Hint: Construct a DFA that runs its input in parallel on multiple copies of A, but starting in different states.

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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Please work on these problems individually, and do not discuss them, verbally or otherwise, with anyone
else. You may email me with any questions you have. You may also consult textbooks, but you must
acknowledge and reference any material you use to solve these problems. You are not allowed to
search for solutions on the Web and you may not post these problems on any Web forum asking for
answers.
Problem 1. Consider the language D = {< A >:A is a DFA such that w e L(A) =ww e L(A)}.
For example, if L(A,) = 0* then A, E D, but if L(A2) is the set of all binary strings without two
consecutive 1's then A2 ¢ D because 101 e L(A2) and 101101 ¢ L(A2). Describe a high-level
algorithm to decide D and give an intuitive argument with enough detail showing that your algorithm is
correct.
Hint: Construct a DFA that runs its input in parallel on multiple copies of A, but starting in different
states.
Transcribed Image Text:Please work on these problems individually, and do not discuss them, verbally or otherwise, with anyone else. You may email me with any questions you have. You may also consult textbooks, but you must acknowledge and reference any material you use to solve these problems. You are not allowed to search for solutions on the Web and you may not post these problems on any Web forum asking for answers. Problem 1. Consider the language D = {< A >:A is a DFA such that w e L(A) =ww e L(A)}. For example, if L(A,) = 0* then A, E D, but if L(A2) is the set of all binary strings without two consecutive 1's then A2 ¢ D because 101 e L(A2) and 101101 ¢ L(A2). Describe a high-level algorithm to decide D and give an intuitive argument with enough detail showing that your algorithm is correct. Hint: Construct a DFA that runs its input in parallel on multiple copies of A, but starting in different states.
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