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A unary constraint (on the Boolean domain) is a function from {0,1} to the set of real numbers. A free use of auxiliary unary constraints given besides input instances has proven to be useful in establishing a complete classification of the…

Computational Complexity · Computer Science 2015-08-25 Tomoyuki Yamakami

Schaefer's dichotomy theorem [Schaefer, STOC'78] states that a boolean constraint satisfaction problem (CSP) is polynomial-time solvable if one of six given conditions holds for every type of constraint allowed in its instances. Otherwise,…

Computational Complexity · Computer Science 2023-07-10 Patrick Schnider , Simon Weber

We study the computational complexity of counting constraint satisfaction problems (#CSPs) whose constraints assign complex numbers to Boolean inputs when the corresponding constraint hypergraphs are acyclic. These problems are called…

Computational Complexity · Computer Science 2024-03-15 Tomoyuki Yamakami

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 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

An active topic in the study of random constraint satisfaction problems (CSPs) is the geometry of the space of satisfying or almost satisfying assignments as the function of the density, for which a precise landscape of predictions has been…

Data Structures and Algorithms · Computer Science 2021-06-25 Jun-Ting Hsieh , Sidhanth Mohanty , Jeff Xu

We study the complexity of local search for the Boolean constraint satisfaction problem (CSP), in the following form: given a CSP instance, that is, a collection of constraints, and a solution to it, the question is whether there is a…

Data Structures and Algorithms · Computer Science 2017-11-13 Andrei Krokhin , Dániel Marx

A Boolean constraint satisfaction instance is a conjunction of constraint applications, where the allowed constraints are drawn from a fixed set B of Boolean functions. We consider the problem of determining whether two given constraint…

Computational Complexity · Computer Science 2007-05-23 E. Boehler , E. Hemaspaandra , Steffen Reith , Heribert Vollmer

The constraint satisfaction problem (CSP) can be formulated as a homomorphism problem between relational structures: given a structure $\mathcal{A}$, for any structure $\mathcal{X}$, whether there exists a homomorphism from $\mathcal{X}$ to…

Logic · Mathematics 2024-03-12 Azza Gaysin

An instance of the Valued Constraint Satisfaction Problem (VCSP) is given by a finite set of variables, a finite domain of labels, and a sum of functions, each function depending on a subset of the variables. Each function can take finite…

Computational Complexity · Computer Science 2017-02-14 Vladimir Kolmogorov , Andrei Krokhin , Michal Rolinek

We initiate the study of constraint satisfaction problems (CSPs) in the presence of counting quantifiers, which may be seen as variants of CSPs in the mould of quantified CSPs (QCSPs). We show that a single counting quantifier strictly…

Computational Complexity · Computer Science 2011-12-14 Florent Madelaine , Barnaby Martin , Juraj Stacho

The Constraint Satisfaction Problem (CSP) is ubiquitous in various areas of mathematics and computer science. Many of its variations have been studied including the Counting CSP, where the goal is to find the number of solutions to a CSP…

Computational Complexity · Computer Science 2025-01-24 Amirhossein Kazeminia , Andrei A. Bulatov

We define and explore a notion of unique prime factorization for constraint functions, and use this as a new tool to prove a complexity classification for counting weighted Eulerian orientation problems with arrow reversal symmetry (ARS).…

Computational Complexity · Computer Science 2021-04-13 Jin-Yi Cai , Zhiguo Fu , Shuai Shao

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

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

Many natural combinatorial problems can be expressed as constraint satisfaction problems. This class of problems is known to be NP-complete in general, but certain restrictions on the form of the constraints can ensure tractability. The…

Computational Complexity · Computer Science 2020-10-05 Dmitriy Zhuk

The study of the complexity of the constraint satisfaction problem (CSP), centred around the Feder-Vardi Dichotomy Conjecture, has been very prominent in the last two decades. After a long concerted effort and many partial results, the…

Computational Complexity · Computer Science 2022-08-30 Andrei Krokhin , Jakub Opršal

We study parameterized Constraint Satisfaction Problem for infinite constraint languages. The parameters that we study are weight of the satisfying assignment, number of constraints, maximum number of occurrences of a variable in the…

Computational Complexity · Computer Science 2017-08-10 Ruhollah Majdoddin

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

A constraint satisfaction problem (CSP) is a computational problem where the input consists of a finite set of variables and a finite set of constraints, and where the task is to decide whether there exists a satisfying assignment of values…

Computational Complexity · Computer Science 2019-04-23 Manuel Bodirsky