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\begin{frame}{Exercises}

  \begin{exampleblock}{}
    Show that the pumping lemma holds for:
    \begin{itemize}
      \item $\{a^nb^n\,|\,n\geq 0\}$
      \item $\{ww^R\,|\,w\in\{a,b\}^*\}$
      \item $\{w\in\{a,b\}^*\,|\,w=w^R\}$
    \end{itemize}
  \end{exampleblock}
  \pause\bigskip

  \begin{exampleblock}{}
    Argue that the pumping lemma does \emph{not} hold for:
    \begin{itemize}
      \item $\{ww\,|\,w\in\{a,b\}^*\}$
      \item $\{a^{2^k}\,|\,k \geq 0\}$
    \end{itemize}
  \end{exampleblock}
\end{frame}