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.

25. Input alphabet = { 0 ,   1 } ; Accepts the set of all strings that end in 10.

(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 ends in 10

Calculation:

Given:

Input alphabet ={0,1}

Accepts all strings that end in 10

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

s0= Initial states1=Input ends with 00 or input is 0s2= Input ends with 11 or input is 1s3= Input ends with 01s4= Input ends with 10

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

(b)

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