English

A Characterisation of First-Order Constraint Satisfaction Problems

Logic in Computer Science 2015-07-01 v2 Computational Complexity

Abstract

We describe simple algebraic and combinatorial characterisations of finite relational core structures admitting finitely many obstructions. As a consequence, we show that it is decidable to determine whether a constraint satisfaction problem is first-order definable: we show the general problem to be NP-complete, and give a polynomial-time algorithm in the case of cores. A slight modification of this algorithm provides, for first-order definable CSP's, a simple poly-time algorithm to produce a solution when one exists. As an application of our algebraic characterisation of first order CSP's, we describe a large family of L-complete CSP's.

Keywords

Cite

@article{arxiv.0707.2562,
  title  = {A Characterisation of First-Order Constraint Satisfaction Problems},
  author = {Benoit Larose and Cynthia Loten and Claude Tardif},
  journal= {arXiv preprint arXiv:0707.2562},
  year   = {2015}
}
R2 v1 2026-06-21T08:59:09.639Z