   Chapter 12.2, Problem 38ES ### 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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# In 29—47, design a finite-state automaton to accept the language defined by the regular expression in the referenced exercise from Section 12.1. 38. Exercise 27

To determine

Design a finite-state automaton to accept the language defined by the regular expression in the referenced exercise from Section 12.1.

Explanation

Given information:

“The language consisting of strings of x'sand y's in which the elements in every pair of

x's are separated by at least one y ”.

Concept used:

Arrow in the given graph played vital role in answer selection.

Calculation:

It is required to design an automaton that accepts language defined by a regular expression which is expressed in words as “The language consisting of strings of x'sand y's in which the elements in every pair of x's are separated by at least one y ”. This regular expression can be written as x|y*|(y*( xy y * )( ε|x))*. To design the automaton consider three non-accepting states s0,s3and s4 and three accepting states s1,s2and s5. Considering s0 to be the initial state of the

automaton, the design of the automaton is given below. Any string having only x or finite concatenation of y is accepted by the automaton and leads the automaton to the accepting states s1ors2

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