Decimations of languages and state complexity

Let the words of a language L be arranged in increasing radix order: L={w"0,w"1,w"2,...}. We consider transformations that extract terms from L in an arithmetic progression. For example, two such transformations are even(L)={w"0,w"2,w"4...} and odd(L)={w"1,w"3,w"5,...}. Lecomte and Rigo observed that if L is regular, then so are even(L), odd(L), and analogous transformations of L. We find good upper and lower bounds on the state complexity of this transformation. We also give an example of a context-free language L such that even(L) is not context-free.

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