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\begin{frame}{Pushdown Automata}
  \begin{block}{}
    A \emph{nondeterministic pushdown automaton} (\emph{NPDA}) is a tuple
    \begin{talign}
      M = (Q,\Sigma,\Gamma,\delta,q_0,z,F)
    \end{talign}
    \begin{itemize}
    \item $Q$ is a finite set of states
    \item $\Sigma$ is a finite input alphabet
    \item \alert{$\Gamma$} is a finite stack alphabet
    \item \alert{$\delta : Q \times (\Sigma \cup \{\, \lambda \,\}) \times \alert{\Gamma} \to 2^{Q \times \alert{\Gamma^*}}$} 
      
      the transition function, where $\delta(q,\alpha,b)$ is always finite
    \item $q_0 \in Q$ the starting state
    \item \alert{$\alert{z} \in \Gamma$} the stack starting symbol
    \item $F \subseteq Q$ a set of final states
    \end{itemize}
  \end{block}
\end{frame}