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Related papers: Boolean PCSPs through the lens of Fourier Analysis

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In the maximum constraint satisfaction problem (Max CSP), one is given a finite collection of (possibly weighted) constraints on overlapping sets of variables, and the goal is to assign values from a given domain to the variables so as to…

Computational Complexity · Computer Science 2007-05-23 Peter Jonsson , Mikael Klasson , Andrei Krokhin

We introduce a problem class we call Polynomial Constraint Satisfaction Problems, or PCSP. Where the usual CSPs from computer science and optimization have real-valued score functions, and partition functions from physics have monomials,…

Discrete Mathematics · Computer Science 2010-01-14 Alexander D. Scott , Gregory B. Sorkin

In this paper, we continue the study of robust satisfiability of promise CSPs (PCSPs), initiated in (Brakensiek, Guruswami, Sandeep, STOC 2023 / Discrete Analysis 2025), and obtain the following results: For the PCSP 1-in-3-SAT vs NAE-SAT…

Data Structures and Algorithms · Computer Science 2026-02-12 Joshua Brakensiek , Lorenzo Ciardo , Venkatesan Guruswami , Aaron Potechin , Stanislav Živný

The complexity of the promise constraint satisfaction problem $\operatorname{PCSP}(\mathbf{A},\mathbf{B})$ is largely unknown, even for symmetric $\mathbf{A}$ and $\mathbf{B}$, except for the case when $\mathbf{A}$ and $\mathbf{B}$ are…

Computational Complexity · Computer Science 2024-08-19 Tamio-Vesa Nakajima , Stanislav Živný

Many AI synthesis problems such as planning or scheduling may be modelized as constraint satisfaction problems (CSP). A CSP is typically defined as the problem of finding any consistent labeling for a fixed set of variables satisfying all…

Artificial Intelligence · Computer Science 2013-03-25 Thomas Schiex

We study a model of constraint satisfaction problems geared towards instances with few variables but with domain of unbounded size (udCSP). Our model is inspired by recent work on FPT algorithms for MinCSP where frequently both upper and…

Data Structures and Algorithms · Computer Science 2025-08-25 Peter Jonsson , Victor Lagerkvist , Jorke M. de Vlas , Magnus Wahlström

The Constraint-satisfaction problem (CSP) is fundamental in mathematics, physics, and theoretical computer science. Continuous local search (CLS) solvers, as recent advancements, can achieve highly competitive results on certain classes of…

Artificial Intelligence · Computer Science 2026-01-29 Yunuo Cen , Zixuan Wang , Jintao Zhang , Zhiwei Zhang , Xuanyao Fong

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 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

Holant problem is a general framework to study the computational complexity of counting problems. We prove a complexity dichotomy theorem for Holant problems over Boolean domain with non-negative weights. It is the first complete Holant…

Computational Complexity · Computer Science 2017-02-21 Jiabao Lin , Hanpin Wang

An important question in the study of constraint satisfaction problems (CSP) is understanding how the graph or hypergraph describing the incidence structure of the constraints influences the complexity of the problem. For binary CSP…

Data Structures and Algorithms · Computer Science 2015-03-13 Dániel Marx

Following the success of the so-called algebraic approach to the study of decision constraint satisfaction problems (CSPs), exact optimization of valued CSPs, and most recently promise CSPs, we propose an algebraic framework for valued…

Computational Complexity · Computer Science 2025-02-05 Libor Barto , Silvia Butti , Alexandr Kazda , Caterina Viola , Stanislav Živný

Schaefer introduced a framework for generalized satisfiability problems on the Boolean domain and characterized the computational complexity of such problems. We investigate an algebraization of Schaefer's framework in which the Fourier…

Logic in Computer Science · Computer Science 2017-04-07 Albert Atserias , Phokion G. Kolaitis , Simone Severini

A subset of Q^n is called semilinear (or piecewise linear) if it is Boolean combination of linear half-spaces. We study the computational complexity of the constraint satisfaction problem (CSP) over the rationals when all the constraints…

Computational Complexity · Computer Science 2018-10-30 Manuel Bodirsky , Marcello Mamino

The constraint satisfaction problem (CSP) is a central generic problem in computer science and artificial intelligence: it provides a common framework for many theoretical problems as well as for many real-life applications. Soft constraint…

Artificial Intelligence · Computer Science 2011-04-25 Martin C. Cooper , Stanislav Zivny

Polynomial threshold functions (PTFs) are an important low-complexity class of Boolean functions, with strong connections to learning theory and approximation theory. Recent work on learning and testing PTFs has exploited structural and…

Computational Complexity · Computer Science 2026-04-28 Fan Chang , Joseph Slote , Alexander Volberg , Haonan Zhang

Constraint satisfaction problem (CSP) is a well-studied combinatorial search problem, in which we are asked to find an assignment of values to given variables so as to satisfy all of given constraints. We study a reconfiguration variant of…

Data Structures and Algorithms · Computer Science 2018-12-31 Tatsuhiko Hatanaka , Takehiro Ito , Xiao Zhou

We study the power of the bounded-width consistency algorithm in the context of the fixed-template Promise Constraint Satisfaction Problem (PCSP). Our main technical finding is that the template of every PCSP that is solvable in bounded…

Computational Complexity · Computer Science 2021-07-14 Albert Atserias , Víctor Dalmau

Valued constraint satisfaction problems (VCSPs) are discrete optimisation problems with a $(\mathbb{Q}\cup\{\infty\})$-valued objective function given as a sum of fixed-arity functions. In Boolean surjective VCSPs, variables take on labels…

Computational Complexity · Computer Science 2020-05-15 Peter Fulla , Hannes Uppman , Stanislav Zivny

We continue the investigation of polynomial-time sparsification for NP-complete Boolean Constraint Satisfaction Problems (CSPs). The goal in sparsification is to reduce the number of constraints in a problem instance without changing the…

Computational Complexity · Computer Science 2018-09-18 Hubie Chen , Bart M. P. Jansen , Astrid Pieterse