Please answer all questions. This question reveals important subtleties of the P
ID: 3794444 • Letter: P
Question
Please answer all questions.
This question reveals important subtleties of the Pumping Lemma. Let B = {0^k x0^k |k greaterthanorequalto and x element sigma *}. Consider the following argument, which claims to prove that B is not regular. Assume B_2 is regular, and let p be the pumping length. Consider string s = 0^P 10^p element B_2, and decompose it as s = xyz with x = epsilon, y = 0^P, z = 10^p. Then, pumping s down by setting i = 0 yields string s' = xy^i z = xy^0 z = 10^p Not Element B_2. Hence, by the Pumping Lemma, we have a contradiction. We conclude that B_2 is not regular. The question is: What is wrong with this proof? Prove that, in fact, B is regular.Explanation / Answer
(a) the proof is absolutely correct and the provided B2 is not an regular as proved . there may be conditions in the same as s'=xz ehich is not a part of Language hence it is not regular
(b)we cannot prove B as regular because there is contradiction in pumping down the string hence language will be chnaged.