QCSP monsters and the demise of the chen conjecture

Zhuk, Dmitriy; Martin, Barnaby

doi:10.1145/3357713.3384232

Cited by 14 publications

(19 citation statements)

References 26 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…If this conjecture was true, then, by Theorem 1, it would complete the classification of the complexity at least for constraint languages with constants. Recently, this conjecture was disproved [14] but the PGP case remains a very important case for the study of the complexity of the Quantified CSP.…”

Section: Theorem 2 [12] a Finite Algebra (A; F ) Has The Pgp Property...mentioning

confidence: 99%

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

Zhuk

2021

Preprint

Self Cite

View full text Add to dashboard Cite

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 the QCSP for constraint languages having the PGP property.

show abstract

Section: Theorem 2 [12] a Finite Algebra (A; F ) Has The Pgp Property...mentioning

confidence: 99%

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

Zhuk

2021

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…At present, we are far from a complexity classification for finite domain QCSPs. The 3element case with constants is settled in [21], where evidence is also given that the classification is more complicated than previously thought. The study of infinite-domain QCSPs is also far less advanced than that for infinite-domain CSPs, with only a partial known classification in the temporal case (see [13,12,15,18]).…”

Section: Introductionmentioning

confidence: 99%

The complete classification for quantified equality constraints

Zhuk¹,

Martin²

2021

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…Motivated by the CSP conjecture, many homomorphism type problems have been introduced and studied under the realm of a dichotomy, e.g., full homomorphism [3], locally injective/surjective homomorphism [28,5], list homomorphism [25], quantified CSP [34], infinite CSP [6], VCSP [26], etc. In this paper, we are interested in the Matrix Partition Problem introduced in [15] which finds its origin in combinatorics as other variants of the CSP conjecture, e.g., list or surjective homomorphism.…”

Section: Introductionmentioning

confidence: 99%

Generalisations of Matrix Partitions : Complexity and Obstructions

Barsukov¹,

Kanté²

2021

Preprint

View full text Add to dashboard Cite

A trigraph is a graph where each pair of vertices is labelled either 0 (a non-edge), 1 (an edge) or (both an edge and a non-edge). In a series of papers, Hell and co-authors (see for instance [Pavol Hell: Graph partitions with prescribed patterns. Eur. J. Comb. 35: 335-353 (2014)]) proposed to study the complexity of homomorphisms from graphs to trigraphs, called Matrix Partition Problems, where edges and non-edges can be both mapped to -edges, while a non-edge cannot be mapped to an edge, and vice-versa. Even though, Matrix Partition Problems are generalisations of Constraint Satisfaction Problems (CSPs), they share with them the property of being "intrinsically" combinatorial. So, the question of a possible dichotomy, i.e. Ptime vs NP-complete, is a very natural one and raised in Hell et al.'s papers. We propose in this paper to study Matrix Partition Problems on relational structures, wrt a dichotomy question, and, in particular, homomorphisms between trigraphs. We first show that trigraph homomorphisms and Matrix Partition Problems are P-time equivalent, and then prove that one can also restrict (wrt dichotomy) to relational structures with one relation. Failing in proving that Matrix Partition Problems on directed graphs are not P-time equivalent to Matrix Partitions on relational structures, we give some evidence that it is unlikely by showing that reductions used in the case of CSPs cannot work. We turn then our attention to Matrix Partitions with finite sets of obstructions. We show that, for a fixed trigraph H, the set of inclusion-wise minimal obstructions, which prevent to have a homomorphism to H, is finite for directed graphs if and only if it is finite for trigraphs. We also prove similar results for relational structures. We conclude by showing that on trees (seen as trigraphs) it is NP-complete to decide whether a given tree has a trigraph homomorphism to another input trigraph. The latter shows a notable difference on tractability between CSP and Matrix Partition as it is well-known that CSP is tractable on the class of trees.

show abstract

QCSP monsters and the demise of the chen conjecture

Cited by 14 publications

References 26 publications

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

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

The complete classification for quantified equality constraints

Generalisations of Matrix Partitions : Complexity and Obstructions

Contact Info

Product

Resources

About