\begin{frame}{Regular Expressions $\iff$ Regular Languages} \begin{block}{Theorem} A language $L$ is \emph{regular} \\ \hfill $\iff$ there is a \emph{regular expression} $r$ with $L(r) = L$. \end{block} \pause\medskip \begin{proof} We need to prove two directions: \begin{itemize} \medskip \item $(\Leftarrow)$ Translate regular expressions into NFAs. \medskip \item $(\Rightarrow)$ Translate NFAs into regular expressions. \medskip \end{itemize} \end{proof} \end{frame}