\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}