\begin{frame}{Right Linear Grammars}
  \begin{block}{}
    A grammar $G=(V,T,S,P)$ is \emph{right linear}
    if all production rules are of the form
    \begin{talign}
      \alert{A} ~\alert{\to}~ \alert{uB} 
      \hspace*{1cm} \mbox{or} \hspace*{1cm} 
      \alert{A} ~\alert{\to}~ \alert{u}
    \end{talign}
    with $A,B \in V$ and $u \in T^*$.
    \smallskip
    
    Moreover $G$ is \emph{\alert{strictly} right linear}
    if $\alert{|u| \le 1}$ (i.e. $\alert{u \in (T \cup \{\lambda\})}$).
  \end{block}
  \pause\medskip

  \begin{exampleblock}{}
    Construct a right linear grammar $G$ such that
    \begin{talign}
      L(G)=\{a,b\}^*\,\{aa\}\,\{b\}^*
    \end{talign}
  \end{exampleblock}
  \pause\medskip
  
  \begin{exampleblock}{}
    Construct a right linear grammar $G$ such that
    \begin{talign}
      L(G) = \{ab\}\,\big(\{a\}^*\,\{cb\}\big)^*\,\{b\}
    \end{talign}
  \end{exampleblock}
\end{frame}