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 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.
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Marsault, V., Sakarovitch, J. (2013). Ultimate Periodicity of b-Recognisable Sets: A Quasilinear Procedure. In: Béal, MP., Carton, O. (eds) Developments in Language Theory. DLT 2013. Lecture Notes in Computer Science, vol 7907. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38771-5_32
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DOI: https://doi.org/10.1007/978-3-642-38771-5_32
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