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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

We define a class of algebras, the semilattices of Mal'cev blocks (for short, SMB algebras). In a nutshell, these algebras are semilattices in which each element gets blown up into a Mal'cev algebra. We publish for the first time our old…

Computational Complexity · Computer Science 2026-04-08 Petar Marković , Miklós Maróti , Ralph McKenzie , Aleksandar Prokić

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

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

We study methods for transforming valued constraint satisfaction problems (VCSPs) to binary VCSPs. First, we show that the standard dual encoding preserves many aspects of the algebraic properties that capture the computational complexity…

Discrete Mathematics · Computer Science 2017-10-31 David A. Cohen , Martin C. Cooper , Peter G. Jeavons , Andrei Krokhin , Robert Powell , Stanislav Zivny

We produce a class of $\omega$-categorical structures with finite signature by applying a model-theoretic construction -- a refinement of the Hrushosvki-encoding -- to $\omega$-categorical structures in a possibly infinite signature. We…

Logic in Computer Science · Computer Science 2021-01-12 Pierre Gillibert , Julius Jonušas , Michael Kompatscher , Antoine Mottet , Michael Pinsker

In the last two decades the study of random instances of constraint satisfaction problems (CSPs) has flourished across several disciplines, including computer science, mathematics and physics. The diversity of the developed methods, on the…

Combinatorics · Mathematics 2025-07-02 Konstantinos Panagiotou , Matija Pasch

Many real world problems naturally appear as constraints satisfaction problems (CSP), for which very efficient algorithms are known. Most of these involve the combination of two techniques: some direct propagation of constraints between…

Artificial Intelligence · Computer Science 2013-04-12 Denis Berthier

This paper describes an extension to the constraint satisfaction problem (CSP) called MUSE CSP (MUltiply SEgmented Constraint Satisfaction Problem). This extension is especially useful for those problems which segment into multiple sets of…

Artificial Intelligence · Computer Science 2014-11-17 R. A Helzerman , M. P. Harper

In this paper, we define the reoptimization variant of the closest substring problem (CSP) under sequence addition. We show that, even with the additional information we have about the problem instance, the problem of finding a closest…

Data Structures and Algorithms · Computer Science 2016-03-09 Jeffrey Aborot , Henry Adorna , Jhoirene Clemente

This thesis investigates the central role of homomorphism problems (structure-preserving maps) in two complementary domains: database querying over finite, graph-shaped data, and constraint solving over (potentially infinite) structures.…

Logic in Computer Science · Computer Science 2025-10-10 Rémi Morvan

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

We study the Constraint Satisfaction Problem CSP(A), where A is first-order definable in (Z;+,1) and contains +. We prove such problems are either in P or NP-complete.

Computational Complexity · Computer Science 2018-07-04 Manuel Bodirsky , Barnaby Martin , Marcello Mamino , Antoine Mottet

We connect the mixing behaviour of random walks over a graph to the power of the local-consistency algorithm for the solution of the corresponding constraint satisfaction problem (CSP). We extend this connection to arbitrary CSPs and their…

Computational Complexity · Computer Science 2024-11-01 Lorenzo Ciardo , Stanislav Živný

The promise constraint satisfaction problem (PCSP) is a recently introduced vast generalisation of the constraint satisfaction problem (CSP) that captures approximability of satisfiable instances. A PCSP instance comes with two forms of…

Computational Complexity · Computer Science 2023-01-31 Alex Brandts , Stanislav Živný

Type systems usually characterize the shape of values but not their free variables. However, many desirable safety properties could be guaranteed if one knew the free variables captured by values. We describe CCsubBox, a calculus where such…

Programming Languages · Computer Science 2022-07-25 Martin Odersky , Aleksander Boruch-Gruszecki , Edward Lee , Jonathan Brachthäuser , Ondřej Lhoták

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

The aim of these notes is to present an accessible overview of some topics in classical algebraic geometry which have applications to aspects of discrete integrable systems. Precisely, we focus on surface theory on the algebraic geometry…

Algebraic Geometry · Mathematics 2025-10-15 Gessica Alecci , Michele Graffeo , Alexander Stokes

We propose a new algorithm for Promise Constraint Satisfaction Problems PCSPs). It is a combination of the $\textbf{C}$onstraint Basic $\textbf{L}$P relaxation and the $\textbf{A}$ffine I$\textbf{P}$ relaxation (CLAP). We give a…

Computational Complexity · Computer Science 2023-01-31 Lorenzo Ciardo , Stanislav Živný

Driven by a wide range of applications, many principal subspace estimation problems have been studied individually under different structural constraints. This paper presents a unified framework for the statistical analysis of a general…

Statistics Theory · Mathematics 2020-11-17 T. Tony Cai , Hongzhe Li , Rong Ma