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Syntactic Complexity of Ultimately Periodic Sets of Integers

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Language and Automata Theory and Applications (LATA 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6638))

Abstract

We compute the cardinality of the syntactic monoid of the language 0*rep b (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.

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Author information

Authors and Affiliations

  1. Institute of Mathematics, University of Liège, Grande Traverse 12, B 37, B-4000, Liège, Belgium

    Michel Rigo & Élise Vandomme

Authors
  1. Michel Rigo
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  2. Élise Vandomme
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Editor information

Editors and Affiliations

  1. Research Group on Mathematical Linguistics, Universitat Rovira i Virgili, Avinguda Catalunya, 35, 43002, Tarragona, Spain

    Adrian-Horia Dediu  & Carlos Martín-Vide  & 

  2. Department of Informatics, Kyushu University, 744 Motooka, 819–0395, Fukuoka, Japan

    Shunsuke Inenaga

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Rigo, M., Vandomme, É. (2011). Syntactic Complexity of Ultimately Periodic Sets of Integers. In: Dediu, AH., Inenaga, S., Martín-Vide, C. (eds) Language and Automata Theory and Applications. LATA 2011. Lecture Notes in Computer Science, vol 6638. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21254-3_38

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  • DOI: https://doi.org/10.1007/978-3-642-21254-3_38

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-21253-6

  • Online ISBN: 978-3-642-21254-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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