In the traditional method for cutting a deck of playing

Chapter , Problem 1.68

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In the traditional method for cutting a deck of playing cards, the deck is arbitrarily split two parts, which are exchanged before reassembling the deck. In a more complex cut, called Scarnes cut, the deck is broken into three parts and the middle part in placed rst in the reassembly. Well take Scarnes cut as the inspiration for an operation on languages. For a language A, let CUT(A) = {yxz| xyz A}. a. Exhibit a language B for which CUT(B) 6= CUT(CUT(B)). b. Show that the class of regular languages is closed under CUT.

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