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

  • Ondřej Klíma
  • Benoît Larose
  • Pascal Tesson
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4162)


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.


Abelian Group Equivalence Relation Direct Product Polynomial Time Algorithm Constraint Satisfaction Problem 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Ondřej Klíma
    • 1
  • Benoît Larose
    • 2
  • Pascal Tesson
    • 3
  1. 1.Department of MathematicsMasaryk University 
  2. 2.Department of Mathematics and StatisticsConcordia University 
  3. 3.Département d’Informatique et de Génie LogicielUniversité Laval 

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