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Discrete Mathematics With Applicat...

5th Edition
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ISBN: 9781337694193

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BuyFindarrow_forward

Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193
Textbook Problem
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Consider the finite-state automaton given by the following transition diagram:

Chapter 12.3, Problem 5ES, Consider the finite-state automaton given by the following transition diagram: a. Find the 0-, 1-,
a. Find the 0-, 1-, 2-, and 3-equivalence classes of states of A.
b. Draw the transition diagram for A ¯ , the quotient automaton of A.

To determine

(a)

Find the 0,1,2and 3 equivalence classes of states of A.

Explanation

Given information:

Concept used:

Arrow in the given graph played vital role in answer selection.

Calculation:

It is required to find the 0,1,2and 3 equivalence classes of states of A.

0 Equivalence classes- Two states are zero equivalent if both are accepting states or both are

non-accepting states. Therefore, the 0 equivalence classes are: {s0,s1,s3,s4},{s2,s5}

1 Equivalence classes- Two states are 1 equivalent if and only if they are

0 equivalent and after input of any symbol, their next state are 0 equivalent. Therefore, the 1 equivalence classes are: {s0,s3,s4},{s2,s5},{s1}

2 Equivalence classes- Two states are called 2 equivalent if and only if they are 1 equivalent and after input of any symbol, their next state are 1 equivalent. Therefore, the 2 equivalent classes are: {s5,s2},{s1},{s3},{s4},{s0}

3 Equivalence classes- Two states are called 3 equivalent if and only if they are 2 equivalent and after input of any symbol, their next state are 2 equivalent

To determine

(b)

Draw the transition diagram for A¯, the quotient automaton of A.

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Chapter 12 Solutions

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Sect-12.1 P-11TYSect-12.1 P-12TYSect-12.1 P-1ESSect-12.1 P-2ESSect-12.1 P-3ESSect-12.1 P-4ESSect-12.1 P-5ESSect-12.1 P-6ESSect-12.1 P-7ESSect-12.1 P-8ESSect-12.1 P-9ESSect-12.1 P-10ESSect-12.1 P-11ESSect-12.1 P-12ESSect-12.1 P-13ESSect-12.1 P-14ESSect-12.1 P-15ESSect-12.1 P-16ESSect-12.1 P-17ESSect-12.1 P-18ESSect-12.1 P-19ESSect-12.1 P-20ESSect-12.1 P-21ESSect-12.1 P-22ESSect-12.1 P-23ESSect-12.1 P-24ESSect-12.1 P-25ESSect-12.1 P-26ESSect-12.1 P-27ESSect-12.1 P-28ESSect-12.1 P-29ESSect-12.1 P-30ESSect-12.1 P-31ESSect-12.1 P-32ESSect-12.1 P-33ESSect-12.1 P-34ESSect-12.1 P-35ESSect-12.1 P-36ESSect-12.1 P-37ESSect-12.1 P-38ESSect-12.1 P-39ESSect-12.1 P-40ESSect-12.1 P-41ESSect-12.2 P-1TYSect-12.2 P-2TYSect-12.2 P-3TYSect-12.2 P-4TYSect-12.2 P-5TYSect-12.2 P-6TYSect-12.2 P-7TYSect-12.2 P-8TYSect-12.2 P-9TYSect-12.2 P-10TYSect-12.2 P-1ESSect-12.2 P-2ESSect-12.2 P-3ESSect-12.2 P-4ESSect-12.2 P-5ESSect-12.2 P-6ESSect-12.2 P-7ESSect-12.2 P-8ESSect-12.2 P-9ESSect-12.2 P-10ESSect-12.2 P-11ESSect-12.2 P-12ESSect-12.2 P-13ESSect-12.2 P-14ESSect-12.2 P-15ESSect-12.2 P-16ESSect-12.2 P-17ESSect-12.2 P-18ESSect-12.2 P-19ESSect-12.2 P-20ESSect-12.2 P-21ESSect-12.2 P-22ESSect-12.2 P-23ESSect-12.2 P-24ESSect-12.2 P-25ESSect-12.2 P-26ESSect-12.2 P-27ESSect-12.2 P-28ESSect-12.2 P-29ESSect-12.2 P-30ESSect-12.2 P-31ESSect-12.2 P-32ESSect-12.2 P-33ESSect-12.2 P-34ESSect-12.2 P-35ESSect-12.2 P-36ESSect-12.2 P-37ESSect-12.2 P-38ESSect-12.2 P-39ESSect-12.2 P-40ESSect-12.2 P-41ESSect-12.2 P-42ESSect-12.2 P-43ESSect-12.2 P-44ESSect-12.2 P-45ESSect-12.2 P-46ESSect-12.2 P-47ESSect-12.2 P-48ESSect-12.2 P-49ESSect-12.2 P-50ESSect-12.2 P-51ESSect-12.2 P-52ESSect-12.2 P-53ESSect-12.2 P-54ESSect-12.3 P-1TYSect-12.3 P-2TYSect-12.3 P-3TYSect-12.3 P-4TYSect-12.3 P-5TYSect-12.3 P-1ESSect-12.3 P-2ESSect-12.3 P-3ESSect-12.3 P-4ESSect-12.3 P-5ESSect-12.3 P-6ESSect-12.3 P-7ESSect-12.3 P-8ESSect-12.3 P-9ESSect-12.3 P-10ESSect-12.3 P-11ESSect-12.3 P-12ESSect-12.3 P-13ESSect-12.3 P-14ESSect-12.3 P-15ESSect-12.3 P-16ESSect-12.3 P-17ESSect-12.3 P-18ES