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Problem 5 [20 pts Prove the following variant of the pumping lemma: Let L be a regular language. Then there exists n (depending on L)

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Problem 5 [20 pts Prove the following variant of the pumping lemma: Let L be a regular language. Then there exists n (depending on L) such that Vw E L with lwl 2 2n, 3 a partition of w as w = xyzu where lxyzl 2n, ye, ze, such that vk, j 0, xykZju E L

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