--- a/slides/slides04.tex	Tue Dec 03 01:22:16 2019 +0000
+++ b/slides/slides04.tex	Tue Dec 03 01:58:19 2019 +0000
@@ -347,99 +347,6 @@
 \end{frame}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\begin{frame}[c]
-\frametitle{DFAs}  
-
-\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},]
-  
-\only<1,3->{\node[state,initial] (Q_0)  {$\mbox{Q}_0$};}
-\only<2>{\node[state,initial,fill=red] (Q_0)  {$\mbox{Q}_0$};}  
-\only<1,2,4->{\node[state] (Q_1) [right=of Q_0] {$\mbox{Q}_1$};}
-\only<3>{\node[state,fill=red] (Q_1) [right=of Q_0] {$\mbox{Q}_1$};}
-\only<-3,5->{\node[state] (Q_2) [below right=of Q_0] {$\mbox{Q}_2$};}
-\only<4>{\node[state,fill=red] (Q_2) [below right=of Q_0] {$\mbox{Q}_2$};}
-\only<-4,6->{\node[state] (Q_3) [right=of Q_2] {$\mbox{Q}_3$};}
-\only<5>{\node[state,fill=red] (Q_3) [right=of Q_2] {$\mbox{Q}_3$};}
-\only<-5>{\node[state, accepting] (Q_4) [right=of Q_1] {$\mbox{Q}_4$};}
-\only<6->{\node[state, accepting,fill=red] (Q_4) [right=of Q_1] {$\mbox{Q}_4$};}
-
-\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}
-
-\begin{textblock}{9}(4,12)
-\LARGE{}
-\only<3->{\boldmath\alert{$a$}}%
-\only<4->{\boldmath\alert{$b$}}%
-\only<5->{\boldmath\alert{$a$}}%
-\only<6->{\boldmath\alert{$a$}}%
-\only<7->{\boldmath\alert{$a\quad\Rightarrow \textbf{yes}$}}% 
-\end{textblock}
-  
-\end{frame}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\begin{frame}[t]
-\frametitle{DFAs}
-
-A \alert{\bf deterministic finite automaton}, DFA, consists of
-5 things:
-
-\begin{itemize}
-\item an alphabet \bl{$\varSigma$}  
-\item a set of states \bl{$\mbox{Qs}$}
-\item one of these states is the start state \bl{$\mbox{Q}_0$}
-\item some states are accepting states \bl{$F$}, and
-\item there is transition function \bl{$\delta$}\bigskip 
-
-\small
-which takes a state  and a character as arguments and produces a 
-new state; this function might not be everywhere defined 
-\end{itemize}
-
-\begin{center}
-\bl{$A(\varSigma, \mbox{Qs}, \mbox{Q}_0, F, \delta)$}
-\end{center}
-
-\end{frame}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\begin{frame}[c]
-\frametitle{NFAs}  
-
-\begin{center}
-\begin{tikzpicture}[>=stealth',very thick, auto,
-    every state/.style={minimum size=0pt,inner sep=3pt,
-      draw=blue!50,very thick,fill=blue!20},scale=2]
-\node[state,initial]  (Q_0)  {$\mbox{Q}_0$};
-\node[state] (Q_1) [right=of Q_0] {$\mbox{Q}_1$};
-\node[state, accepting] (Q_2) [right=of Q_1] {$\mbox{Q}_2$};
-\path[->] (Q_0) edge [loop above] node  {\alert{$b$}} ();
-\path[<-] (Q_0) edge node [below]  {\alert{$b$}} (Q_1);
-\path[->] (Q_0) edge [bend left] node [above]  {\alert{$a$}} (Q_1);
-\path[->] (Q_0) edge [bend right=45,looseness=1.3] node [below]  {\alert{$a$}} (Q_2);
-\path[->] (Q_1) edge [loop above] node  {\alert{$a,b$}} ();
-\path[->] (Q_1) edge node  [above] {\alert{$a$}} (Q_2);
-\end{tikzpicture}
-\end{center}
-
-\end{frame}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
-
 
 
 \begin{frame}[t]