2007/07/31 by Benoît Larose, Benoit Larose, Cynthia Loten +1 · 66 citations
Computer Science · Mathematics · #Advanced Graph Theory Research #Algebraic number #Algorithm #Backtracking #Combinatorics #Complexity and Algorithms in Graphs #Computer science #Constraint (computer-aided design) #Constraint Satisfaction and Optimization #Constraint satisfaction #Constraint satisfaction problem #Decidability #Discrete mathematics #Mathematics #Order (exchange) #Simple (philosophy) #Time complexity #cs.CC #cs.LO
paper · pdf · doi:10.2168/lmcs-3(4:6)2007
published in Logical Methods in Computer Science Volume 3, Issue 4 (Logical Methods in Computer Science e.V.)
arxiv created 2007/11/06 · openalex publication_date 2007/11/06 · arxiv updated 2015/07/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.