Syntactic complexity of ultimately periodic sets of integers

Authors:
Michel Rigo;Élise Vandomme
Affiliations:
Institute of Mathematics, University of Liège, Liège, Belgium;Institute of Mathematics, University of Liège, Liège, Belgium
Venue:
LATA'11 Proceedings of the 5th international conference on Language and automata theory and applications
Year:
2011

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Abstract

We compute the cardinality of the syntactic monoid of the language 0* repb(mN) made of base b expansions of the multiples of the integer m. We also give lower bounds for the syntactic complexity of any (ultimately) periodic set of integers written in base b. We apply our results to some well studied problem: decide whether or not a b-recognizable sets of integers is ultimately periodic.