   Chapter 12.2, Problem 22ES ### 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 each of 20—28, (a) design an automaton with the given input alphabet that accepts the given set of strings, and (b) find a regular expression that defines the language accepted by the automaton.22. Input alphabet = { 0 ,   1 } ; Accepts the set of all strings of length at least 2 for which the final two input symbols are the same.

To determine

(a)

To design an automaton with the given input alphabet that accepts the given set of strings.

Explanation

Given information:

Input alphabet ={a,b} ; Accepts the set of all strings of length at least 2 for which the final two input symbols are the same.

Calculation:

Given:

Input alphabet ={a,b}

Accepts all strings of length at least 2 that end in two identical characters.

Let us design an automaton with 5 states s0,s1,s2,s3 and s4 where s0 is the initial state and s3,s4 are the accepting state.

s0= Initial states1= Input ends with ab (or is the string b)s2= Input ends with ba (or is the string a)s3= Input ends with aas4= input ends with bb

When we are at state s0 and the input is an a, then we need to move to state s2

To determine

(b)

A regular expression that defines the language accepted by the automaton.

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