395 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

   396 \begin{frame}[c]

   397 

   398 \bl{$r ::= \ZERO \,\;|\;\, \ONE \,\;|\;\, c \,\;|\;\, r_1 + r_2 \,\;|\;\, r_1 \cdot r_2 \,\;|\;\, r^{*} \,\;|\;\, r^{\{n\}}$}  

   399 

   400 \end{frame}

   401 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   

   402 

   403   

   404 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

   405 \begin{frame}[c]

   406 

   407 \begin{center}

   408 \begin{tabular}{@ {}l@ {\hspace{2mm}}c@ {\hspace{2mm}}l@ {}}

   409 \bl{$nullable(\ZERO)$}    & \bl{$\dn$} & \bl{\textit{false}}\\

   410 \bl{$nullable(\ONE)$}       & \bl{$\dn$} & \bl{\textit{true}}\\

   411 \bl{$nullable (c)$}             & \bl{$\dn$} & \bl{\textit{false}}\\

   412 \bl{$nullable (r_1 + r_2)$}     & \bl{$\dn$} & \bl{$nullable(r_1) \vee nullable(r_2)$} \\ 

   413 \bl{$nullable (r_1 \cdot r_2)$} & \bl{$\dn$} & \bl{$nullable(r_1) \wedge nullable(r_2)$} \\

   414 \bl{$nullable (r^*)$}           & \bl{$\dn$} & \bl{\textit{true}}\\

   415 \bl{$nullable (r^{\{n\}})$}      & \bl{$\dn$} & \bl{if $n = 0$ then \textit{true} else $nullable(r)$}\\  

   416 \end{tabular}

   417 \end{center}

   418 

   419 \end{frame}

   420 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   

   421 

   422 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

   423 \begin{frame}[c]

   424 

   425 \begin{center}

   426 \begin{tabular}{@ {}l@ {\hspace{2mm}}c@ {\hspace{2mm}}l@ {\hspace{-10mm}}l@ {}}

   427   \bl{$\der\, c\, (\ZERO)$}      & \bl{$\dn$} & \bl{$\ZERO$} & \\

   428   \bl{$\der\, c\, (\ONE)$}           & \bl{$\dn$} & \bl{$\ZERO$} & \\

   429   \bl{$\der\, c\, (d)$}                     & \bl{$\dn$} & \bl{if $c = d$ then $\ONE$ else $\ZERO$} & \\

   430   \bl{$\der\, c\, (r_1 + r_2)$}        & \bl{$\dn$} & \bl{$\der\, c\, r_1 + \der\, c\, r_2$} & \\

   431   \bl{$\der\, c\, (r_1 \cdot r_2)$}  & \bl{$\dn$}  & \bl{if $nullable (r_1)$}\\

   432   & & \bl{then $(\der\,c\,r_1) \cdot r_2 + \der\, c\, r_2$}\\ 

   433   & & \bl{else $(\der\, c\, r_1) \cdot r_2$}\\

   434   \bl{$\der\, c\, (r^*)$}  & \bl{$\dn$} & \bl{$(\der\,c\,r) \cdot (r^*)$}\\

   435 

   436   \bl{$\der\, c\, (r^{\{n\}})$}  & \bl{$\dn$} & \bl{if $n = 0$ then $\ZERO$ else $(\der\,c\,r) \cdot r^{\{n-1\}}$}\\

   437                                                 

   438   \end{tabular}

   439 \end{center}

   440 

   441 \end{frame}

   442 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   

   443 

   444