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.

24. Input alphabet = { 0 ,   1 } ; Accepts the set of all strings that start with 101.

(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 start with 101

Calculation:

Given:

Input alphabet ={0,1}

Accepts all strings that start with 101

Let us design an automaton with 5 states s0,s1,s2,s3 and s4 where s0 is the initial state and s3 is the accepting state. We draw each of the states as a circle with the name of the state within the circle. We draw an arrow towards the initial state and draw a second circle within the accepting states.

s0= Initial states1=Input is 1s2= Input is 10s3= Input starts with 101s4= Input starts with 0 or 11 or 100

When we are at state s0 and the input is a 1, then we need to move to state s1

(b)

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