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PyCSP$^3$ provides a productive way to build constraint models for solving combinatorial constrained problems and export them to XCSP$^3$, preserving a complete separation between modeling and solving. However, it lacks native support for…

Artificial Intelligence · Computer Science 2026-05-26 Sohaib Afifi

We propose a major revision of the format XCSP 2.1, called XCSP3, to build integrated representations of combinatorial constrained problems. This new format is able to deal with mono/multi optimization, many types of variables, cost…

Artificial Intelligence · Computer Science 2024-08-30 Frederic Boussemart , Christophe Lecoutre , Gilles Audemard , Cédric Piette

In this document, we introduce XCSP3-core, a subset of XCSP3 that allows us to represent constraint satisfaction/optimization problems. The interest of XCSP3-core is multiple: (i) focusing on the most popular frameworks (CSP and COP) and…

Artificial Intelligence · Computer Science 2024-08-30 Frédéric Boussemart , Christophe Lecoutre , Gilles Audemard , Cédric Piette

Constraint Programming (CP) is a useful technology for modeling and solving combinatorial constrained problems. On the one hand, on can use a library like PyCSP3 for easily modeling problems arising in various application fields (e.g.,…

Artificial Intelligence · Computer Science 2024-09-04 Christophe Lecoutre

A wide range of problems can be modelled as constraint satisfaction problems (CSPs), that is, a set of constraints that must be satisfied simultaneously. Constraints can either be represented extensionally, by explicitly listing allowed…

Artificial Intelligence · Computer Science 2015-02-10 Evgenij Thorstensen

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

The quantified constraint satisfaction problem (QCSP) is a powerful framework for modelling computational problems. The general intractability of the QCSP has motivated the pursuit of restricted cases that avoid its maximal complexity. In…

Computational Complexity · Computer Science 2007-05-23 Hubie Chen

This paper presents PyJobShop, an open-source Python library for solving scheduling problems with constraint programming. PyJobShop provides an easy-to-use modeling interface that supports a wide variety of scheduling problems, including…

Optimization and Control · Mathematics 2025-02-20 Leon Lan , Joost Berkhout

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

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

The constraint satisfaction problem (CSP) is a computational problem that includes a range of important problems in computer science. We point out that fundamental concepts of the CSP, such as the solution set of an instance and…

Category Theory · Mathematics 2022-11-04 Soichiro Fujii , Yuni Iwamasa , Kei Kimura

The constraint satisfaction probem (CSP) is a well-acknowledged framework in which many combinatorial search problems can be naturally formulated. The CSP may be viewed as the problem of deciding the truth of a logical sentence consisting…

Logic in Computer Science · Computer Science 2007-05-23 Hubie Chen

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

A wide range of problems can be modelled as constraint satisfaction problems (CSPs), that is, a set of constraints that must be satisfied simultaneously. Constraints can either be represented extensionally, by explicitly listing allowed…

Artificial Intelligence · Computer Science 2013-07-09 Evgenij Thorstensen

Constraint satisfaction problems (CSPs) are a class of problems that are ubiquitous in science and engineering. It features a collection of constraints specified over subsets of variables. A CSP can be solved either directly or by reducing…

Computational Physics · Physics 2025-01-03 Xuanzhao Gao , Xiaofeng Li , Jinguo Liu

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

Feature model configuration can be supported on the basis of various types of reasoning approaches. Examples thereof are SAT solving, constraint solving, and answer set programming (ASP). Using these approaches requires technical expertise…

Artificial Intelligence · Computer Science 2023-08-15 Alexander Felfernig , Viet-Man Le , Sebastian Lubos

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 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

Discrete Combinatorial Problems (DCPs) are prevalent in industrial decision-making and optimisation. However, while constraint solving technologies for DCPs have advanced significantly, the core process of formalising them, namely…

Artificial Intelligence · Computer Science 2026-01-29 Kostis Michailidis , Dimos Tsouros , Tias Guns
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