• Corpus ID: 239016177

The complexity of the Quantified CSP having the polynomially generated powers property

@article{Zhuk2021TheCO,
  title={The complexity of the Quantified CSP having the polynomially generated powers property},
  author={Dmitriy Zhuk},
  journal={ArXiv},
  year={2021},
  volume={abs/2110.09504}
}
It is known that if an algebra of polymorphisms of the constraint language has the Polynomially Generated Powers (PGP) Property then the Quantified CSP can be reduced to the CSP over the same constraint language with constants. The only limitation of this reduction is that it is applicable only for the constraint languages with constants. We drastically simplified the reduction and generalized it for constraint languages without constants. As a result, we completely classified the complexity of… 

References

SHOWING 1-10 OF 12 REFERENCES
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 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.
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
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.
The Complexity of Quantified Constraints Using the Algebraic Formulation
TLDR
A full dichotomy for the QCSP is derived, justifying the moral correctness of the Chen Conjecture, and it is proved that for every finite subset Delta of Inv(A), Pol(Delta) is Collapsible.
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.
From Complexity to Algebra and Back: Digraph Classes, Collapsibility, and the PGP
TLDR
It is proved that partially reflexive paths bequeath a set of idem potent polymorphisms whose associated clone algebra has: either the polynomially generated powers property (PGP), or the exponentially generated power property (EGP).
A Dichotomy Theorem for Nonuniform CSPs
  • A. Bulatov
  • Mathematics
    2017 IEEE 58th Annual Symposium on Foundations of Computer Science (FOCS)
  • 2017
TLDR
The Dichotomy Conjecture for the non-uniform CSP states that for every constraint language \Gm the problem CSP is either solvable in polynomial time or is NP-complete.
The size of generating sets of powers
Meditations on Quantified Constraint Satisfaction
  • Hubie Chen
  • Business
    Logic and Program Semantics
  • 2012
TLDR
A viewpoint on the research program of understanding the complexity of the problems QCSP( B ) on finite structures is offered and a group of conjectures are proposed and discussed.
...
1
2
...