slides02.tex
changeset 19 f702fd716bd8
parent 17 4d81b2dc8271
child 20 32af6d4de262
equal deleted inserted replaced
18:d48cfc286cb1 19:f702fd716bd8
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   312 \mode<presentation>{
   312 \mode<presentation>{
   313 \begin{frame}[c]
   313 \begin{frame}[c]
   314 \frametitle{\begin{tabular}{c}The Derivative\end{tabular}}
   314 \frametitle{\begin{tabular}{c}The Derivative of a Rexp (2)\end{tabular}}
   315 
   315 
   316 \begin{center}
   316 \begin{center}
   317 \begin{tabular}{@ {}l@ {\hspace{2mm}}c@ {\hspace{2mm}}l@ {\hspace{-10mm}}l@ {}}
   317 \begin{tabular}{@ {}l@ {\hspace{2mm}}c@ {\hspace{2mm}}l@ {\hspace{-10mm}}l@ {}}
   318   \bl{der c ($\varnothing$)}            & \bl{$\dn$} & \bl{$\varnothing$} & \\
   318   \bl{der c ($\varnothing$)}            & \bl{$\dn$} & \bl{$\varnothing$} & \\
   319   \bl{der c ($\epsilon$)}           & \bl{$\dn$} & \bl{$\varnothing$} & \\
   319   \bl{der c ($\epsilon$)}           & \bl{$\dn$} & \bl{$\varnothing$} & \\
   320   \bl{der c (d)}           & \bl{$\dn$} & \bl{if c $=$ d then [] else $\varnothing$} & \\
   320   \bl{der c (d)}           & \bl{$\dn$} & \bl{if c $=$ d then [] else $\varnothing$} & \\
   321   \bl{der c (r$_1$ + r$_2$)} & \bl{$\dn$} & \bl{(der c r$_1$) + (der c r$_2$)} & \\
   321   \bl{der c (r$_1$ + r$_2$)} & \bl{$\dn$} & \bl{(der c r$_1$) + (der c r$_2$)} & \\
   322   \bl{der c (r$_1$ $\cdot$ r$_2$)} & \bl{$\dn$} & \bl{((der c r$_1$) $\cdot$ r$_2$) + } & \\
   322   \bl{der c (r$_1$ $\cdot$ r$_2$)} & \bl{$\dn$}  & \bl{if nullable r$_1$}\\
   323        &          & \bl{\hspace{3mm}(if nullable r$_1$ then der c r$_2$ else $\varnothing$)}\\
   323   & & \bl{then ((der c r$_1$) $\cdot$ r$_2$) + (der c r$_2$)}\\ 
       
   324   & & \bl{else (der c r$_1$) $\cdot$ r$_2$}\\
   324   \bl{der c (r$^*$)}          & \bl{$\dn$} & \bl{(der c r) $\cdot$ (r$^*$)} &\smallskip\\\pause
   325   \bl{der c (r$^*$)}          & \bl{$\dn$} & \bl{(der c r) $\cdot$ (r$^*$)} &\smallskip\\\pause
   325 
   326 
   326   \bl{ders [] r}     & \bl{$\dn$} & \bl{r} & \\
   327   \bl{ders [] r}     & \bl{$\dn$} & \bl{r} & \\
   327   \bl{ders (c::s) r} & \bl{$\dn$} & \bl{ders s (der c r)} & \\
   328   \bl{ders (c::s) r} & \bl{$\dn$} & \bl{ders s (der c r)} & \\
   328   \end{tabular}
   329   \end{tabular}
   428 already holds for \bl{s}
   429 already holds for \bl{s}
   429 \end{itemize}
   430 \end{itemize}
   430 \end{frame}}
   431 \end{frame}}
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   433 
       
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   435 \mode<presentation>{
       
   436 \begin{frame}[c]
       
   437 \frametitle{\begin{tabular}{c}Proofs about Strings (2)\end{tabular}}
       
   438 
       
   439 Let \bl{Der c A} be the set defined as
       
   440 
       
   441 \begin{center}
       
   442 \bl{Der c A $\dn$ $\{$ s $|$  c::s $\in$ A$\}$ } 
       
   443 \end{center}
       
   444 
       
   445 Assume that \bl{$L$(der c r) = Der c ($L$(r))}. Prove that
       
   446 
       
   447 \begin{center}
       
   448 \bl{matcher(r, s)  if and only if  s $\in$ $L$(r)} 
       
   449 \end{center}
       
   450 
       
   451 
       
   452 \end{frame}}
       
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   435 \mode<presentation>{
   456 \mode<presentation>{
   436 \begin{frame}[c]
   457 \begin{frame}[c]
   437 \frametitle{\begin{tabular}{c}Regular Languages\end{tabular}}
   458 \frametitle{\begin{tabular}{c}Regular Languages\end{tabular}}