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ICALP
2007
Springer

Universal Algebra and Hardness Results for Constraint Satisfaction Problems

9 years 1 months ago
Universal Algebra and Hardness Results for Constraint Satisfaction Problems
We present algebraic conditions on constraint languages Γ that ensure the hardness of the constraint satisfaction problem CSP(Γ) for complexity classes L, NL, P, NP and ModpL. These criteria also give non-expressibility results for various restrictions of Datalog. Furthermore, we show that if CSP(Γ) is not first-order definable then it is L-hard. Our proofs rely on tame congruence theory and on a fine-grain analysis of the complexity of reductions used in the algebraic study of CSP. The results pave the way for a refinement of the dichotomy conjecture stating that each CSP(Γ) lies in P or is NP-complete and they match the recent classification of [2] for Boolean CSP. We also infer a partial classification theorem for the complexity of CSP(Γ) when the associated algebra of Γ is the full idempotent reduct of a preprimal algebra. Constraint satisfaction problems (CSP) provide a unifying framework to study various computational problems arising naturally in artificial intellig...
Benoit Larose, Pascal Tesson
Added 08 Jun 2010
Updated 08 Jun 2010
Type Conference
Year 2007
Where ICALP
Authors Benoit Larose, Pascal Tesson
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