English
Related papers

Related papers: Promise Constraint Satisfaction: Algebraic Structu…

200 papers

We study the complexity of valued constraint satisfaction problems (VCSP). A problem from VCSP is characterised by a \emph{constraint language}, a fixed set of cost functions over a finite domain. An instance of the problem is specified by…

Computational Complexity · Computer Science 2010-08-10 Vladimir Kolmogorov , Stanislav Zivny

This paper gives a dichotomy theorem for the complexity of computing the partition function of an instance of a weighted Boolean constraint satisfaction problem. The problem is parameterised by a finite set F of non-negative functions that…

Computational Complexity · Computer Science 2009-02-23 Martin Dyer , Leslie Ann Goldberg , Mark Jerrum

In this paper we study the approximability of (Finite-)Valued Constraint Satisfaction Problems (VCSPs) with a fixed finite constraint language {\Gamma} consisting of finitary functions on a fixed finite domain. An instance of VCSP is given…

Computational Complexity · Computer Science 2018-03-22 Victor Dalmau , Andrei Krokhin , Rajsekar Manokaran

We study minimum cost constraint satisfaction problems (MinCostCSP) through the algebraic lens. We show that for any constraint language $\Gamma$ which has the dual discriminator operation as a polymorphism, there exists a…

Data Structures and Algorithms · Computer Science 2025-07-14 Ian DeHaan , Neng Huang , Euiwoong Lee

Given a satisfiable instance of 1-in-3 SAT, it is NP-hard to find a satisfying assignment for it, but it may be possible to efficiently find a solution subject to a weaker (not necessarily Boolean) predicate than `1-in-3'. There is a…

Computational Complexity · Computer Science 2025-08-21 Andrei Krokhin , Danny Vagnozzi

A constraint satisfaction problem (CSP) is a problem of computing a homomorphism ${\bf R} \rightarrow {\bf \Gamma}$ between two relational structures. Analyzing its complexity has been a very fruitful research direction, especially for…

Computational Complexity · Computer Science 2017-08-29 Rustem Takhanov

Finite-domain constraint satisfaction problems are either solvable by Datalog, or not even expressible in fixed-point logic with counting. The border between the two regimes coincides with an important dichotomy in universal algebra; in…

Logic · Mathematics 2022-06-08 Manuel Bodirsky , Jakub Rydval

We prove complexity dichotomies for \#CSP problems (not necessarily symmetric) with Boolean domain and complex range on several typical minor-closed graph classes. These dichotomies give a complete characterization of the complexity of…

Computational Complexity · Computer Science 2025-04-03 Boning Meng , Yicheng Pan

The role of polymorphisms in determining the complexity of constraint satisfaction problems is well established. In this context we study the stability of CSP complexity and polymorphism properties under some basic graph theoretic…

Combinatorics · Mathematics 2016-07-22 Marcel Jackson , Tomasz Kowalski , Todd Niven

We give a complexity dichotomy theorem for the counting Constraint Satisfaction Problem (#CSP in short) with complex weights. To this end, we give three conditions for its tractability. Let F be any finite set of complex-valued functions,…

Computational Complexity · Computer Science 2015-03-19 Jin-Yi Cai , Xi Chen

Random instances of Constraint Satisfaction Problems (CSP's) appear to be hard for all known algorithms, when the number of constraints per variable lies in a certain interval. Contributing to the general understanding of the structure of…

Discrete Mathematics · Computer Science 2009-04-20 Andrea Montanari , Ricardo Restrepo , Prasad Tetali

The Feder-Vardi dichotomy conjecture for Constraint Satisfaction Problems (CSPs) with finite templates, confirmed independently by Bulatov and Zhuk, has an extension to certain well-behaved infinite templates due to Bodirsky and Pinsker…

Logic · Mathematics 2026-05-07 Michael Pinsker , Jakub Rydval , Moritz Schöbi , Christoph Spiess , Paul Winkler

Symmetric Datalog, a fragment of the logic programming language Datalog, is conjectured to capture all constraint satisfaction problems (CSP) in L. Therefore developing tools that help us understand whether or not a CSP can be defined in…

Computational Complexity · Computer Science 2013-12-18 Laszlo Egri

In a valued constraint satisfaction problem (VCSP), the goal is to find an assignment of labels to variables that minimizes a given sum of functions. Each function in the sum depends on a subset of variables, takes values which are rational…

Computational Complexity · Computer Science 2015-07-08 Robert Powell , Andrei Krokhin

Mermin and Peres showed that there are boolean constraint systems (BCSs) which are not satisfiable, but which are satisfiable with quantum observables. This has led to a burgeoning theory of quantum satisfiability for constraint systems,…

Quantum Physics · Physics 2025-01-16 Connor Paddock , William Slofstra

Constraint satisfaction problems (CSPs) are an important formal framework for the uniform treatment of various prominent AI tasks, e.g., coloring or scheduling problems. Solving CSPs is, in general, known to be NP-complete and…

Computational Complexity · Computer Science 2020-07-29 Hubie Chen , Georg Gottlob , Matthias Lanzinger , Reinhard Pichler

In a constraint satisfaction problem (CSP) the goal is to find an assignment of a given set of variables subject to specified constraints. A global cardinality constraint is an additional requirement that prescribes how many variables must…

Logic in Computer Science · Computer Science 2015-07-01 Andrei A. Bulatov , Daniel Marx

We study interactions between Skolem Arithmetic and certain classes of Constraint Satisfaction Problems (CSPs). We revisit results of Glass er et al. in the context of CSPs and settle the major open question from that paper, finding a…

Computational Complexity · Computer Science 2015-04-17 Christian Glasser , Peter Jonsson , Barnaby Martin

We show that the metaproblem for coset-generating polymorphisms is NP-complete, answering a question of Chen and Larose: given a finite structure, the computational question is whether this structure has a polymorphism of the form $(x,y,z)…

Computational Complexity · Computer Science 2026-05-12 Manuel Bodirsky , Armin Weiß

In this work, we focus on the Partial Constraint Satisfaction Problem (PCSP) over control-flow graphs (CFGs) of programs. PCSP serves as a generalization of the well-known Constraint Satisfaction Problem (CSP). In the CSP framework, we…

Computation and Language · Computer Science 2026-02-04 Xuran Cai , Amir Goharshady