Explanation Given information: Given that M is a finite state automaton. Calculation: For any input symbol a let us prove that f ( s , a ) = t ..... ( 1 ) is same as that f ¯ ( [ s ] R , a ) = [ f ( s , a ) ] R .... ( 2 ) . Substituting the equation ( 1 ) into equation ( 2 ) - f ¯ ( [ s ] R , a ) = [ t ] R .... ( 3 ) On the basis of the above three equations, it is proven that every transition in M results in an equivalent transition in M ¯ . So the language of M is contained within the language of M ¯ To determine (b) To show that a quotient automaton M ¯ constructed from the given automaton has the least number of states that automatons equivalent to M can have.

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ISBN: 9781260521337

Author: ROSEN

Publisher: MCG

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Chapter 13.3, Problem 61E

To determine

(a)

To show that a quotient automaton M¯ recognizes the same language as M.

To determine

(b)

To show that a quotient automaton M¯ constructed from the given automaton has the least number of states that automatons equivalent to M can have.

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Chapter 13.3, Problem 60E

Chapter 13.3, Problem 62E

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Chapter 13 Solutions

DISCRETE MATHEMATICS+ITS APPL. (LL)-W/A

Ch. 13.1 - Exercises 1-3 refer to the grammar with start...Ch. 13.1 - Exercises 1-3 refer to the grammar with start...Ch. 13.1 - Prob. 3E Ch. 13.1 - Let G=(V,T,S,P) be the phrase-structure grammar...Ch. 13.1 - Prob. 5E Ch. 13.1 - Prob. 6E Ch. 13.1 - Prob. 7E Ch. 13.1 - Show that the grammar given in Example 5 generates...Ch. 13.1 - Prob. 9E Ch. 13.1 - Prob. 10E

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(a) To show that a quotient automaton M ¯ recognizes the same language as M .

Solution Summary: The author demonstrates that a quotient automaton stackrelM recognizes the same language as M.

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(a)

To show that a quotient automaton M¯ recognizes the same language as M.

(b)

To show that a quotient automaton M¯ constructed from the given automaton has the least number of states that automatons equivalent to M can have.

Want to see the full answer?

Chapter 13 Solutions

(a) To show that a quotient automaton M ¯ recognizes the same language as M .

Solution Summary: The author demonstrates that a quotient automaton stackrelM recognizes the same language as M.

Videos

(a) To show that a quotient automaton M¯ recognizes the same language as M.

(b) To show that a quotient automaton M¯ constructed from the given automaton has the least number of states that automatons equivalent to M can have.

Want to see the full answer?

Chapter 13 Solutions

(a)

To show that a quotient automaton M¯ recognizes the same language as M.

(b)

To show that a quotient automaton M¯ constructed from the given automaton has the least number of states that automatons equivalent to M can have.