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The Promise Constraint Satisfaction Problem (PCSP for short) is a generalization of the well-studied Constraint Satisfaction Problem (CSP). The PCSP has its roots in such classic problems as the Approximate Graph Coloring and the…

Computational Complexity · Computer Science 2025-12-08 Arash Beikmohammadi , Andrei A. Bulatov

The constraint satisfaction problem (CSP) on a relational structure B is to decide, given a set of constraints on variables where the relations come from B, whether or not there is a assignment to the variables satisfying all of the…

Logic in Computer Science · Computer Science 2014-06-03 Hubie Chen

We study the optimization version of constraint satisfaction problems (Max-CSPs) in the framework of parameterized complexity; the goal is to compute the maximum fraction of constraints that can be satisfied simultaneously. In standard…

Computational Complexity · Computer Science 2018-04-24 Holger Dell , Eun Jung Kim , Michael Lampis , Valia Mitsou , Tobias Mömke

Quadratically constrained quadratic programs (QCQPs) are an expressive family of optimization problems that occur naturally in many applications. It is often of interest to seek out sparse solutions, where many of the entries of the…

Optimization and Control · Mathematics 2022-10-03 Kevin Shu

Constraint satisfaction problems (CSPs) are about finding values of variables that satisfy the given constraints. We show that Transformer extended with recurrence is a viable approach to learning to solve CSPs in an end-to-end manner,…

Artificial Intelligence · Computer Science 2023-07-12 Zhun Yang , Adam Ishay , Joohyung Lee

We address a specific but recurring problem related to sampled linear systems. In particular, we provide a numerical method for the rigorous verification of constraint satisfaction for linear continuous-time systems between sampling…

Optimization and Control · Mathematics 2016-03-30 Moritz Schulze Darup

Query evaluation over probabilistic databases is known to be intractable in many cases, even in data complexity, i.e., when the query is fixed. Although some restrictions of the queries [19] and instances [4] have been proposed to lower the…

Databases · Computer Science 2019-08-28 Antoine Amarilli , Mikaël Monet , Pierre Senellart

The model of Dynamic Meta-Constraints has special activity constraints which can activate other constraints. It also has meta-constraints which range over other constraints. An algorithm is presented in which constraints can be assigned one…

Programming Languages · Computer Science 2007-05-23 Janet van der Linden

Answer Set Programming with Quantifiers (ASP(Q)) has been introduced to provide a natural extension of ASP modeling to problems in the polynomial hierarchy (PH). However, ASP(Q) lacks a method for encoding in an elegant and compact way…

Artificial Intelligence · Computer Science 2025-01-22 Giuseppe Mazzotta , Francesco Ricca , Mirek Truszczynski

The fixed template Promise Constraint Satisfaction Problem (PCSP) is a recently proposed significant generalization of the fixed template CSP, which includes approximation variants of satisfiability and graph coloring problems. All the…

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

Functional constraints and bi-functional constraints are an important constraint class in Constraint Programming (CP) systems, in particular for Constraint Logic Programming (CLP) systems. CP systems with finite domain constraints usually…

Artificial Intelligence · Computer Science 2010-06-17 Yuanlin Zhang , Roland H. C. Yap

Quantified Integer Programming (QIP) bridges multiple domains by extending Quantified Boolean Formulas (QBF) to incorporate general integer variables and linear constraints while also generalizing Integer Programming through variable…

Discrete Mathematics · Computer Science 2025-06-06 Michael Hartisch , Leroy Chew

We study special systems with infinitely many degrees of freedom with regard to dynamical evolution and fulfillment of constraint conditions. Attention is focused on establishing a meaningful functional framework, and for that purpose,…

Quantum Physics · Physics 2007-05-23 John R. Klauder

This paper studies a class of probabilistic models on graphs, where edge variables depend on incident node variables through a fixed probability kernel. The class includes planted con- straint satisfaction problems (CSPs), as well as more…

Probability · Mathematics 2013-07-01 Emmanuel Abbe , Andrea Montanari

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

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

Quadratically constrained quadratic programming (QCQP) has long been recognized as a computationally challenging problem, particularly in large-scale or high-dimensional settings where solving it directly becomes intractable. The complexity…

Optimization and Control · Mathematics 2025-10-09 Shuai Li , Shenglong Zhou , Ziyan Luo

The constraint satisfaction problem (CSP) of a first-order theory T is the computational problem of deciding whether a given conjunction of atomic formulas is satisfiable in some model of T. We study the computational complexity of CSP$(T_1…

Logic · Mathematics 2023-06-22 Manuel Bodirsky , Johannes Greiner , Jakub Rydval

We study the complexity of the Distributed Constraint Satisfaction Problem (DCSP) on a synchronous, anonymous network from a theoretical standpoint. In this setting, variables and constraints are controlled by agents which communicate with…

Data Structures and Algorithms · Computer Science 2021-01-25 Silvia Butti , Victor Dalmau

The Promise Constraint Satisfaction Problem (PCSP) is a recently introduced vast generalization of the Constraint Satisfaction Problem (CSP). We investigate the computational complexity of a class of PCSPs beyond the most studied cases -…

Computational Complexity · Computer Science 2020-10-12 Libor Barto , Diego Battistelli , Kevin M. Berg