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Systems of Equations over Finite Semigroups and the #CSP Dichotomy Conjecture

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Book cover Mathematical Foundations of Computer Science 2006 (MFCS 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4162))

Abstract

We study the complexity of counting the number of solutions to a system of equations over a fixed finite semigroup. We show that this problem is always either in FP or #P-complete and describe the borderline precisely. We use these results to convey some intuition about the conjectured dichotomy for the complexity of counting the number of solutions in constraint satisfaction problems.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Masaryk University,  

    Ondřej Klíma

  2. Department of Mathematics and Statistics, Concordia University,  

    Benoît Larose

  3. Département d’Informatique et de Génie Logiciel, Université Laval,  

    Pascal Tesson

Authors
  1. Ondřej Klíma
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  2. Benoît Larose
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  3. Pascal Tesson
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Editor information

Editors and Affiliations

  1. Department of Computer Science, Comenius University, Mlynská dolina, 84248, Bratislava, Slovakia

    Rastislav Královič

  2. Institute of Informatics, University of Warsaw, Poland

    Paweł Urzyczyn

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© 2006 Springer-Verlag Berlin Heidelberg

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Klíma, O., Larose, B., Tesson, P. (2006). Systems of Equations over Finite Semigroups and the #CSP Dichotomy Conjecture. In: Královič, R., Urzyczyn, P. (eds) Mathematical Foundations of Computer Science 2006. MFCS 2006. Lecture Notes in Computer Science, vol 4162. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11821069_51

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  • DOI: https://doi.org/10.1007/11821069_51

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-37791-7

  • Online ISBN: 978-3-540-37793-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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