Constraint Satisfaction Problems with Infinite Templates
Complexity of Constraints
Systems of equations satisfied in all commutative finite semigroups
FOSSACS'08/ETAPS'08 Proceedings of the Theory and practice of software, 11th international conference on Foundations of software science and computational structures
Systems of equations over finite semigroups and the #CSP dichotomy conjecture
MFCS'06 Proceedings of the 31st international conference on Mathematical Foundations of Computer Science
Algebraic Foundations in Computer Science
Hi-index | 0.00 |
We consider the problem of testing whether a given system of equations over a fixed finite semigroup S has a solution. For the case where S is a monoid, we prove that the problem is computable in polynomial time when S is commutative and is the union of its subgroups but is NP-complete otherwise. When S is a monoid or a regular semigroup, we obtain similar dichotomies for the restricted version of the problem where no variable occurs on the right-hand side of each equation. We stress connections between these problems and constraint satisfaction problems. In particular, for any finite domain D and any finite set of relations Γ over D, we construct a finite semigroup SΓ such that CSP(Γ) is polynomial-time equivalent to the satifiability problem for systems of equations over SΓ.