Let L be a language over the alphabet Σ = {a,b,c}. Prove that L = {abman for any positive integers n ‡m} is not regular. Proof: Assume that L is regular, so that the pumping lemma applies. Therefore L has a pumping length p. Let Since s belongs to L and S = This string is a member of L because has length longer than p, there exist strings x, y, and z such that s = xyz, where - xz is a member of L, xyz is a member of L for all positive integers i, - ly >0, and - |xy| ≤p. Now consider the following argument: (You finish the rest of the proof.)

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
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Let L be a language over the alphabet Σ = {a, b, c}.
Prove that
L = {aªbman for any positive integers n ‡m}
is not regular.
Proof: Assume that L is regular, so that the pumping lemma applies. Therefore L has a pumping length p. Let
Since s belongs to L and
S =
This string is a member of L because
has length longer than p, there exist strings x, y, and z such that s = xyz, where
xz is a member of L,
xyz is a member of L for all positive integers i,
− [y] >0, and
− |xy| ≤ p.
Now consider the following argument: (You finish the rest of the proof.)
Transcribed Image Text:Let L be a language over the alphabet Σ = {a, b, c}. Prove that L = {aªbman for any positive integers n ‡m} is not regular. Proof: Assume that L is regular, so that the pumping lemma applies. Therefore L has a pumping length p. Let Since s belongs to L and S = This string is a member of L because has length longer than p, there exist strings x, y, and z such that s = xyz, where xz is a member of L, xyz is a member of L for all positive integers i, − [y] >0, and − |xy| ≤ p. Now consider the following argument: (You finish the rest of the proof.)
Expert Solution
Step 1: Introduction

Regular language is a language which can be expressed using a regular expression or using finite automata. It accepts some set of strings that are present in the language and generated by regular grammar. 

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