   Chapter 12.2, Problem 13ES ### 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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# Consider again the finite-state automaton of exercise 3. a. To what state does the automaton go when the symbols of the following strings are input to it in sequence, starting from the initial state?(i) bb (ii) aabbbaba (iii) babbbbbabaa (iv) bbaaaabaa b. Which of the strings in part (a) send the automaton to an accepting state? c. What is the language accepted by the automaton? d. Find a regular expression that defines the language.

To determine

(a)

To find:

The state for which given finite-state automaton, goes for each sequence of inputs.

Explanation

Given information:

The automaton is as follows.

The automaton given has only two inputs a and b and the set of states includes four states U0,U1,U2 and U3. From these states, U3 is the accepting state.

Four sequences of inputs have been given as follows.

1. bb
2. aabbbaba
3. babbbbbabaa
4. bbaaaabaa

Calculation:

The automaton that we are discussing here is in the initial state U0. For the both inputs a and b, U0 responses and for b, the automaton goes to U1 and for a, the state changes to U2

To determine

(b)

To find:

The sequences of strings that bring the automaton to an accepting state.

To determine

(c)

To find:

The accepted language of the automaton.

To determine

(d)

To find:

The regular expression that represents the language accepted by this automaton.

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