\begin{frame}{Operations on Languages}  
  \begin{block}{Complement}
    The complement \alert{$\overline{L}$} = all words that are not in the language $L$:
    \begin{talign}
      \overline{L} = \Sigma^* \setminus L
    \end{talign}
  \end{block}

  \begin{exampleblock}{}
    For $\Sigma = \{\,a\,\}$ and $L = \{\,a,aaa\,\}$. Then $\overline{L} = \{\,\lambda, aa\,\} \cup \{\,a^n \mid n \ge 4\,\}$.
  \end{exampleblock}
  \pause\bigskip
  
  \begin{block}{Reverse}
    The reverse of a language $L$ is
    \begin{talign}
      \alert{L^R} &= \{\, x^R \mid x \in L \,\}
    \end{talign}
  \end{block}

  \begin{exampleblock}{}
    The reverse of $L = \{\,\lambda,ab,bbaba\,\}$ is $L^R = \{\,\lambda,ba,ababb\,\}$.
  \end{exampleblock}
\end{frame}