\begin{frame}{Languages Generated by Grammars}

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

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