Capturing complexity classes by fragments of second-order logic
Theoretical Computer Science - Special issue on logic and applications to computer science
Resolution for quantified Boolean formulas
Information and Computation
Complexity classifications of boolean constraint satisfaction problems
Complexity classifications of boolean constraint satisfaction problems
On the Computational Complexity of Quantified Horn Clauses
CSL '87 Proceedings of the 1st Workshop on Computer Science Logic
Tractable conservative Constraint Satisfaction Problems
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
The computational complexity of quantified constraint satisfaction
The computational complexity of quantified constraint satisfaction
Classifying the Complexity of Constraints Using Finite Algebras
SIAM Journal on Computing
Generalized Majority-Minority Operations are Tractable
LICS '05 Proceedings of the 20th Annual IEEE Symposium on Logic in Computer Science
The expressive rate of constraints
Annals of Mathematics and Artificial Intelligence
A dichotomy theorem for constraint satisfaction problems on a 3-element set
Journal of the ACM (JACM)
A Simple Algorithm for Mal'tsev Constraints
SIAM Journal on Computing
Fixed-Parameter Hierarchies inside PSPACE
LICS '06 Proceedings of the 21st Annual IEEE Symposium on Logic in Computer Science
On Tractability and Congruence Distributivity
LICS '06 Proceedings of the 21st Annual IEEE Symposium on Logic in Computer Science
A rendezvous of logic, complexity, and algebra
ACM SIGACT News
Tractability and learnability arising from algebras with few subpowers
LICS '07 Proceedings of the 22nd Annual IEEE Symposium on Logic in Computer Science
The complexity of quantified constraint satisfaction problems under structural restrictions
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
CSL'05 Proceedings of the 19th international conference on Computer Science Logic
Tractability and Learnability Arising from Algebras with Few Subpowers
SIAM Journal on Computing
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The quantified constraint satisfaction probem (QCSP) is the problem of deciding, given a relational structure and a sentence consisting of a quantifier prefix followed by a conjunction of atomic formulas, whether or not the sentence is true in the structure. The general intractability of the QCSP has led to the study of restricted versions of this problem. In this article, we study restricted versions of the QCSP that arise from prespecifying the relations that may occur via a set of relations called a constraint language. A basic tool used is a correspondence that associates an algebra to each constraint language; this algebra can be used to derive information on the behavior of the constraint language.We identify a new combinatorial property on algebras, the polynomially generated powers(PGP) property, which we show is tightly connected to QCSP complexity. We also introduce another new property on algebras, switchability, which both implies the PGP property and implies positive complexity results on the QCSP. Our main result is a classification theorem on a class of three-element algebras: each algebra is either switchable and hence has the PGP, or provably lacks the PGP. The description of non-PGP algebras is remarkably simple and robust.