--- a/slides/slides02.tex	Tue Oct 01 23:59:36 2013 +0100
+++ b/slides/slides02.tex	Wed Oct 02 00:10:52 2013 +0100
@@ -765,21 +765,48 @@
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \mode<presentation>{
 \begin{frame}[c]
-\frametitle{\begin{tabular}{c}Problem\end{tabular}}
+\frametitle{\begin{tabular}{c}A Problem\end{tabular}}
 
-We represented ``n-times'' as a sequence regular expression:
+We represented the ``n-times'' \bl{$a\{n\}$} as a sequence regular expression:
 
 \begin{center}
-\begin{tabular}{ll}
-1:
+\begin{tabular}{rl}
+1: & \bl{$a$}\\
+2: & \bl{$a\cdot a$}\\
+3: & \bl{$a\cdot a\cdot a$}\\
+& \ldots\\
+13: & \bl{$a\cdot a\cdot a\cdot a\cdot a\cdot a\cdot a\cdot a\cdot a\cdot a\cdot a\cdot a\cdot a$}\\
+& \ldots\\
+20:
 \end{tabular}
 \end{center}
 
+This problem is aggravated with \bl{$a?$} being represented as \bl{$\epsilon + a$}.
 \end{frame}}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \mode<presentation>{
+\begin{frame}[c]
+\frametitle{\begin{tabular}{c}Solving the Problem\end{tabular}}
+
+What happens if we extend our regular expressions
+
+\begin{center}
+\begin{tabular}{rcl}
+\bl{$r$} & \bl{$::=$} & \bl{\ldots}\\
+             & \bl{$\mid$} & \bl{$r\{n\}$}\\
+             & \bl{$\mid$} & \bl{$r?$} 
+\end{tabular}
+\end{center}
+
+What is their meaning? What are the cases for \bl{$nullable$} and \bl{$der$}?
+\end{frame}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
 \begin{frame}[t]
 \frametitle{\begin{tabular}{c}\bl{$(a?\{n\}) \cdot a\{n\}$}\end{tabular}}