On the expressive power of Datalog: tools and a case study
Selected papers of the 9th annual ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
On the algebraic structure of combinatorial problems
Theoretical Computer Science
Universal Algebra and Applications in Theoretical Computer Science
Universal Algebra and Applications in Theoretical Computer Science
Constraint Satisfaction Problems and Finite Algebras
ICALP '00 Proceedings of the 27th International Colloquium on Automata, Languages and Programming
Homomorphism Closed vs. Existential Positive
LICS '03 Proceedings of the 18th Annual IEEE Symposium on Logic in Computer Science
The complexity of satisfiability problems
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
On Digraph Coloring Problems and Treewidth Duality
LICS '05 Proceedings of the 20th Annual IEEE Symposium on Logic in Computer Science
A Characterisation of First-Order Constraint Satisfaction Problems
LICS '06 Proceedings of the 21st Annual IEEE Symposium on Logic in Computer Science
The complexity of satisfiability problems: refining Schaefer's theorem
MFCS'05 Proceedings of the 30th international conference on Mathematical Foundations of Computer Science
Directed st-Connectivity Is Not Expressible in Symmetric Datalog
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part II
Recent Results on the Algebraic Approach to the CSP
Complexity of Constraints
Dualities for Constraint Satisfaction Problems
Complexity of Constraints
The complexity of satisfiability problems: Refining Schaefer's theorem
Journal of Computer and System Sciences
European Journal of Combinatorics
Constraint satisfaction problems and global cardinality constraints
Communications of the ACM
On the CSP dichotomy conjecture
CSR'11 Proceedings of the 6th international conference on Computer science: theory and applications
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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 CSPs. 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 [1] for Boolean CSP. We also infer a partial classification theorem for the complexity of CSP(Γ) when the associated algebra of Γ is the idempotent reduct of a preprimal algebra.