Abstract
For any language L, let pow(L) = u j ∣ j ≥ 0, u ε L be the set of powers of elements of L. Given a rational language L (over a finite alphabet), we study the question, posed in [3], whether pow(L) is rational or not. While leaving open the problem in general, we provide an algorithmic solution for the case of one-letter alphabets. This case is still non trivial; our solution is based on Dirichlet’s result that for two relatively prime numbers, their associated arithmetic progression contains infinitely many primes.
This work was done at IRISA, Rennes, France in 2000.
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Cachat, T. (2002). The Power of One-Letter Rational Languages. In: Kuich, W., Rozenberg, G., Salomaa, A. (eds) Developments in Language Theory. DLT 2001. Lecture Notes in Computer Science, vol 2295. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46011-X_11
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DOI: https://doi.org/10.1007/3-540-46011-X_11
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