Explanation Given: Suppose that S, I, and O are finite sets such that | S | = n , | I | = k and | O | = m . To specify a finite- state machine, first step is to choose the starting state. Now, here | S | = n , that is there are n ways to choose this starting state. Next step is to find number of ways to implement transitions. For this first choose the corresponding pair of input and state. Since | S | = n and | I | = k so, it can be done in n k ways. Since, there are n numbers of states available for transition to To determine (b) The number of different Moore machines M = ( S , I , O , f , g , S 0 ) that can be constructed, where the starting state S 0 can be arbitrarily chosen.

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ISBN: 9781260521337

Author: ROSEN

Publisher: MCG

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Set Theory

Every field in the present world involves a set. The theory of sets was developed by German mathematician Georg Cantor while working on the “problems of trigonometric series”.

Question

Chapter 13, Problem 17SE

To determine

(a)

The number of different finite-state machines (Mealy machines) M=(S,I,O,f,g,S0) that can be constructed, where the starting state S0 can be arbitrarily chosen.

To determine

(b)

The number of different Moore machines M=(S,I,O,f,g,S0) that can be constructed, where the starting state S0 can be arbitrarily chosen.

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Chapter 13, Problem 16SE

Chapter 13, Problem 18SE

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Chapter 13 Solutions

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(a) The number of different finite-state machines (Mealy machines) M = ( S , I , O , f , g , S 0 ) that can be constructed, where the starting state S 0 can be arbitrarily chosen.

Solution Summary: The author explains that to specify a finite-state machine, first step is to choose the starting state, then find number of ways to implement transitions.

Concept explainers

(a)

The number of different finite-state machines (Mealy machines) M=(S,I,O,f,g,S0) that can be constructed, where the starting state S0 can be arbitrarily chosen.

(b)

The number of different Moore machines M=(S,I,O,f,g,S0) that can be constructed, where the starting state S0 can be arbitrarily chosen.

Want to see the full answer?

Chapter 13 Solutions

(a) The number of different finite-state machines (Mealy machines) M = ( S , I , O , f , g , S 0 ) that can be constructed, where the starting state S 0 can be arbitrarily chosen.

Solution Summary: The author explains that to specify a finite-state machine, first step is to choose the starting state, then find number of ways to implement transitions.

Concept explainers

(a) The number of different finite-state machines (Mealy machines) M=(S,I,O,f,g,S0) that can be constructed, where the starting state S0 can be arbitrarily chosen.

(b) The number of different Moore machines M=(S,I,O,f,g,S0) that can be constructed, where the starting state S0 can be arbitrarily chosen.

Want to see the full answer?

Chapter 13 Solutions

(a)

The number of different finite-state machines (Mealy machines) M=(S,I,O,f,g,S0) that can be constructed, where the starting state S0 can be arbitrarily chosen.

(b)

The number of different Moore machines M=(S,I,O,f,g,S0) that can be constructed, where the starting state S0 can be arbitrarily chosen.