   Chapter 12.2, Problem 52ES ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193

#### Solutions

Chapter
Section ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193
Textbook Problem
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# Let L be the language consisting of all strings of the form a m b n , where m and n are positive integers and m ≥ n .Show that there is no finite-state automaton that accepts L.

To determine

To prove:

That there is no finite-state automaton that accepts language consisting all strings the form ambn.

Explanation

Given information:

L be a language that contain strings in the form ambn where m,n are positive integers such that mn.

Proof:

Let l be a language with the string in the form ambn for all m and n such that mn.

Then, it is clear that there are infinitely many strings belongs to L such that L={w1,w2,w3,....}.

Suppose there is a finite-state automaton with n states such that the set of states is S={s1,s2,s3,...,sk}.

Let sr be a state of the automaton and apbr,aqbr are two strings in L where pqr

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