\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}

\subsection{Derivation Trees}

\themex{Derivation Trees and Ambiguity}