Larose, Benoit and Loten, Cynthia and Tardif, Claude - A Characterisation of First-Order Constraint Satisfaction Problems

lmcs:1097 - Logical Methods in Computer Science, November 6, 2007, Volume 3, Issue 4
A Characterisation of First-Order Constraint Satisfaction Problems

Authors: Larose, Benoit and Loten, Cynthia and Tardif, Claude

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.


Source : oai:arXiv.org:0707.2562
DOI : 10.2168/LMCS-3(4:6)2007
Volume: Volume 3, Issue 4
Published on: November 6, 2007
Submitted on: March 2, 2007
Keywords: Computer Science - Logic in Computer Science,Computer Science - Computational Complexity,F.4.1


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