A rendezvous of logic, complexity, and algebra
ACM SIGACT News
Majority constraints have bounded pathwidth duality
European Journal of Combinatorics
European Journal of Combinatorics
Forbidden lifts (NP and CSP for combinatorialists)
European Journal of Combinatorics
Majority functions on structures with finite duality
European Journal of Combinatorics
Homomorphism preservation theorems
Journal of the ACM (JACM)
Partially Ordered Connectives and Monadic Monotone Strict NP
Journal of Logic, Language and Information
A Logical Approach to Constraint Satisfaction
Complexity of Constraints
The complexity of satisfiability problems: Refining Schaefer's theorem
Journal of Computer and System Sciences
Universal algebra and hardness results for constraint satisfaction problems
Theoretical Computer Science
A rendezvous of logic, complexity, and algebra
ACM Computing Surveys (CSUR)
Dualities in full homomorphisms
European Journal of Combinatorics
Theoretical Computer Science
European Journal of Combinatorics
Generalised dualities and finite maximal antichains
WG'06 Proceedings of the 32nd international conference on Graph-Theoretic Concepts in Computer Science
Datalog and constraint satisfaction with infinite templates
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
NP by means of lifts and shadows
MFCS'07 Proceedings of the 32nd international conference on Mathematical Foundations of Computer Science
Universal algebra and hardness results for constraint satisfaction problems
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
Datalog and constraint satisfaction with infinite templates
Journal of Computer and System Sciences
Ontology-based data access: a study through disjunctive datalog, CSP, and MMSNP
Proceedings of the 32nd symposium on Principles of database systems
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It is known that every constraint satisfaction problem (CSP) reduces, and is in fact polynomially equivalent, to a digraph coloring problem. By carefully analyzing the constructions, we observe that the reduction is quantifier-free. Using this, we illustrate the power of the logical approach to CSPs by resolving two conjectures about treewidth duality in the digraph case. The point is that the analogues of these conjectures for general CSPs were resolved long ago by proof techniques that seem to break down for digraphs. We also completely characterize those CSPs that are first-order definable and show that they coincide with those that have finitary tree duality. The combination of this result with an older result by Nesetril and Tardif shows that it is semi-decidable, given H, whether the H-coloring problem is definable in full first-order logic. Finally, we provide new width lower bounds for some tractable CSPs. The novelty is that our bounds are a tight function of the treewidth of the underlying instance.