1059 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

  1060 \begin{frame}[c]

  1061 \frametitle{The Meaning of a Regex}

  1062 

  1063  ...all the strings a regular expression can match.   

  1064 

  1065 \begin{center}

  1066  \begin{tabular}{rcl}

  1067  \bl{$L(\ZERO)$}  & \bl{$\dn$} & \bl{$\{\}$}\\

  1068  \bl{$L(\ONE)$}     & \bl{$\dn$} & \bl{$\{[]\}$}\\

  1069  \bl{$L(c)$}            & \bl{$\dn$} & \bl{$\{[c]\}$}\\

  1070  \bl{$L(r_1 + r_2)$}    & \bl{$\dn$} & \bl{$L(r_1) \cup L(r_2)$}\\

  1071  \bl{$L(r_1 \cdot r_2)$} & \bl{$\dn$} & \bl{$L(r_1) \,@\, L(r_2)$}\\

  1072  \bl{$L(r^*)$}           & \bl{$\dn$} & \\

  1073   \end{tabular}

  1074 \end{center}

  1075 

  1076 \begin{textblock}{14}(1.5,13.5)\small

  1077 \bl{$L$} is a function from regular expressions to 

  1078 sets of strings (languages):\smallskip\\

  1079 \bl{\quad$L$ : Rexp $\Rightarrow$ Set$[$String$]$}

  1080 \end{textblock}

  1081 

  1082 \end{frame}

  1083 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

  1084