   Chapter 12.3, Problem 13ES ### 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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# Prove property (12.3.3).

To determine

To prove:

That there mutually disjoint subsets in the set of states in a finite-state automaton partitioned by the k equivalence classes.

Explanation

Given information:

For a finite-state automaton, there are k equivalence classes for each integer k0.

Proof:

Let A be finite state automaton that has a set of states S. Suppose s and t are two states of S.

If s is k equivalent to t, sRkt then the eventual function Nk for an input string w that the length is less than or equal k.

Nk(s,w)Nk(t,w)

If Nk(s,w) is a nonaccepting state Nk(t,w) is also a nonaccepting state

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