\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}
  
\themex{From Context-Free Grammars to NPDA's}