--- a/slides/slides03.tex	Mon Oct 19 14:17:18 2020 +0100
+++ b/slides/slides03.tex	Mon Oct 19 17:50:11 2020 +0100
@@ -1492,111 +1492,6 @@
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
 
 
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\begin{frame}[c]
-
-\begin{center}
-\begin{tikzpicture}[scale=2,>=stealth',very thick,
-                             every state/.style={minimum size=0pt,draw=blue!50,very thick,fill=blue!20},]
-  \only<-7>{\node[state, initial] (q0) at ( 0,1) {$\mbox{Q}_0$};}
-  \only<8->{\node[state, initial,accepting] (q0) at ( 0,1) {$\mbox{Q}_0$};}                           
-  \only<-7>{\node[state] (q1) at ( 1,1) {$\mbox{Q}_1$};}
-  \only<8->{\node[state,accepting] (q1) at ( 1,1) {$\mbox{Q}_1$};}
-  \node[state] (q2) at ( 2,1) {$\mbox{Q}_2$};
-  \path[->] (q0) edge[bend left] node[above] {\alert{$a$}} (q1)
-                  (q1) edge[bend left] node[above] {\alert{$b$}} (q0)
-                  (q2) edge[bend left=50] node[below] {\alert{$b$}} (q0)
-                  (q1) edge node[above] {\alert{$a$}} (q2)
-                  (q2) edge [loop right] node {\alert{$a$}} ()
-                  (q0) edge [loop below] node {\alert{$b$}} ()
-            ;
-\end{tikzpicture}
-\end{center}\bigskip
-
-\begin{center}
-\begin{tabular}{r@ {\hspace{2mm}}c@ {\hspace{2mm}}l}
-\bl{$\mbox{Q}_0$} & \bl{$=$} & \bl{$\ONE + \mbox{Q}_0\,b + \mbox{Q}_1\,b +  \mbox{Q}_2\,b$}\\
-\bl{$\mbox{Q}_1$} & \bl{$=$} & \bl{$\mbox{Q}_0\,a$}\\
-\bl{$\mbox{Q}_2$} & \bl{$=$} & \bl{$\mbox{Q}_1\,a + \mbox{Q}_2\,a$}\\
-\end{tabular}
-\end{center}
-
-
-Arden's Lemma:
-\begin{center}
-If \bl{$q = q\,r + s$}\; then\; \bl{$q = s\, r^*$}
-\end{center}
-
-\only<2-6>{\small
-\begin{textblock}{6}(1,0.8)
-\begin{bubble}[6.7cm]
-\begin{tabular}{r@ {\hspace{1mm}}c@ {\hspace{1mm}}l}
-\multicolumn{3}{@{}l}{substitute \bl{$\mbox{Q}_1$} into \bl{$\mbox{Q}_0$} \& \bl{$\mbox{Q}_2$}:}\\    
-\bl{$\mbox{Q}_0$} & \bl{$=$} & \bl{$\ONE + \mbox{Q}_0\,b + \mbox{Q}_0\,a\,b +  \mbox{Q}_2\,b$}\\
-\bl{$\mbox{Q}_2$} & \bl{$=$} & \bl{$\mbox{Q}_0\,a\,a + \mbox{Q}_2\,a$}
-\end{tabular}
-\end{bubble}
-\end{textblock}}
-
-\only<3-6>{\small
-\begin{textblock}{6}(2,4.15)
-\begin{bubble}[6.7cm]
-\begin{tabular}{r@ {\hspace{1mm}}c@ {\hspace{1mm}}l}
-\multicolumn{3}{@{}l}{simplifying \bl{$\mbox{Q}_0$}:}\\    
-\bl{$\mbox{Q}_0$} & \bl{$=$} & \bl{$\ONE + \mbox{Q}_0\,(b + a\,b) + \mbox{Q}_2\,b$}\\
-\bl{$\mbox{Q}_2$} & \bl{$=$} & \bl{$\mbox{Q}_0\,a\,a + \mbox{Q}_2\,a$}
-\end{tabular}
-\end{bubble}
-\end{textblock}}
-
-\only<4-6>{\small
-\begin{textblock}{6}(3,7.55)
-\begin{bubble}[6.7cm]
-\begin{tabular}{r@ {\hspace{1mm}}c@ {\hspace{1mm}}l}
-  \multicolumn{3}{@{}l}{Arden for \bl{$\mbox{Q}_2$}:}\\    
-\bl{$\mbox{Q}_0$} & \bl{$=$} & \bl{$\ONE + \mbox{Q}_0\,(b + a\,b) + \mbox{Q}_2\,b$}\\
-\bl{$\mbox{Q}_2$} & \bl{$=$} & \bl{$\mbox{Q}_0\,a\,a\,(a^*)$}
-\end{tabular}
-\end{bubble}
-\end{textblock}}
-
-\only<5-6>{\small
-\begin{textblock}{6}(4,10.9)
-\begin{bubble}[7.5cm]
-\begin{tabular}{r@ {\hspace{1mm}}c@ {\hspace{1mm}}l}
-  \multicolumn{3}{@{}l}{Substitute \bl{$\mbox{Q}_2$} and simplify:}\\    
-\bl{$\mbox{Q}_0$} & \bl{$=$} & \bl{$\ONE + \mbox{Q}_0\,(b + a\,b + a\,a\,(a^*)\,b)$}\\
-\end{tabular}
-\end{bubble}
-\end{textblock}}
-
-\only<6>{\small
-\begin{textblock}{6}(5,13.4)
-\begin{bubble}[7.5cm]
-\begin{tabular}{r@ {\hspace{1mm}}c@ {\hspace{1mm}}l}
-  \multicolumn{3}{@{}l}{Arden again for \bl{$\mbox{Q}_0$}:}\\    
-\bl{$\mbox{Q}_0$} & \bl{$=$} & \bl{$(b + a\,b + a\,a\,(a^*)\,b)^*$}\\
-\end{tabular}
-\end{bubble}
-\end{textblock}}
-
-
-\only<7->{\small
-\begin{textblock}{6}(6,11.5)
-\begin{bubble}[6.7cm]
-\begin{tabular}{r@ {\hspace{1mm}}c@ {\hspace{1mm}}l}
-\multicolumn{3}{@{}l}{Finally:}\\    
-\bl{$\mbox{Q}_0$} & \bl{$=$} & \bl{$(b + a\,b + a\,a\,(a^*)\,b)^*$}\\
-\bl{$\mbox{Q}_1$} & \bl{$=$} & \bl{$(b + a\,b + a\,a\,(a^*)\,b)^*\,a$}\\
-\bl{$\mbox{Q}_2$} & \bl{$=$} & \bl{$(b + a\,b + a\,a\,(a^*)\,b)^*\,a\,a\,(a^*)$}\\
-\end{tabular}
-\end{bubble}
-\end{textblock}}
-
-\end{frame}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
-
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \begin{frame}[c]
 \frametitle{Regexps and Automata}