   Chapter 12.2, Problem 21ES ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193

#### Solutions

Chapter
Section ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193
Textbook Problem
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# 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.21. Input alphabet = { 0 ,   1 } ; Accepts the set of all strings that start with 01.

To determine

(a)

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

Explanation

Given information:

Input alphabet ={0,1} ; Accepts the set of all strings that start with 01

Calculation:

Given:

Input alphabet ={0,1}

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. 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 0s2= Input starts with a 1 or 00s3= Input starts with 01

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

To determine

(b)

Find a regular expression that defines the language accepted by the automaton.

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