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Related papers: Testing the complexity of a valued CSP language

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Valued constraint satisfaction problems (VCSPs) are a large class of combinatorial optimisation problems. The computational complexity of VCSPs depends on the set of allowed cost functions in the input. Recently, the computational…

Logic in Computer Science · Computer Science 2022-04-04 Manuel Bodirsky , Marcello Mamino , Caterina Viola

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

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 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

We study the parameterized problem of satisfying ``almost all'' constraints of a given formula $F$ over a fixed, finite Boolean constraint language $\Gamma$, with or without weights. More precisely, for each finite Boolean constraint…

Computational Complexity · Computer Science 2025-04-23 Eun Jung Kim , Stefan Kratsch , Marcin Pilipczuk , Magnus Wahlström

A first-order formula is called primitive positive (pp) if it only admits the use of existential quantifiers and conjunction. Pp-formulas are a central concept in (fixed-template) constraint satisfaction since CSP($\Gamma$) can be viewed as…

Logic in Computer Science · Computer Science 2026-01-28 Jakub Bulín , Michael Kompatscher

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

The CSP (constraint satisfaction problems) is a class of problems deciding whether there exists a homomorphism from an instance relational structure to a target one. The CSP dichotomy is a profound result recently proved by Zhuk (2020, J.…

Logic · Mathematics 2023-01-13 Azza Gaysin

An instance of the Constraint Satisfaction Problem (CSP) is given by a family of constraints on overlapping sets of variables, and the goal is to assign values from a fixed domain to the variables so that all constraints are satisfied. In…

Data Structures and Algorithms · Computer Science 2018-12-06 Víctor Dalmau , Marcin Kozik , Andrei Krokhin , Konstantin Makarychev , Yury Makarychev , Jakub Opršal

We study the complexity of constraint satisfaction problems for templates $\Gamma$ that are first-order definable in $(\Bbb Z; succ)$, the integers with the successor relation. Assuming a widely believed conjecture from finite domain…

Computational Complexity · Computer Science 2016-04-27 Manuel Bodirsky , Victor Dalmau , Barnaby Martin , Antoine Mottet , Michael Pinsker

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

In the constraint satisfaction problem ($CSP$), the aim is to find an assignment of values to a set of variables subject to specified constraints. In the minimum cost homomorphism problem ($MinHom$), one is additionally given weights…

Machine Learning · Computer Science 2010-04-06 Rustem Takhanov

The constrained synchronization problem (CSP) asks for a synchronizing word of a given input automaton contained in a regular set of constraints. It could be viewed as a special case of synchronization of a discrete event system under…

Formal Languages and Automata Theory · Computer Science 2021-08-03 Stefan Hoffmann

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 truth of a logical sentence consisting…

Logic in Computer Science · Computer Science 2007-05-23 Hubie Chen

The constraint satisfaction problem (CSP) involves deciding, given a set of variables and a set of constraints on the variables, whether or not there is an assignment to the variables satisfying all of the constraints. One formulation of…

Computational Complexity · Computer Science 2017-01-09 Hubie Chen , Benoit Larose

Raghavendra (STOC 2008) gave an elegant and surprising result: if Khot's Unique Games Conjecture (STOC 2002) is true, then for every constraint satisfaction problem (CSP), the best approximation ratio is attained by a certain simple…

Data Structures and Algorithms · Computer Science 2010-11-01 Yuichi Yoshida

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 prove a complexity dichotomy theorem for all non-negative weighted counting Constraint Satisfaction Problems (CSP). This caps a long series of important results on counting problems including unweighted and weighted graph homomorphisms…

Computational Complexity · Computer Science 2010-12-30 Jin-Yi Cai , Xi Chen , Pinyan Lu

In this paper we study the computational complexity of the (extended) minimum cost homomorphism problem (Min-Cost-Hom) as a function of a constraint language, i.e. a set of constraint relations and cost functions that are allowed to appear…

Computational Complexity · Computer Science 2013-10-01 Hannes Uppman

Vertex Subset Problems (VSPs) are a class of combinatorial optimization problems on graphs where the goal is to find a subset of vertices satisfying a predefined condition. Two prominent approaches for solving VSPs are dynamic programming…

Data Structures and Algorithms · Computer Science 2026-01-14 Mateus de Oliveira Oliveira , Wim Van den Broeck