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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39 Citations
Highly Influential Citations
5
Background Citations
17
Methods Citations
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39 Citations

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Citation Type

Asking the Metaquestions in Constraint Tractability
TLDR
This article systematically studies—for various classes of polymorphisms—the computational complexity of deciding whether or not a given structure ℍ admits a polymorphism from the class, and proves the NP-completeness of deciding a condition conjectured to characterize the tractable problems CSP(ℍ).
Containment, Equivalence and Coreness from CSP to QCSP and beyond
TLDR
Previous results on containment, equivalence and "coreness" for QCSP are recalled and extended before initiating a preliminary study of cores for QC SP which turns out to be more elusive.
Tractability Frontier for Dually-Closed Temporal Quantified Constraint Satisfaction Problems
TLDR
It is proved that QCSP for such a language is either solvable in polynomial time or it is hard for NP or coNP, a dichotomy for the restricted class of duallyclosed temporal languages.
Decomposing Quantified Conjunctive (or Disjunctive) Formulas
  • Hubie Chen, V. Dalmau
  • Computer Science
    2012 27th Annual IEEE Symposium on Logic in Computer Science
  • 2012
TLDR
A comprehensive classification of the sets of prefixed graphs on which model checking is tractable is given, based on a novel generalization of treewidth, that generalizes and places into a unified framework a number of existing results.
Fixed-Template Promise Model Checking Problems
TLDR
A class of problems that generalizes the CSP simultaneously in two directions is studied: a set L of quantifiers and Boolean connectives, and two versions of each constraint are specified, one strong and one weak.
The complexity of quantified constraints: collapsibility, switchability and the algebraic formulation
TLDR
It is proved a complexity-theoretic converse in the case of infinite constraint languages encoded in propositional logic, that if Inv(A) satisfies the exponentially generated powers property (EGP), then QCSP(Inv(A)) is co-NP-hard.
A Proof of the CSP Dichotomy Conjecture
TLDR
This article presents an algorithm that solves Constraint Satisfaction Problem in polynomial time for constraint languages having a weak near unanimity polymorphism, which proves the remaining part of the conjecture.
A Proof of CSP Dichotomy Conjecture
  • Dmitriy Zhuk
  • Mathematics, Computer Science
    2017 IEEE 58th Annual Symposium on Foundations of Computer Science (FOCS)
  • 2017
TLDR
An algorithm is presented that solves Constraint Satisfaction Problem in polynomial time for constraint languages having a weak near unanimity polymorphism, which proves the remaining part of the conjecture.
QCSP monsters and the demise of the chen conjecture
TLDR
A surprising classification for the computational complexity of the Quantified Constraint Satisfaction Problem over a constraint language Γ, QCSP(Γ), where Γ is a finite language over 3 elements which contains all constants and the Chen Conjecture is refuted.
The Constraint Satisfaction Problem: Complexity and Approximability
TLDR
This report documents the material presented during the course of the Dagstuhl Seminar 18231 “The Constraint Satisfaction Problem: Complexity and Approximability”, aimed at bringing together researchers using all the different techniques in the study of the CSP to share their insights obtained.
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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 constraint satisfaction games and QCSP
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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