768 \frametitle{\begin{tabular}{c}Problem\end{tabular}}

   768 \frametitle{\begin{tabular}{c}A Problem\end{tabular}}

   769 

   769 

   770 We represented ``n-times'' as a sequence regular expression:

   770 We represented the ``n-times'' \bl{$a\{n\}$} as a sequence regular expression:

   771 

   771 

   772 \begin{center}

   772 \begin{center}

   773 \begin{tabular}{ll}

   773 \begin{tabular}{rl}

   774 1:

   774 1: & \bl{$a$}\\

   775 2: & \bl{$a\cdot a$}\\

   776 3: & \bl{$a\cdot a\cdot a$}\\

   777 & \ldots\\

   778 13: & \bl{$a\cdot a\cdot a\cdot a\cdot a\cdot a\cdot a\cdot a\cdot a\cdot a\cdot a\cdot a\cdot a$}\\

   779 & \ldots\\

   780 20:

   778 \end{frame}}

   784 This problem is aggravated with \bl{$a?$} being represented as \bl{$\epsilon + a$}.

   779 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   

   785 \end{frame}}

   786 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   

   787 

   788 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

   789 \mode<presentation>{

   790 \begin{frame}[c]

   791 \frametitle{\begin{tabular}{c}Solving the Problem\end{tabular}}

   792 

   793 What happens if we extend our regular expressions

   794 

   795 \begin{center}

   796 \begin{tabular}{rcl}

   797 \bl{$r$} & \bl{$::=$} & \bl{\ldots}\\

   798              & \bl{$\mid$} & \bl{$r\{n\}$}\\

   799              & \bl{$\mid$} & \bl{$r?$} 

   800 \end{tabular}

   801 \end{center}

   802 

   803 What is their meaning? What are the cases for \bl{$nullable$} and \bl{$der$}?

   804 \end{frame}}

   805 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   

   806