\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}