Meditations on Quantified Constraint Satisfaction

@inproceedings{Chen2012MeditationsOQ,
  title={Meditations on Quantified Constraint Satisfaction},
  author={Hubie Chen},
  booktitle={Logic and Program Semantics},
  year={2012}
}
  • Hubie Chen
  • Published in Logic and Program Semantics 30 January 2012
  • Business
The quantified constraint satisfaction problem (QCSP) is the problem of deciding, given a structure and a first-order prenex sentence whose quantifier-free part is the conjunction of atoms, whether or not the sentence holds on the structure. One obtains a family of problems by defining, for each structure B , the problem QCSP( B ) to be the QCSP where the structure is fixed to be B . In this article, we offer a viewpoint on the research program of understanding the complexity of the problems… 
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References

SHOWING 1-10 OF 38 REFERENCES
Quantified constraint satisfaction and the polynomially generated powers property
TLDR
This article identifies a new combinatorial property on algebras, the polynomially generated powers (PGP) property, which it is shown is tightly connected to QCSP complexity, and introduces another new property, switchability, which both implies the PGP property and implies positive complexity results on the QCSP.
Quantified Constraint Satisfaction and the Polynomially Generated Powers Property
TLDR
This article studies restricted versions of the quantified constraint satisfaction probem that arise from prespecifying the relations that may occur via a set of relations called a constraint language, and identifies a new combinatorial property on algebras, the polynomially generated powers(PGP) property, which it is shown is tightly connected to QCSP complexity.
Quantified Constraint Satisfaction and 2-Semilattice Polymorphisms
TLDR
A complete classification of 2-semilattice polymorphisms is proved, demonstrating that each gives rise to a case of the QCSP that is either tractable in polynomial time, or coNP-hard.
Quantified Constraint Satisfaction, Maximal Constraint Languages, and Symmetric Polymorphisms
TLDR
The quantified constraint satisfaction problem (QCSP), a more general framework in which variables can be quantified both universally and existentially, is concerned with and a complete complexity classification of maximal constraint languages is given.
Existentially restricted quantified constraint satisfaction
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 complexity of temporal constraint satisfaction problems
TLDR
This work presents a complete complexity classification of the constraint satisfaction problem (CSP) for temporal constraint languages: if the constraint language is contained in one out of nine temporal constraint language, then the CSP can be solved in polynomial time; otherwise, the C SP is NP-complete.
Universal Algebra and Hardness Results for Constraint Satisfaction Problems
TLDR
Algebraic conditions on constraint languages Γ are presented that ensure the hardness of the constraint satisfaction problem CSP(Γ) for complexity classes L, NL, P, NP and ModpL and it is shown that if C SP( Γ) is not first-order definable then it is L-hard.
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.
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