Ultimate periodicity of b-recognisable sets : a quasilinear procedure
Formal Languages and Automata Theory
2013-06-11 v2
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.
Keywords
Cite
@article{arxiv.1301.2691,
title = {Ultimate periodicity of b-recognisable sets : a quasilinear procedure},
author = {Victor Marsault and Jacques Sakarovitch},
journal= {arXiv preprint arXiv:1301.2691},
year = {2013}
}
Comments
presented at DLT 2013