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On Sets of Numbers Rationally Represented in a Rational Base Number System

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Algebraic Informatics (CAI 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8080))

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Abstract

In this work, it is proved that a set of numbers closed under addition and whose representations in a rational base numeration system is a rational language is not a finitely generated additive monoid.

A key to the proof is the definition of a strong combinatorial property on languages : the bounded left iteration property. It is both an unnatural property in usual formal language theory (as it contradicts any kind of pumping lemma) and an ideal fit to the languages defined through rational base number systems.

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References

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Authors and Affiliations

  1. Telecom-ParisTech and CNRS, 46 rue Barrault, 75013, Paris, France

    Victor Marsault & Jacques Sakarovitch

Authors
  1. Victor Marsault
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  2. Jacques Sakarovitch
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Editor information

Editors and Affiliations

  1. ERISCS Research Group, Parc Scientifique de, Aix-Marseille University, Luminy, 13288, Marseille CEDEX 9, France

    Traian Muntean

  2. Department of Mathematics, Aristotle University of Thessaloniki, University Campus, 54124, Thessaloniki, Greece

    Dimitrios Poulakis

  3. ERISCS Research Group and IML Research Laboratory, Parc Scientifique de, Aix-Marseille University, Luminy, 13288, Marseille, France

    Robert Rolland

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Marsault, V., Sakarovitch, J. (2013). On Sets of Numbers Rationally Represented in a Rational Base Number System. In: Muntean, T., Poulakis, D., Rolland, R. (eds) Algebraic Informatics. CAI 2013. Lecture Notes in Computer Science, vol 8080. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40663-8_10

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  • DOI: https://doi.org/10.1007/978-3-642-40663-8_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-40662-1

  • Online ISBN: 978-3-642-40663-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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