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arXiv · 1301.2691

Ultimate periodicity of b-recognisable sets : a quasilinear procedure

Victor Marsault·Jacques Sakarovitch
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Abstract

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 verified in linear time if a given minimal automaton meets this description. This thus yields a O(n log(n)) procedure for deciding whether a general deterministic automaton accepts an ultimately periodic set of numbers.

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Victor Marsault, Jacques Sakarovitch. 2013-06-07. Ultimate periodicity of b-recognisable sets : a quasilinear procedure. https://arxiv.org/abs/1301.2691

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