\begin{frame}{Exercise} \begin{exampleblock}{} \begin{malign} S &\to AAc & A &\to Ba\mid \lambda & B &\to Ab\mid d \end{malign} \pause\vspace{-1ex} The erasable variables ($V \Rightarrow^+ \lambda$) are: \pause $A$\;. \pause\medskip We determine \( \text{PreFirst}(A) \), \( \text{PreFirst}(B) \) and \(\text{PreFirst}(S) \):\pause \begin{talign} \text{PreFirst}(A) &= \{\, \mpause[1]{A} \mpause{, \underbrace{Ba}_{\text{from $A$}}} \mpause{, \underbrace{\lambda}_{\text{from $A$}}} \mpause{, \underbrace{B}_{\text{from $Ba$}}} \mpause{, \underbrace{Ab}_{\text{from $B$}}} \mpause{, \underbrace{d}_{\text{from $B$}}} \mpause{, \underbrace{b}_{\text{from $Ab$}}} \,\} \\ \text{PreFirst}(B) &= \{\, \mpause{B} \mpause{, \underbrace{Ab}_{\text{from $B$}}} \mpause{, \underbrace{d}_{\text{from $B$}}} \mpause{, \underbrace{b}_{\text{from $Ab$}}} \mpause{, \underbrace{A}_{\text{from $Ab$}}} \,\} \mpause{\cup \text{PreFirst}(A)} \\ &\mpause{= \{\, A, Ba, \lambda, B, Ab, d, b \,\}} \\ \text{PreFirst}(S) &= \{\, \mpause{S} \mpause{, \underbrace{AAc}_{\text{from $S$}}} \mpause{, \underbrace{Ac}_{\text{from $AAc$}}} \mpause{, \underbrace{c}_{\text{from $Ac$}}} \mpause{, \underbrace{A}_{\text{from $AAc$}}} \,\} \mpause{\cup \text{PreFirst}(A)} \\ &\mpause{= \{\, S, AAc, Ac, c, A, Ba, \lambda, B, Ab, d, b \,\}} \end{talign} \smallskip \mpause{ Thus we get \begin{malign} \text{First}(A) &= \mpause{\{\, b, d, \lambda \,\}} & \text{First}(B) &= \mpause{\{\, b, d \,\}} & \text{First}(S) &= \mpause{\{\, b, c, d \,\}} \end{malign} } \end{exampleblock} \end{frame}