\begin{frame}{Context-Free Languages and NPDA's} \begin{goal}{Theorem} A language $L$ is context-free \\ ~\hfill $\iff$ there exists an NPDA $M$ with $L(M) = L$\,. \end{goal} \pause\medskip \begin{proof} We need to prove two directions: \begin{itemize} \medskip \item $(\Rightarrow)$ Translate context-free grammars into NPDA's. \medskip \item $(\Leftarrow)$ Translate NPDA's into context-free grammars. \medskip \end{itemize} \end{proof} \end{frame}