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Related papers: The complexity of conservative finite-valued CSPs

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Bulatov (2008) gave a dichotomy for the counting constraint satisfaction problem #CSP. A problem from #CSP is characterised by a constraint language, which is a fixed, finite set of relations over a finite domain D. An instance of the…

Computational Complexity · Computer Science 2011-08-18 Martin Dyer , David Richerby

We study the complexity of the valued constraint satisfaction problem (VCSP) for every valued structure with the domain ${\mathbb Q}$ that is preserved by all order-preserving bijections. Such VCSPs will be called temporal, in analogy to…

Logic · Mathematics 2026-01-21 Manuel Bodirsky , Édouard Bonnet , Žaneta Semanišinová

A finite constraint language $\mathscr{R}$ is a finite set of relations over some finite domain $A$. We show that intractability of the constraint satisfaction problem $\operatorname{CSP}(\mathscr{R})$ can, in all known cases, be replaced…

Computational Complexity · Computer Science 2017-05-02 Lucy Ham , Marcel Jackson

We report new results on the complexity of the valued constraint satisfaction problem (VCSP). Under the unique games conjecture, the approximability of finite-valued VCSP is fairly well-understood. However, there is yet no characterisation…

Computational Complexity · Computer Science 2011-04-29 Peter Jonsson , Fredrik Kuivinen , Johan Thapper

We study the computational complexity of planar valued constraint satisfaction problems (VCSPs), which require the incidence graph of the instance be planar. First, we show that intractable Boolean VCSPs have to be self-complementary to be…

Computational Complexity · Computer Science 2017-04-12 Peter Fulla , Stanislav Zivny

We study the complexity of approximately solving the weighted counting constraint satisfaction problem #CSP(F). In the conservative case, where F contains all unary functions, there is a classification known for the case in which the domain…

Computational Complexity · Computer Science 2014-07-08 Xi Chen , Martin Dyer , Leslie Ann Goldberg , Mark Jerrum , Pinyan Lu , Colin McQuillan , David Richerby

Constraint satisfaction problems (CSPs) are a natural class of decision problems where one must decide whether there is an assignment to variables that satisfies a given formula. Schaefer's dichotomy theorem, and its extension to all…

Quantum Physics · Physics 2025-02-27 Eric Culf , Kieran Mastel

An instance of Max CSP is a finite collection of constraints on a set of variables, and the goal is to assign values to the variables that maximises the number of satisfied constraints. Max CSP captures many well-known problems (such as Max…

Computational Complexity · Computer Science 2007-12-11 Peter Jonsson , Andrei Krokhin , Fredrik Kuivinen

Assume $D$ is a finite set and $R$ is a finite set of functions from $D$ to the natural numbers. An instance of the minimum $R$-cost homomorphism problem ($MinHom_R$) is a set of variables $V$ subject to specified constraints together with…

Computational Complexity · Computer Science 2012-10-09 Rustem Takhanov

We study constraint satisfaction problems (CSPs) where the constraint languages are defined by finite automata, giving rise to automata-based CSPs. The key notion is the concept of Automatic Constraint Satisfaction Problem ($AutCSP$), where…

Logic in Computer Science · Computer Science 2026-04-22 Andrei Bulatov , Xiaoyang Gong , Bakh Khoussainov , Xinyao Wang

A temporal (constraint) language is a relational structure with a first-order definition in the rational numbers with the order. We study here the complexity of the Quantified Constraint Satisfaction Problem (QCSP) for temporal constraint…

Logic in Computer Science · Computer Science 2021-09-08 Michał Wrona

A counting constraint satisfaction problem (#CSP) asks for the number of ways to satisfy a given list of constraints, drawn from a fixed constraint language \Gamma. We study how hard it is to evaluate this number approximately. There is an…

Computational Complexity · Computer Science 2012-04-26 Colin McQuillan

We study the complexity of approximate counting Constraint Satisfaction Problems (#CSPs) in a bounded degree setting. Specifically, given a Boolean constraint language $\Gamma$ and a degree bound $\Delta$, we study the complexity of…

Data Structures and Algorithms · Computer Science 2020-08-21 Andreas Galanis , Leslie Ann Goldberg , Kuan Yang

A discrete temporal constraint satisfaction problem is a constraint satisfaction problem (CSP) whose constraint language consists of relations that are first-order definable over $(\Bbb Z,<)$. Our main result says that every distance CSP is…

Logic · Mathematics 2016-04-27 Manuel Bodirsky , Barnaby Martin , Antoine Mottet

We study the parameterized complexity of MinCSP for so-called equality languages, i.e., for finite languages over an infinite domain such as $\mathbb{N}$, where the relations are defined via first-order formulas whose only predicate is $=$.…

Data Structures and Algorithms · Computer Science 2023-05-19 George Osipov , Magnus Wahlström

In the constraint satisfaction problem (CSP) corresponding to a constraint language (i.e., a set of relations) $\Gamma$, the goal is to find an assignment of values to variables so that a given set of constraints specified by relations from…

Computational Complexity · Computer Science 2014-01-21 Andrei A. Bulatov , Dániel Marx

A classic result due to Schaefer (1978) classifies all constraint satisfaction problems (CSPs) over the Boolean domain as being either in $\mathsf{P}$ or $\mathsf{NP}$-hard. This paper considers a promise-problem variant of CSPs called…

Computational Complexity · Computer Science 2021-05-07 Joshua Brakensiek , Venkatesan Guruswami

The degree of a CSP instance is the maximum number of times that any variable appears in the scopes of constraints. We consider the approximate counting problem for Boolean CSP with bounded-degree instances, for constraint languages…

Computational Complexity · Computer Science 2011-09-19 Martin Dyer , Leslie Ann Goldberg , Markus Jalsenius , David Richerby

Constraint Satisfaction Problem on finite sets is known to be NP-complete in general but certain restrictions on the constraint language can ensure tractability. It was proved that if a constraint language has a weak near unanimity…

Computational Complexity · Computer Science 2019-03-07 Dmitriy Zhuk

The degree of a CSP instance is the maximum number of times that a variable may appear in the scope of constraints. We consider the approximate counting problem for Boolean CSPs with bounded-degree instances, for constraint languages…

Computational Complexity · Computer Science 2010-02-03 Martin E. Dyer , Leslie Ann Goldberg , Markus Jalsenius , David Richerby