Using the pumping lemma for regular languages show that the following language is notregular: L3 = {a"bm+2 | m > 0} Assumebe the pumping length (specified by the Pumping Lemma)Set upis,and letPick a stringLet%3Dwhereandsatisfying the conditions of the Pumping Lemma (1)parts C,and (3)Thenmay be divided intoConstraints- (2)DecompositionLet,andwhre conditions I and 2 hold asandPumpLet set i=The stringIssuesThis means thatTherefore, sincecannot be decompose to satisfy the conditions of the pumping lemma, our initial assumption waswhich contradicts conditionConclusionincorrect, which meansis not regular.

Answered: Using the pumping lemma for regular…

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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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Question

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

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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