Quantified Constraint Satisfaction and the Polynomially Generated Powers Property

@inproceedings{Chen2008QuantifiedCS,
  title={Quantified Constraint Satisfaction and the Polynomially Generated Powers Property},
  author={Hubie Chen},
  booktitle={ICALP},
  year={2008}
}
  • Hubie Chen
  • Published in ICALP 7 July 2008
  • Mathematics, Computer Science
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… 
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References

SHOWING 1-10 OF 32 REFERENCES
The Complexity of Quantified Constraint Satisfaction: Collapsibility, Sink Algebras, and the Three-Element Case
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
The Computational Complexity of Quantified Constraint Satisfaction
TLDR
This dissertation investigates the computational complexity of cases of the QCSP where the types of constraints that may appear are restricted and introduces a new concept for proving QCSP tractability results called collapsibility.
Quantified Constraints: Algorithms and Complexity
TLDR
This paper considers a more general framework for constraint satisfaction problems which allows arbitrary quantifiers over constrained variables, rather than just existential quantifiers, and shows that the complexity of such extended problems is determined by the surjective polymorphisms of the constraint predicates.
Classifying the Complexity of Constraints Using Finite Algebras
TLDR
It is shown that any set of relations used to specify the allowed forms of constraints can be associated with a finite universal algebra and how the computational complexity of the corresponding constraint satisfaction problem is connected to the properties of this algebra is explored.
The Complexity of Quantified Constraint Satisfaction Problems under Structural Restrictions
We give a clear picture of the tractability/intractability frontier for quantified constraint satisfaction problems (QCSPs) under structural restrictions. On the negative side, we prove that checking
The complexity of satisfiability problems
TLDR
An infinite class of satisfiability problems is considered which contains these two particular problems as special cases, and it is shown that every member of this class is either polynomial-time decidable or NP-complete.
On Tractability and Congruence Distributivity
  • E. Kiss, M. Valeriote
  • Mathematics
    21st Annual IEEE Symposium on Logic in Computer Science (LICS'06)
  • 2006
TLDR
It is proved that constraint languages consisting of relations that are invariant under a short sequence of Jonsson terms are tractable by showing that such languages have bounded width.
A Linear-Time Algorithm for Testing the Truth of Certain Quantified Boolean Formulas
A dichotomy theorem for constraint satisfaction problems on a 3-element set
TLDR
Every subproblem of the CSP is either tractable or NP-complete, and the criterion separating them is that conjectured in Bulatov et al.
Tractable conservative constraint satisfaction problems
  • A. Bulatov
  • Computer Science
    18th Annual IEEE Symposium of Logic in Computer Science, 2003. Proceedings.
  • 2003
TLDR
This work completely characterize conservative constraint languages that give rise to CSP classes solvable in polynomial time, and obtains a complete description of those (directed) graphs H for which the List H-Coloring problem is poynomial time solvable.
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