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\begin{frame}{Example}
\begin{exampleblock}{}
Consider the following NPDA $M$:
\begin{center}
\vspace{-1ex}
\begin{tikzpicture}[default,node distance=25mm,->,s/.style={minimum size=5mm}]
\node (q0) [state,s] {$q_0$}; \draw ($(q0) + (-8mm,0mm)$) -- (q0);
\draw (q0) to[tloop] node [label,above] {$a[z/1]$} (q0);
\draw (q0) to[bloop] node [label,below] {$a[1/11]$} (q0);

\node (q1) [fstate,s,right of=q0] {$q_1$};
\draw (q0) to node [label,above] {$b[1/\lambda]$} (q1);
\draw (q1) to[tloop] node [label,above] {$b[1/\lambda]$} (q1);
\end{tikzpicture}
\vspace{-2ex}
\end{center}
What is the language accepted by this automaton?
\begin{talign}
L(M) = \mpause[1]{ \{\, a^n b^m \mid n \ge m \ge 1 \,\} }
\end{talign}
\pause\pause
The empty stack language of $M$ is
\begin{talign}
L_\lambda(M) = \mpause[1]{ \{\, a^n b^n \mid n \ge 1 \,\} }
\end{talign}
\end{exampleblock}

\pause\pause

\begin{goal}{}
For a language $L$ the following two are equivalent:
\begin{itemize}
\item There is an NDPA $M$ with $L(M) = L$.
\item There is an NDPA $M$ with $L_\lambda(M) = L$.
\end{itemize}
\end{goal}
\end{frame}