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.

26. Input alphabet = { 0 ,   1 } ; Accepts the set of all strings that contain exactly two b’s.

(a)

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

Given information:

Input alphabet ={a,b} ; Accepts the set of all strings that contain exactly two b’s

Calculation:

Given:

Input alphabet ={a,b}

Accepts all strings that contain exactly two b’s

Let us design an automaton with 4 states s0,s1,s2 and s3 where s0 is the initial state and s2 is the accepting state.

s0= Input contains no b'ss1= Input contains exactly 1 bs2= Input contains exactly 2 b'ss3= Input contains 3 or more b's<

(b)

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