Generic expression hardness results for primitive positive formula comparison

Bova, Simone; Chen, Hubie; Valeriote, Matthew

doi:10.1016/j.ic.2012.10.008

Cited by 9 publications

(10 citation statements)

References 23 publications

(34 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The most important open problem related to this work is the Valeriote conjecture (also known as the Edinburgh conjecture [7]).…”

Section: Valeriote's Conjecturementioning

confidence: 99%

Finitely Related Algebras In Congruence Distributive Varieties Have Near Unanimity Terms

Barto

2013

Can. j. math.

View full text Add to dashboard Cite

Abstract. We show that every finite, finitely related algebra in a congruence distributive variety has a near unanimity term operation. As a consequence we solve the near unanimity problem for relational structures: it is decidable whether a given finite set of relations on a finite set admits a compatible near unanimity operation. This consequence also implies that it is decidable whether a given finite constraint language defines a constraint satisfaction problem of bounded strict width.

show abstract

“…The most important open problem related to this work is the Valeriote conjecture (also known as the Edinburgh conjecture [7]).…”

Section: Valeriote's Conjecturementioning

confidence: 99%

Finitely Related Algebras In Congruence Distributive Varieties Have Near Unanimity Terms

Barto

2013

Can. j. math.

View full text Add to dashboard Cite

show abstract

“…The structure P 2 is defined on signature {R} and has R P 2 = {(b, c, c ′ ) ∈ B P × C P × C P | (c, c ′ ) ∈ α P b }. The definition of P 2 comes from [8]. In forming conjunctive queries over this signature {R} each variable has a sort (first or second) associated with each variable; an atom R(x, y, y ′ ) may be formed if x is of the first sort and y and y ′ are of the second sort.…”

Section: Sublinear-query Testabilitymentioning

confidence: 99%

“…Hence, to establish the main result of this section, Theorem 6.6, it suffices to show that ∃CSP(A) is not sublinear-query testable with one-sided error when V(Alg(A)) is not congruence modular. The results in this section make use of ideas developed in [8] and [14].…”

Section: Non Sublinear-query Testabilitymentioning

confidence: 99%

Testing Assignments to Constraint Satisfaction Problems

Chen

Valeriote

Yoshida

2016

2016 IEEE 57th Annual Symposium on Foundations of Computer Science (FOCS)

Self Cite

View full text Add to dashboard Cite

For a finite relational structure A, let CSP(A) denote the CSP instances whose constraint relations are taken from A. The resulting family of problems CSP(A) has been considered heavily in a variety of computational contexts. In this article, we consider this family from the perspective of property testing: given an instance of a CSP and query access to an assignment, one wants to decide whether the assignment satisfies the instance, or is far from so doing. While previous works on this scenario studied concrete templates or restricted classes of structures, this article presents comprehensive classification theorems.Our first contribution is a dichotomy theorem completely characterizing the structures A such that CSP(A) is constant-query testable:• If A has a majority polymorphism and a Maltsev polymorphism, then CSP(A) is constantquery testable with one-sided error.• Else, testing CSP(A) requires a super-constant number of queries.Let ∃CSP(A) denote the extension of CSP(A) to instances which may include existentially quantified variables. Our second contribution is to classify all structures A in terms of the number of queries needed to test assignments to instances of ∃CSP(A), with one-sided error. More specifically, we show the following trichotomy:• If A has a majority polymorphism and a Maltsev polymorphism, then ∃CSP(A) is constantquery testable with one-sided error.• Else, if A has a (k + 1)-ary near-unanimity polymorphism for some k ≥ 2, and no Maltsev polymorphism then ∃CSP(A) is not constant-query testable (even with two-sided error) but is sublinear-query testable with one-sided error.• Else, testing ∃CSP(A) with one-sided error requires a linear number of queries.

show abstract

“…One example variant is the QCSP; as another, one can name the counting CSP, wherein one wants to count the number of satisfying assignments, in place of deciding if one exists [10]. (See [25,18,7] for further examples.) Complexity classification results typically give broad sufficient conditions for tractability, intractability, or (more generally) completeness for a complexity class; they can often be used as the basis for analyzing the complexity of further problems.…”

Section: Introductionmentioning

confidence: 99%

Meditations on Quantified Constraint Satisfaction

Chen

2012

Logic and Program Semantics

Self Cite

View full text Add to dashboard Cite

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 QCSP(B) on finite structures. In particular, we propose and discuss a group of conjectures; throughout, we attempt to place the conjectures in relation to existing results and to emphasize open issues and potential research directions.This article is dedicated to Dexter Kozen on the occasion of his 60th birthday.Congratulations and thanks, Dexter, for all that you have given us.

show abstract

Generic expression hardness results for primitive positive formula comparison

Cited by 9 publications

References 23 publications

Finitely Related Algebras In Congruence Distributive Varieties Have Near Unanimity Terms

Finitely Related Algebras In Congruence Distributive Varieties Have Near Unanimity Terms

Testing Assignments to Constraint Satisfaction Problems

Meditations on Quantified Constraint Satisfaction

Contact Info

Product

Resources

About