Theoretical Computer Science
Introduction To Automata Theory, Languages, And Computation
Introduction To Automata Theory, Languages, And Computation
Context-freeness of the power of context-free languages is undecidable
Theoretical Computer Science
Roots and powers of regular languages
DLT'02 Proceedings of the 6th international conference on Developments in language theory
Some non-semi-decidability problems for linear and deterministic context-free languages
CIAA'04 Proceedings of the 9th international conference on Implementation and Application of Automata
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For any language L, let pow(L) = {uj | j 驴 0, u 驴 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.