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A continuous constraint satisfaction problem (CCSP) is a constraint satisfaction problem (CSP) with an interval domain $U \subset \mathbb{R}$. We engage in a systematic study to classify CCSPs that are complete of the Existential Theory of…

Computational Complexity · Computer Science 2024-08-07 Tillmann Miltzow , Reinier F. Schmiermann

We prove a complexity dichotomy theorem for symmetric complex-weighted Boolean #CSP when the constraint graph of the input must be planar. The problems that are #P-hard over general graphs but tractable over planar graphs are precisely…

Computational Complexity · Computer Science 2013-08-07 Heng Guo , Tyson Williams

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

We develop a unified framework to characterize the power of higher-level algorithms for the constraint satisfaction problem (CSP), such as $k$-consistency, the Sherali-Adams LP hierarchy, and the affine IP hierarchy. As a result,…

Logic in Computer Science · Computer Science 2026-04-09 Libor Barto , Maximilian Hadek , Dmitriy Zhuk

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

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

The paper presents an algebraic framework for optimization problems expressible as Valued Constraint Satisfaction Problems. Our results generalize the algebraic framework for the decision version (CSPs) provided by Bulatov et al. [SICOMP…

Computational Complexity · Computer Science 2016-05-03 Marcin Kozik , Joanna Ochremiak

A PCSP is a combination of two CSPs defined by two similar templates; the computational question is to distinguish a YES instance of the first one from a NO instance of the second. The computational complexity of many PCSPs remains unknown.…

Computational Complexity · Computer Science 2019-04-30 Miron Ficak , Marcin Kozik , Miroslav Olsak , Szymon Stankiewicz

What makes a computational problem easy (e.g., in P, that is, solvable in polynomial time) or hard (e.g., NP-hard)? This fundamental question now has a satisfactory answer for a quite broad class of computational problems, so called…

Computational Complexity · Computer Science 2019-09-12 Libor Barto

We investigate the Constraint Satisfaction Problem (CSP) over templates with a group structure, and algorithms solving CSP that are equivariant, i.e. invariant under a natural group action induced by a template. Our main result is a method…

Logic in Computer Science · Computer Science 2016-04-06 Sławomir Lasota

Feder and Vardi showed that the class Monotone Monadic SNP without inequality (MMSNP) has a P vs NP-complete dichotomy if and only if such a dichotomy holds for finite-domain Constraint Satisfaction Problems (CSPs). Moreover, they showed…

Computational Complexity · Computer Science 2025-11-05 Alexey Barsukov , Florent R. Madelaine

Promise Constraint Satisfaction Problems (PCSPs) are a generalization of Constraint Satisfaction Problems (CSPs) where each predicate has a strong and a weak form and given a CSP instance, the objective is to distinguish if the strong form…

Computational Complexity · Computer Science 2023-06-22 Joshua Brakensiek , Venkatesan Guruswami , Sai Sandeep

A finite constraint language $\mathscr{R}$ is a finite set of relations over some finite domain $A$. We show that intractability of the constraint satisfaction problem $\operatorname{CSP}(\mathscr{R})$ can, in all known cases, be replaced…

Computational Complexity · Computer Science 2017-05-02 Lucy Ham , Marcel Jackson

We adapt tools from the algebraic approach to constraint satisfaction problems to answer descriptive set theoretic questions about Borel CSPs. We show that if a structure $\mathcal D$ does not have a Taylor polymorphism, then the…

Logic · Mathematics 2022-04-01 Riley Thornton

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

The 1-in-3 and Not-All-Equal satisfiability problems for Boolean CNF formulas are two well-known NP-hard problems. In contrast, the promise 1-in-3 vs. Not-All-Equal problem can be solved in polynomial time. In the present work, we…

Computational Complexity · Computer Science 2025-05-09 Lorenzo Ciardo , Marcin Kozik , Andrei Krokhin , Tamio-Vesa Nakajima , Stanislav Živný

We study the design of stochastic local search methods to prove unsatisfiability of a constraint satisfaction problem (CSP). For a binary CSP, such methods have been designed using the microstructure of the CSP. Here, we develop a method to…

Artificial Intelligence · Computer Science 2020-02-11 Daya Gaur , Muhammad Khan

We study the (non-uniform) quantified constraint satisfaction problem QCSP(H) as H ranges over partially reflexive forests. We obtain a complexity-theoretic dichotomy: QCSP(H) is either in NL or is NP-hard. The separating condition is…

Computational Complexity · Computer Science 2011-04-01 Barnaby Martin

We develop the novel machinery of smooth approximations, and apply it to confirm the CSP dichotomy conjecture for first-order reducts of the random tournament, various homogeneous graphs including the random graph, and for expansions of the…

Logic in Computer Science · Computer Science 2021-06-08 Antoine Mottet , Michael Pinsker

An elegant characterization of the complexity of constraint satisfaction problems has emerged in the form of the the algebraic dichotomy conjecture of [BKJ00]. Roughly speaking, the characterization asserts that a CSP {\Lambda} is tractable…

Computational Complexity · Computer Science 2015-01-08 Jonah Brown-Cohen , Prasad Raghavendra