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Automaticity of primitive words and irreducible polynomials

Abstract : If L is a language, the automaticity function A_L(n) (resp. N_L(n)) of L counts the number of states of a smallest deterministic (resp. non-deterministic) finite automaton that accepts a language that agrees with L on all inputs of length at most n. We provide bounds for the automaticity of the language of primitive words and the language of unbordered words over a k-letter alphabet. We also give a bound for the automaticity of the language of base-b representations of the irreducible polynomials over a finite field. This latter result is analogous to a result of Shallit concerning the base-k representations of the set of prime numbers.
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Anne Lacroix, Narad Rampersad. Automaticity of primitive words and irreducible polynomials. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2013, Vol. 15 no. 1 (1), pp.29--36. ⟨hal-00990604⟩

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