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\begin{frame}{Lambda Rules and Erasable Variables}
\begin{block}{}
A production rule $A \to \lambda$ is called \emph{$\boldsymbol{\lambda}$-production rule}.
\end{block}
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\begin{goal}{}
A variable $$A$$ is called \emph{erasable} if $$A \Rightarrow^+ \lambda$$.
\end{goal}
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%   The set of erasable variables is the smallest set such that:
%
%   \begin{itemize}
%     \item If $$A \to \lambda$$, then $$A$$ is erasable.
%     \item If $$A \to B_1 \cdots B_n$$ and $$B_1 , \ldots, B_n$$ are erasable,\\ then $$A$$ is erasable.
%   \end{itemize}
%   \pause\medskip

The set of erasable variables can be computed as follows:
\begin{itemize}
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\item
If $A \to \lambda$,
then $A$ is erasable.
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\item
If $A \to B_1 \cdots B_n$ and $B_1$,\ldots,$B_n$ are erasable,
then so is $A$.
\end{itemize}
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\begin{exampleblock}{}
\vspace{-1ex}
\begin{talign}
S &\to AcB &
A &\to CBC &
B &\to abB &
C &\to cCd \\
&& &&
B &\to \lambda &
C &\to BB
\end{talign}

We determine the set of erasable variables:
\begin{itemize}
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\item $$B$$ is erasable because of the rule $$B \to \lambda$$
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\item $$C$$ is erasable because of $$C \to BB$$ and $$B$$ is erasable
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\item  $$A$$ is erasable because of $$A \to CBC$$ and $$B$$, $$C$$ are erasable
\end{itemize}

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So the variables $$A,B,C$$ are erasable.
\end{exampleblock}
\end{frame}