Ultimate Periodicity of b-Recognisable Sets: A Quasilinear Procedure
Résumé
It is decidable if a set of numbers, whose representation in a base b is a regular language, is ultimately periodic. This was established by Honkala in 1986. We give here a structural description of minimal automata that accept an ultimately periodic set of numbers. We then show that it can be verified in linear time if a given minimal automaton meets this description. This yields a O(n log(n)) procedure for deciding whether a gen-eral deterministic automaton accepts an ultimately periodic set of numbers.
Domaines
Mathématique discrète [cs.DM]Origine | Fichiers produits par l'(les) auteur(s) |
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