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.

20. Input alphabet = { 0 ,   1 } ; Accepts the set of all strings for which the final three input symbols are 1.

(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 for which the final three input symbols are 1.

Calculation:

Given:

Input alphabet ={0,1}

Accepts all strings for which the final three input symbols are 1.

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. Let si represent that the input ended with i ones (i=0,1,2,3). 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.

When we are at state s0 and the input is a 1, then we need to move to state s1 (as the input ends with 1 more one)

(b)

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