Decimations of languages and state complexity

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Let the words of a language L be arranged in increasing radix order: L = {w0, w1, w2, ...}. We consider transformations that extract terms from L in an arithmetic progression. For example, two such transformations are even (L) = {w0, w2, w4...} and odd (L) = {w1, w3, w5, ...}. 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. © 2009 Elsevier B.V. All rights reserved.




Krieger, D., Miller, A., Rampersad, N., Ravikumar, B., & Shallit, J. (2009). Decimations of languages and state complexity. Theoretical Computer Science, 410(24–25), 2401–2409.

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