Systems of equations over finite semigroups and the #CSP dichotomy conjecture

Authors:
Ondřej Klíma;Benoît Larose;Pascal Tesson
Affiliations:
Department of Mathematics, Masaryk University;Department of Mathematics and Statistics, Concordia University;Département d'Informatique et de Génie Logiciel, Université Laval
Venue:
MFCS'06 Proceedings of the 31st international conference on Mathematical Foundations of Computer Science
Year:
2006

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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.