   Chapter 12.2, Problem 28ES ### 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
1 views

# 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.

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 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

To determine

(b)

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

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started 