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.

28. Input alphabet = { 0 ,   1 } ; Accepts the set of all strings that contain the pattern 010.

(a)

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

Given information:

Input alphabet ={0,1} ; Accepts the set of all strings that contain the pattern 010

Calculation:

Given:

Input alphabet ={0,1}

Accepts all strings that contain the pattern 010

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

s0= Input is the empty string or ends with a 1(but does not end with 01)s1=Input ends with a 0(but not with 010)s2= Input ends with 01s3= Input contains the pattern 010

When we are at state s0 and the input is a 0, then the input ends with a 0 and thus we need to move to state s₁

(b)

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