\begin{frame}{Exercise}
  \begin{block}{}
  \begin{itemize}\setlength{\itemsep}{-.5ex}
    \item $\follow{S} \supseteq \{\,\$\,\}$
    \item $\follow{A} \supseteq \first{w} \setminus \{\,\lambda\,\}$ for every rule $B \rightarrow v A w$
    \item $\follow{A} \supseteq \follow{B}$ for rules $B \to v A w$ with $\lambda \in \first{w}$
  \end{itemize}
  \end{block}

  \begin{exampleblock}{}
    \begin{malign}
      S &\to Dc &
      A &\to Ba\mid \lambda \\
      D &\to AA &
      B &\to Ab\mid d
    \end{malign}
    We have
    \begin{talign}
      \first{S} &= \{\, b,\, c,\, d \,\} &
      \first{A} &= \{\,\lambda,\, b,\, d \,\} \\
      \first{D} &= \{\,\lambda,\, b,\, d \,\} &
      \first{B} &= \{\, b,\, d \,\} &
    \end{talign}
    Determine $\follow{S}$, $\follow{D}$, $\follow{A}$, $\follow{B}$:
    \pause
    \begin{talign}
      \follow{S} &\supseteq \mpause[1]{\{\,\$\,\}} \\
      \mpause{\follow{D} &\supseteq} 
        \mpause{ \{\,c\,\} } \\
      \mpause{ \follow{A} &\supseteq } 
        \mpause{ (\first{A} \setminus \{\,\lambda\,\}) }
        \mpause{ \cup \{\,b\,\} }
        \mpause{ \cup \follow{D} }
        \mpause{ \supseteq \{\,b,c,d\,\} }
        \\
      \mpause{ \follow{B} &\supseteq } 
        \mpause{ \{\,a\,\} }
    \end{talign}
  \end{exampleblock}
\end{frame}

\themex{Parser Tables}