Ultimate Periodicity of b-Recognisable Sets: A Quasilinear Procedure

  • Victor Marsault
  • Jacques Sakarovitch
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7907)


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 general deterministic automaton accepts an ultimately periodic set of numbers.


Linear Time Regular Language Chinese Remainder Theorem Free Monoid Deterministic Automaton 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Victor Marsault
    • 1
  • Jacques Sakarovitch
    • 1
  1. 1.Telecom-ParisTech and CNRSParisFrance

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