   Chapter 12.2, Problem 51ES ### 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 does not exist any finite-state automaton which accepts all the strings in the form ambn.

Explanation

Given information:

The language L consisting only the strings in the form ambn where m and n are positive integers and mn

Proof:

Suppose there is a finite-state automaton such that accept the string apbq where m=p and n=q

Then, we can observe that from the initial state, the automaton accept p number of a ’s as inputs in a row and next q number of b ’s in a row and then it reaches to the accepting state.

Notice that, p+1 and q+1 are integers and p+1q+1

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