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International Symposium on Fundamentals of Computation Theory

FCT 1999: Fundamentals of Computation Theory pp 246–257Cite as

On recognizable languages in divisibility monoids

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1684))

Abstract

Kleene’s theorem on recognizable languages in free monoids is considered to be of eminent importance in theoretical computer science. It has been generalized into various directions, including trace and rational monoids. Here, we investigate divisibility monoids which are defined by and capture algebraic properties sufficient to obtain a characterization of the recognizable languages by certain rational expressions as known from trace theory. The proofs rely on Ramsey’s theorem, distributive lattice theory and on Hashigushi’s rank function generalized to our divisibility monoids. We obtain Ochma’nski’s theorem on recognizable languages in free partially commutative monoids as a consequence.

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Author information

Authors and Affiliations

  1. Institut für Algebra, Technische Universität Dresden, D-01062, Dresden, Germany

    Manfred Droste & Dietrich Kuske

Authors
  1. Manfred Droste
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  2. Dietrich Kuske
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Editor information

Editors and Affiliations

  1. Faculty of Computer Science, “A.I.Cuza” University, 6600, Iaşi, Romania

    Gabriel Ciobanu

  2. Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, 70700, Bucharest, Romania

    Gheorghe Păun

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© 1999 Springer-Verlag Berlin Heidelberg

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Droste, M., Kuske, D. (1999). On recognizable languages in divisibility monoids. In: Ciobanu, G., Păun, G. (eds) Fundamentals of Computation Theory. FCT 1999. Lecture Notes in Computer Science, vol 1684. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48321-7_20

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  • DOI: https://doi.org/10.1007/3-540-48321-7_20

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66412-3

  • Online ISBN: 978-3-540-48321-2

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