Explanation Given information: G = ( V , T , S , P ) V = { 0 , 1 , S } T = { 0 , 1 } Set of production P : S → 0 S 1 S → λ Concept used: We start from the start state S and use the set of productions to derive the given string. Proof: Basis step n = 0 , m = 0 If we start by suing the production step S → λ then the string S = λ = 0 0 1 0 is generated. Thus, P ( 0 ) is true. Inductive step: Let P ( k , j ) be true, thus the given grammar generates 0 k 1 j . We need to prove that P ( k + 1 , j ) and P ( j , k + 1 ) and P ( k + 1 , j + 1 ) is true. The last production step used in the derivation of 0 k 1 j was S → λ and thus the string was of the form 0 k S 1 j before S → λ was applied. If we now use the production step S → 0 S on 0 k S 1 j instead, then we obtain 0 k S 1 j = 0 k + 1 S 1 j To determine (b) To show: The grammar G 2 in example 6 generates the same set.

Discrete Mathematics and Its Applications ( 8th International Edition ) ISBN:9781260091991

8th Edition

ISBN: 9781259676512

Author: Kenneth H Rosen

Publisher: McGraw-Hill Education

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Chapter 13.1, Problem 10E

To determine

(a)

To show:

The grammar G1 given in example 6 generates the set {0m1n|m,n=0,1,2.....}

To determine

(b)

To show:

The grammar G2 in example 6 generates the same set.

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Chapter 13.1, Problem 9E

Chapter 13.1, Problem 11E

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Chapter 13 Solutions

Discrete Mathematics and Its Applications ( 8th International Edition ) ISBN:9781260091991

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: The grammar G 1 given in example 6 generates the set { 0 m 1 n | m , n = 0 , 1 , 2..... }

Solution Summary: The author illustrates how the grammar G_1 generates the set left0m,n=0,1,mathrm2.....right

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(a)

To show:

The grammar G1 given in example 6 generates the set {0m1n|m,n=0,1,2.....}

(b)

To show:

The grammar G2 in example 6 generates the same set.

Want to see the full answer?

Chapter 13 Solutions

(a) To show: The grammar G 1 given in example 6 generates the set { 0 m 1 n | m , n = 0 , 1 , 2..... }

Solution Summary: The author illustrates how the grammar G_1 generates the set left0m,n=0,1,mathrm2.....right

Videos

(a) To show: The grammar G1 given in example 6 generates the set {0m1n|m,n=0,1,2.....}

(b) To show: The grammar G2 in example 6 generates the same set.

Want to see the full answer?

Chapter 13 Solutions

(a)

To show:

The grammar G1 given in example 6 generates the set {0m1n|m,n=0,1,2.....}

(b)

To show:

The grammar G2 in example 6 generates the same set.