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Question 1 Let LCE* be a regular language over some alphabet E. The Kleene-closure L* of L is given by L* = { V₁ V₂ Vn | n ≥ 0, V₁, V2, ..., Un € L}. (Q, E, 6, qo, F) satisfies L(D) L*. (a) Suppose DFA D such that L(N) = = L. Construct an NFA N = (Q', Σ, δ', 4%, F') (b) Prove by induction on n that each word v₁v2 Un with n ≥ 0, V₁, V2, ..., Un € L is accepted by the NFA N proposed in item (a). (c) Prove that each word accepted/recognized by the NFA N proposed in item (a) is a word of the language L*.

Question 1 Let LCE* be a regular language over some alphabet E. The Kleene-closure L* of L is given by L* = { V₁ V₂ Vn | n ≥ 0, V₁, V2, ..., Un € L}. (Q, E, 6, qo, F) satisfies L(D) L*. (a) Suppose DFA D such that L(N) = = L. Construct an NFA N = (Q', Σ, δ', 4%, F') (b) Prove by induction on n that each word v₁v2 Un with n ≥ 0, V₁, V2, ..., Un € L is accepted by the NFA N proposed in item (a). (c) Prove that each word accepted/recognized by the NFA N proposed in item (a) is a word of the language L*.

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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Question 1 Let LC * be a regular language over some alphabet Σ. The Kleene-closure L* of L is given by {V1V2 • Vn | n ≥ 0, V1, V2, . . . , Vn € L}. (a) Suppose DFA D = (Q, Σ, 8, qo, F) satisfies L(D) = L. Construct an NFA N = (Q', Σ, 8', %, F') such that L(N) = L*. L* (b) Prove by induction on n that each word v₁v2 Un with n ≥ 0, V₁, V2, ..., Un E L is accepted by the NFA N proposed in item (a). (c) Prove that each word accepted/recognized by the NFA N proposed in item (a) is a word of the language L*.
Transcribed Image Text:Question 1 Let LC * be a regular language over some alphabet Σ. The Kleene-closure L* of L is given by {V1V2 • Vn | n ≥ 0, V1, V2, . . . , Vn € L}. (a) Suppose DFA D = (Q, Σ, 8, qo, F) satisfies L(D) = L. Construct an NFA N = (Q', Σ, 8', %, F') such that L(N) = L*. L* (b) Prove by induction on n that each word v₁v2 Un with n ≥ 0, V₁, V2, ..., Un E L is accepted by the NFA N proposed in item (a). (c) Prove that each word accepted/recognized by the NFA N proposed in item (a) is a word of the language L*.
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