First-Order Model Checking Problems Parameterized by the Model
CiE '08 Proceedings of the 4th conference on Computability in Europe: Logic and Theory of Algorithms
Quantified Constraint Satisfaction and the Polynomially Generated Powers Property
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part II
The complexity of satisfiability problems: Refining Schaefer's theorem
Journal of Computer and System Sciences
A rendezvous of logic, complexity, and algebra
ACM Computing Surveys (CSUR)
The complexity of constraint satisfaction games and QCSP
Information and Computation
Low-level dichotomy for quantified constraint satisfaction problems
Information Processing Letters
QCSP on partially reflexive forests
CP'11 Proceedings of the 17th international conference on Principles and practice of constraint programming
The Complexity of Positive First-Order Logic without Equality
ACM Transactions on Computational Logic (TOCL)
Meditations on quantified constraint satisfaction
Logic and Program Semantics
An Algebraic Preservation Theorem for Aleph-Zero Categorical Quantified Constraint Satisfaction
LICS '12 Proceedings of the 2012 27th Annual IEEE/ACM Symposium on Logic in Computer Science
Unordered constraint satisfaction games
MFCS'12 Proceedings of the 37th international conference on Mathematical Foundations of Computer Science
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The constraint satisfaction probem (CSP) is a well-acknowledged framework in which many combinatorial search problems can be naturally formulated. The CSP may be viewed as the problem of deciding the truth of a logical sentence consisting of a conjunction of constraints, in front of which all variables are existentially quantified. The quantified constraint satisfaction problem (QCSP) is the generalization of the CSP where universal quantification is permitted in addition to existential quantification. The general intractability of these problems has motivated research studying the complexity of these problems under a restricted constraint language, which is a set of relations that can be used to express constraints. This paper introduces collapsibility, a technique for deriving positive complexity results on the QCSP. In particular, this technique allows one to show that, for a particular constraint language, the QCSP reduces to the CSP. We show that collapsibility applies to three known tractable cases of the QCSP that were originally studied using disparate proof techniques in different decades: Quantified 2-SAT (Aspvall, Plass, and Tarjan in 1979), Quantified Horn-SAT (Karpinski, Kleine Büning, and Schmitt in 1987), and Quantified Affine-SAT (Creignou, Khanna, and Sudan in 2001). This reconciles and reveals common structure among these cases, which are describable by constraint languages over a two-element domain. In addition to unifying these known tractable cases, we study constraint languages over domains of larger size.