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L1 = {u ∈ Σ∗| u ends with aa}. L2 = {u ∈ Σ∗| u ends and begins with different letters }. L3 = {u ∈ Σ∗| u contains abba}. L4 = {u ∈ Σ∗| u is of the form anbamfor n,m > 0}. Given the above languages: (a) Use the set operators ‘union’ and ‘complement’ to describe L5 = L1 ∩ L2. (b) Prove that L5 is regular. (c) Construct an NFA M that accepts L5, and prove its correctness.

L1 = {u ∈ Σ∗| u ends with aa}. L2 = {u ∈ Σ∗| u ends and begins with different letters }. L3 = {u ∈ Σ∗| u contains abba}. L4 = {u ∈ Σ∗| u is of the form anbamfor n,m > 0}. Given the above languages: (a) Use the set operators ‘union’ and ‘complement’ to describe L5 = L1 ∩ L2. (b) Prove that L5 is regular. (c) Construct an NFA M that accepts L5, and prove its correctness.

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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L1 = {u ∈ Σ∗| u ends with aa}.
L2 = {u ∈ Σ∗| u ends and begins with different letters }.
L3 = {u ∈ Σ∗| u contains abba}.
L4 = {u ∈ Σ∗| u is of the form anbamfor n,m > 0}.

Given the above languages:
(a) Use the set operators ‘union’ and ‘complement’ to describe L5 = L1 ∩ L2.
(b) Prove that L5 is regular.
(c) Construct an NFA M that accepts L5, and prove its correctness.
(d) Convert such NFA (from question above) to a DFA using the algorithm from class.
(e) Given the DFA you’ve designed in Q3(d), what is δ(s,au), for u ∈ Σ∗. What is δ(s,buaa), for
u ∈ Σ∗. Justify your answers. Note that s is the starting state of the given DFA.

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