$}} (q_1);
+\path[->] (q_1) edge node [above]  {\alert{$a$}} (q_4);
+\path[->] (q_4) edge [loop right] node  {\alert{$a, b$}} ();
+\path[->] (q_3) edge node [right]  {\alert{$a$}} (q_4);
+\path[->] (q_2) edge node [above]  {\alert{$a$}} (q_3);
+\path[->] (q_1) edge node [right]  {\alert{$b$}} (q_2);
+\path[->] (q_0) edge node [above]  {\alert{$b$}} (q_2);
+\path[->] (q_2) edge [loop left] node  {\alert{$b$}} ();
+\path[->] (q_3) edge [bend left=95, looseness=1.3] node [below]  {\alert{$b$}} (q_0);
+\end{tikzpicture}
+\end{center}
+
+\mbox{}\\[-20mm]\mbox{}
+
+\begin{center}
+\begin{tikzpicture}[>=stealth',very thick,auto,
+                             every state/.style={minimum size=0pt,inner sep=2pt,draw=blue!50,very thick,fill=blue!20},]
+\node[state,initial]  (q_02)  {$q_{0, 2}$};
+\node[state] (q_13) [right=of q_02] {$q_{1, 3}$};
+\node[state, accepting] (q_4) [right=of q_13] {$q_{4\phantom{,0}}$};
+\path[->] (q_02) edge [bend left] node [above]  {\alert{$a$}} (q_13);
+\path[->] (q_13) edge [bend left] node [below]  {\alert{$b$}} (q_02);
+\path[->] (q_02) edge [loop below] node  {\alert{$b$}} ();
+\path[->] (q_13) edge node [above]  {\alert{$a$}} (q_4);
+\path[->] (q_4) edge [loop above] node  {\alert{$a, b$}} ();
+\end{tikzpicture}\\
+minimal automaton
+\end{center}
+
+\end{frame}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
+\begin{frame}[c]
+
+\begin{enumerate}
+\item Take all pairs \bl{(q, p)} with \bl{q $\not=$ p}
+\item Mark all pairs that are accepting and non-accepting states
+\item For  all unmarked pairs \bl{(q, p)} and all characters \bl{c} tests wether
+\begin{center}
+\bl{($\delta$(q,c), $\delta$(p,c))}
+\end{center} 
+are marked. If yes, then also mark \bl{(q, p)} 
+\item Repeat last step until no chance.
+\item All unmarked pairs can be merged.
+\end{enumerate}
+
+\end{frame}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
+
+
+
+
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \mode<presentation>{
 \begin{frame}[c]