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(aba)n  is accepted by this NFA

(aba)n  is accepted by this NFA

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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Given the Nondeterministic Finite Automaton (NFA). Need help proving, by induction on  n, that for all positive integers  n, the string  (aba)n  is accepted by this NFA.  (This string is obtained by  n  repetitions of  aba.) Thank you :)

 

Consider the following Nondeterministic Finite Automaton (NFA). a 1 a a 4 (a) What are the possible states that this NFA could be in, after reading the input string aba? (b) Prove, by induction on n, that for all positive integers n, the string (aba)" is accepted by this NFA. (This string is obtained by n repetitions of aba.) Paragraph B (a) |(b) Path: p 3.
Transcribed Image Text:Consider the following Nondeterministic Finite Automaton (NFA). a 1 a a 4 (a) What are the possible states that this NFA could be in, after reading the input string aba? (b) Prove, by induction on n, that for all positive integers n, the string (aba)" is accepted by this NFA. (This string is obtained by n repetitions of aba.) Paragraph B (a) |(b) Path: p 3.
Expert Solution
Step 1

(a) There are two possible states after string (aba)^n, that is 

1. 1 -> a -> 2 -> b -> 4 -> a -> 1, which is non final state

2. Final state, 1 -> a -> 4 -> b -> 2 -> a -> 3

 

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