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Annual Symposium on Theoretical Aspects of Computer Science

STACS 1992: STACS 92 pp 83–94Cite as

Joining k- and l-recognizable sets of natural numbers

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 577))

Abstract

We show that the first order theory of < IN, +, V k , V l >, where V r : IN{0} → IN is the function which sends x to V r (x), the greatest power of r which divides x and k, l are multiplicatively independent (i.e. they have no common power) is undecidable. Actually we prove that multiplication is definable in < IN, +, V k , V l >. This shows that the theorem of Büchi cannot be generalized to a class containing all k- and all l-recognizable sets.

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Authors and Affiliations

  1. Département de mathématiques et d'informatique, U.Q.A.M., C.P. 8888 succ. A, H3C 3P8, Montréal, Québec, Canada

    Roger Villemaire

Authors
  1. Roger Villemaire
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Alain Finkel Matthias Jantzen

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© 1992 Springer-Verlag Berlin Heidelberg

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Villemaire, R. (1992). Joining k- and l-recognizable sets of natural numbers. In: Finkel, A., Jantzen, M. (eds) STACS 92. STACS 1992. Lecture Notes in Computer Science, vol 577. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-55210-3_175

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  • DOI: https://doi.org/10.1007/3-540-55210-3_175

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-55210-9

  • Online ISBN: 978-3-540-46775-5

  • eBook Packages: Springer Book Archive

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