\begin{frame}{Example}
  \begin{exampleblock}{}
    The language
    \begin{talign}
      \{\, a^n b^n c^n \mid n \geq 1 \,\}
    \end{talign}
    is generated by the context-sensitive grammar:
    \begin{talign}
      S &\to aAbc\mid abc \\
      A &\to aAB \mid aB \\
      Bb &\to bB \\
      Bc &\to bcc
    \end{talign}
    Example derivation:
    \begin{talign}
      \begin{array}{ccccccc}
      \alert{S} &\Rightarrow& a\alert{A}bc &\Rightarrow& aa\alert{AB}bc &\Rightarrow& aa\alert{A}b\alert{B}c \\
      &\Rightarrow& aa\alert{A}bbcc &\Rightarrow& aaa\alert{B}bbcc &\Rightarrow& aaab\alert{B}bcc \\
      &\Rightarrow& aaabb\alert{B}cc &\Rightarrow& aaabbbccc
      \end{array}
    \end{talign}   
  \end{exampleblock}  
\end{frame}

\themex{Linear Bounded Automata}