Show a derivation tree for w = aaabbaaa using the grammar in Example 5.1. EXAMPLE 5.1 The grammar G = ({S}, {a, b}, S, P), with productions S→aSa,S→bSb,S→λ,S→aSa,S→bSb,S→λ, is context-free. A typical derivation in this grammar is S ⇒ aSa ⇒ aaSaa ⇒ aabSbaa ⇒ aabbaa. This, and similar derivations, make it clear that L (G) = {wwR : w ∈ {a, b}*}.

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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Show a derivation tree for w = aaabbaaa using the grammar in Example 5.1.

EXAMPLE 5.1

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

S→aSa,S→bSb,S→λ,S→aSa,S→bSb,S→λ,

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

S ⇒ aSa ⇒ aaSaa ⇒ aabSbaa ⇒ aabbaa.

This, and similar derivations, make it clear that

L (G) = {wwR : w ∈ {a, b}*}.

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