\begin{frame}{Acceptance with Empty Stack} All automata we have seen so far had the following property: \begin{talign} (q_0,w,z) \vdash^* (q',w',u') \quad\implies\quad (q' \in F \iff u' = \lambda) \end{talign} They reach an accepting state if and only if the stack is empty. \medskip \begin{exampleblock}{} \begin{center} \input{tikz/npda1.tex} \end{center} \end{exampleblock} \medskip\pause \begin{block}{Acceptance with Empty Stack} \emph{Empty stack language of} NPDA $M=(Q,\Sigma,\Gamma,\delta,q_0,z,F)$ is \begin{talign} \alert{L_\lambda}(M) = \{\, w \in \Sigma^* \mid (q_0,w,z) \vdash^* (q',\lambda,\alert{\lambda}) \,\}. \end{talign} \end{block} (No need for final states in this definition.) \end{frame}