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Related papers: On the induced problem for fixed-template CSPs

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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

Promise Constraint Satisfaction Problems (PCSP) were proposed recently by Brakensiek and Guruswami arXiv:1704.01937 as a framework to study approximations for Constraint Satisfaction Problems (CSP). Informally a PCSP asks to distinguish…

Computational Complexity · Computer Science 2020-03-18 Guofeng Deng , Ezzeddine El Sai , Trevor Manders , Peter Mayr , Poramate Nakkirt , Athena Sparks

Constraint Satisfaction Problems (CSPs) form a broad class of combinatorial problems, which can be formulated as homomorphism problems between relational structures. The CSP dichotomy theorem classifies all such problems over finite domains…

Logic · Mathematics 2025-08-04 Azza Gaysin

The universal-algebraic approach has proved a powerful tool in the study of the complexity of CSPs. This approach has previously been applied to the study of CSPs with finite or (infinite) omega-categorical templates, and relies on two…

Logic in Computer Science · Computer Science 2015-07-01 Barnaby Martin , Manuel Bodirsky , Martin Hils

The Constraint Satisfaction Problem (CSP) and its counting counterpart appears under different guises in many areas of mathematics, computer science, and elsewhere. Its structural and algorithmic properties have demonstrated to play a…

Combinatorics · Mathematics 2020-07-15 Raimundo Briceño , Andrei Bulatov , Victor Dalmau , Benoit Larose

A Datalog program solves a constraint satisfaction problem (CSP) if and only if it derives the goal predicate precisely on the unsatisfiable instances of the CSP. There are three Datalog fragments that are particularly important for…

Rings and Algebras · Mathematics 2026-05-07 Manuel Bodirsky , Florian Starke

Although the CSP (constraint satisfaction problem) is NP-complete, even in the case when all constraints are binary, certain classes of instances are tractable. We study classes of instances defined by excluding subproblems. This approach…

Artificial Intelligence · Computer Science 2012-01-19 Martin C. Cooper , Guillaume Escamocher

The study of phase transition phenomenon of NP complete problems plays an important role in understanding the nature of hard problems. In this paper, we follow this line of research by considering the problem of counting solutions of…

Artificial Intelligence · Computer Science 2011-02-25 Minghao Yin , Ping Huang

We define and study a statistical mechanics ensemble that characterizes connected solutions in constraint satisfaction problems (CSPs). Built around a well-known local entropy bias, it allows us to better identify hardness transitions in…

Disordered Systems and Neural Networks · Physics 2026-04-17 Damien Barbier

Finding actions that satisfy the constraints imposed by both external inputs and internal representations is central to decision making. We demonstrate that some important classes of constraint satisfaction problems (CSPs) can be solved by…

Neurons and Cognition · Quantitative Biology 2018-01-16 Ueli Rutishauser , Jean-Jacques Slotine , Rodney J. Douglas

This paper focuses on the branching process for solving any constraint satisfaction problem (CSP). A parametrised schema is proposed that (with suitable instantiations of the parameters) can solve CSP's on both finite and infinite domains.…

Programming Languages · Computer Science 2007-05-23 Antonio J. Fernandez , Patricia M. Hill

We describe simple algebraic and combinatorial characterisations of finite relational core structures admitting finitely many obstructions. As a consequence, we show that it is decidable to determine whether a constraint satisfaction…

Logic in Computer Science · Computer Science 2015-07-01 Benoit Larose , Cynthia Loten , Claude Tardif

The quantified constraint satisfaction problem $\mathrm{QCSP}(\mathcal{A})$ is the problem to decide whether a positive Horn sentence, involving nothing more than the two quantifiers and conjunction, is true on some fixed structure…

Logic in Computer Science · Computer Science 2017-01-11 Barnaby D. Martin , Hubie Chen , Florent R. Madelaine

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 present a Transformer-based framework for Constraint Satisfaction Problems (CSPs). CSPs find use in many applications and thus accelerating their solution with machine learning is of wide interest. Most existing approaches rely on…

Machine Learning · Computer Science 2025-06-11 Yudong W. Xu , Wenhao Li , Scott Sanner , Elias B. Khalil

A computational problem exhibits a "gap property" when there is no tractable boundary between two disjoint sets of instances. We establish a Gap Trichotomy Theorem for a family of constraint problem variants, completely classifying the…

Computational Complexity · Computer Science 2017-03-28 Lucy Ham

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

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 establish a framework that allows us to transfer results between some constraint satisfaction problems with infinite templates and promise constraint satisfaction problems. On the one hand, we obtain new algebraic results for…

Logic in Computer Science · Computer Science 2025-03-21 Antoine Mottet

We study the complexity of the parameterised counting constraint satisfaction problem: given a set of constraints over a set of variables and a positive integer $k$, how many ways are there to assign $k$ variables to 1 (and the others to 0)…

Computational Complexity · Computer Science 2026-04-29 Panagiotis Aivasiliotis , Andreas Göbel , Marc Roth