Draw the derivation tree corresponding to the derivation in Example 5.1.

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
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Draw the derivation tree corresponding to the derivation in Example 5.1.
Transcribed Image Text:Draw the derivation tree corresponding to the derivation in Example 5.1.
**Example 5.1**

The grammar \( G = (\{S\}, \{a, b\}, S, P) \), with productions:

\[
\begin{align*}
S &\rightarrow aSa, \\
S &\rightarrow bSb, \\
S &\rightarrow \lambda,
\end{align*}
\]

is context-free. A typical derivation in this grammar is:

\[
S \Rightarrow aSa \Rightarrow aaSaa \Rightarrow aabSbaa \Rightarrow aabbaa.
\]

This, and similar derivations, make it clear that:

\[
L(G) = \{ ww^R : w \in \{a, b\}^* \}.
\]

The language is context-free, but as shown in Example 4.8, it is not regular.
Transcribed Image Text:**Example 5.1** The grammar \( G = (\{S\}, \{a, b\}, S, P) \), with productions: \[ \begin{align*} S &\rightarrow aSa, \\ S &\rightarrow bSb, \\ S &\rightarrow \lambda, \end{align*} \] is context-free. A typical derivation in this grammar is: \[ S \Rightarrow aSa \Rightarrow aaSaa \Rightarrow aabSbaa \Rightarrow aabbaa. \] This, and similar derivations, make it clear that: \[ L(G) = \{ ww^R : w \in \{a, b\}^* \}. \] The language is context-free, but as shown in Example 4.8, it is not regular.
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