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

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
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2. Show a derivation tree for w= aaabbaaa using the grammar in Example 5.1.
Transcribed Image Text:2. 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 → X,
is context-free. A typical derivation in this grammar is
SaSa⇒ aaSaa⇒ aabSbaaaabbaa.
This, and similar derivations, make it clear that
L (G) = {ww: w ≤ {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 S → aSa, S bSb, S → X, is context-free. A typical derivation in this grammar is SaSa⇒ aaSaa⇒ aabSbaaaabbaa. This, and similar derivations, make it clear that L (G) = {ww: w ≤ {a,b}*}. The language is context-free, but as shown in Example 4.8, it is not regular.
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