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    26   \end{tabular}} | 
    26   \end{tabular}} | 
    27   | 
    27   | 
    28   \normalsize  | 
    28   \normalsize  | 
    29   \begin{center} | 
    29   \begin{center} | 
    30   \begin{tabular}{ll} | 
    30   \begin{tabular}{ll} | 
    31   Email:  & christian.urban at kcl.ac.uk\\  | 
    31     Email:  & christian.urban at kcl.ac.uk\\  | 
    32   Office: & N\liningnums{7.07} (North Wing, Bush House)\\ | 
    32     Office Hours: & Thursdays 12 -- 14\\  | 
    33   Slides: & KEATS (also homework is there)\\  | 
    33     Location: & N7.07 (North Wing, Bush House)\\  | 
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    34     Slides \& Progs: & KEATS (also homework is there)\\    | 
    34   \end{tabular} | 
    35   \end{tabular} | 
    35   \end{center} | 
    36   \end{center} | 
    36   | 
    37   | 
    37 \end{frame} | 
    38 \end{frame} | 
    38 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%       | 
    39 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%       | 
    84   | 
    85   | 
    85 % \end{frame} | 
    86 % \end{frame} | 
    86 % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     | 
    87 % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     | 
    87   | 
    88   | 
    88 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  | 
    89 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  | 
    89 \begin{frame}[c] | 
    90 \begin{frame}[t] | 
    90 \frametitle{\begin{tabular}{c}Hierarchy of Languages\end{tabular}} | 
    91 \frametitle{Starting Symbol} | 
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    92   | 
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    93 \bl{\begin{plstx}[margin=1cm] | 
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    94   : \meta{S} ::= \meta{A}\cdot\meta{S}\cdot\meta{B} | | 
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    95                  \meta{B}\cdot\meta{S}\cdot\meta{A} | \epsilon\\ | 
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    96   : \meta{A} ::= a | \epsilon\\ | 
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    97   : \meta{B} ::= b\\   | 
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    98 \end{plstx}} | 
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    99   | 
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   100 \end{frame} | 
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   101 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     | 
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   102   | 
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   103   | 
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   104 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  | 
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   105 \begin{frame}[c] | 
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   106 \frametitle{Hierarchy of Languages} | 
    91   | 
   107   | 
    92 Recall that languages are sets of strings.  | 
   108 Recall that languages are sets of strings.  | 
    93   | 
   109   | 
    94 \begin{center} | 
   110 \begin{center} | 
    95 \begin{tikzpicture} | 
   111 \begin{tikzpicture} |