NDLI: The Complexity of Quantified Constraint Satisfaction: Collapsibility, Sink Algebras, and the Three-Element Case

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Chen, Hubie
Copyright Year	2008
Abstract	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 Bning, 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.
Starting Page	1674
Ending Page	1701
Page Count	28
File Format	PDF
ISSN	00975397
DOI	10.1137/060668572
e-ISSN	10957111
Journal	SIAM Journal on Computing (SMJCAT)
Issue Number	5
Volume Number	37
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2008-02-14
Access Restriction	Subscribed
Subject Keyword	Computational difficulty of problems Analysis of algorithms and problem complexity Applications of universal algebra in computer science constraint satisfaction quantified satisfiability universal algebra computational complexity
Content Type	Text
Resource Type	Article
Subject	Mathematics Computer Science

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