\begin{frame}{Exercises}
  \begin{exampleblock}{}
    Which of these languages are deterministic context-free?
    \begin{itemize}
      \item $\{\, a^nb^n \mid n\geq 0 \,\}$
      \item $\{\, ww^R \mid w\in\{a,b\}^+ \,\}$
      \item $\{\, wcw^R \mid w\in\{a,b\}^+ \,\}$
    \end{itemize}
  \end{exampleblock}
  \pause\medskip

  \begin{block}{Conclusion}
    Not all context-free languages are deterministic context-free.
  \end{block}
  \pause\bigskip

  \begin{block}{Theorem}
    It is \alert{decidable} if two DPDA's generate the same language.\\
    ~~~ \hfill \alert{(G\'eraud S\'enizergues, 1997)}
  \end{block}
\end{frame}