\begin{frame}{Languages Generated by Grammars}

  \begin{block}{}
    The \emph{language generated} by a grammar $G = (V,T,S,P)$ is  
    \begin{talign}
      L(G) = \{\, w \in T^* \mid S \Rightarrow^* w \,\}
    \end{talign}
  \end{block}
  \bigskip
  
  The language consists of all words that 
  \begin{itemize}
    \smallskip
    \item contain only terminal letters (no variables), and
    \item can be derived from the start symbol
  \end{itemize}
  \pause\bigskip

  \begin{exampleblock}{}
    $G = (\{S\}, \{a,b\}, S, P)$, where $P$ consists of
    \begin{talign}
      S &\to aSb &
      S &\to \lambda
    \end{talign}    
    What is the language generated by $G$?
    \begin{talign}
      L(G) = \mpause[1]{\{\, a^nb^n \mid n \geq 0 \,\}}
    \end{talign}    
  \end{exampleblock}
  \pause
  Recall that this language is not regular.
\end{frame}