Let A be the set of palindromes over {a, b}. Suppose you are trying to prove tha

Question

Let A be the set of palindromes over {a, b}. Suppose you are trying to prove that A is not regular using the pumping lemma. Your proof starts (correctly) like this: Suppose for a contradiction that A is regular. Let p be the pumping length given by the pumping lemma. Now you have to choose string s. For each choice of s below, you have to state whether or not this choice of s can be used to finish the proof that A is not regular. If you answer that s cannot be used, you should also briefly and clearly explain why it cannot be used. If you answer that s can be used, you do not have explain anything. (a) s = b^p a^pb^p. Can this s be used? yes / no. If you said no, briefly explain your answer. (b) s = a^p. Can this s be used? yes / no. If you said no, briefly explain your answer. (c) s = a^pb^p. Can this s be used? yes / no. If you said no briefly explain your answer. (d) s = a^p - 1 ba^p - 1. Can this s be used? yes / no. If you said no, briefly explain your answer. (e) s = aaabbaaa. Can this s be used? yes / no. If you said no, briefly explain your answer. (f) s = (ab)^p a. Can this s be used? yes / no. If you said no, briefly explain your answer. (g) s = a^pba^p. Can this s be used? yes / no. If you said no, briefly explain your answer.

Explanation / Answer

a) s = bpapbp

b) s = ap

c) s = apbp

d) s = ap-1bap-1

e) s = aaabbaaa

f) s = (ab)pa

g) s = apbap

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