\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}