Question: Let k = {0, 1,...,k 1}. Let L k , and consider the set L(L) of lexicographically largest strings of each length in L. Thus,

Let k = {0, 1,...,k 1}. Let L k , and consider the set L(L) of lexicographically largest strings of each length in L. Thus, for example, in L({0, 1}) = 1 and L( + 1(0 + 01) ) = (10) (+1). Show that if L is regular, so is L(L).

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