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
Section: Chapter Questions
Problem 1PE
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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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F704b827e-deaa-44d8-a770-4a53587ae624%2F12af3240-4cab-480a-9ad6-3c6c6e83fb87%2Foly8ojn_processed.png&w=3840&q=75)
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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