English

Constraint Satisfaction Problems over semilattice block Mal'tsev algebras

Logic in Computer Science 2017-05-16 v2

Abstract

There are two well known types of algorithms for solving CSPs: local propagation and generating a basis of the solution space. For several years the focus of the CSP research has been on `hybrid' algorithms that somehow combine the two approaches. In this paper we present a new method of such hybridization that allows us to solve certain CSPs that has been out of reach for a quite a while. We consider these method on a fairly restricted class of CSPs given by algebras we will call semilattice block Mal'tsev. An algebra A is called semilattice block Mal'tsev if it has a binary operation f, a ternary operation m, and a congruence s such that the quotient A/s with operation ff is a semilattice, ff is a projection on every block of s, and every block of s is a Mal'tsev algebra with Mal'tsev operation m. We show that the constraint satisfaction problem over a semilattice block Mal'tsev algebra is solvable in polynomial time.

Keywords

Cite

@article{arxiv.1701.02623,
  title  = {Constraint Satisfaction Problems over semilattice block Mal'tsev algebras},
  author = {Andrei A. Bulatov},
  journal= {arXiv preprint arXiv:1701.02623},
  year   = {2017}
}

Comments

This version features a different proof of the main result, which uses an approach closer to that in [Andrei A. Bulatov: A dichotomy theorem for nonuniform CSPs. CoRR abs/1703.03021 (2017)], and is much simplified

R2 v1 2026-06-22T17:46:10.418Z