\begin{frame}{Exercises (3)} % (Groups of two, 1 minute) \begin{exampleblock}{} \emph{Is the following language context-free?} \begin{talign} L = \{\, ww \mid w \in \Sigma^* \,\} \end{talign} where $\Sigma = \{a,b\}$. \bigskip On the previous slide, we have shown that $\overline{L}$ is context-free. \end{exampleblock} \pause\bigskip \begin{alertblock}{} This language is not context-free. \end{alertblock} We will prove this using the context-free pumping lemma. \pause\bigskip \begin{goal}{} The class of context-free languages is not \emph{closed under complement}. \end{goal} \end{frame}