Using the pumping lemma for regular languages show that the following language is not regular: L3 = {a™bm+2 | m > 0}
Using the pumping lemma for regular languages show that the following language is not regular: L3 = {a™bm+2 | m > 0}
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:Using the pumping lemma for regular languages show that the following language is not
regular: L3 = {a"bm+2 | m > 0}

Transcribed Image Text:Assume
be the pumping length (specified by the Pumping Lemma)
Set up
is
,and let
Pick a string
Let
%3D
where
and
satisfying the conditions of the Pumping Lemma (1)
parts C
,and (3)
Then
may be divided into
Constraints
- (2)
Decomposition
Let
,and
whre conditions I and 2 hold as
and
Pump
Let set i=
The string
Issues
This means that
Therefore, since
cannot be decompose to satisfy the conditions of the pumping lemma, our initial assumption was
which contradicts condition
Conclusion
incorrect, which means
is not regular.
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