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In this paper, we study the possibility of designing non-trivial random CSP models by exploiting the intrinsic connection between structures and typical-case hardness. We show that constraint consistency, a notion that has been developed to…

Artificial Intelligence · Computer Science 2011-10-12 J. Culberson , Y. Gao

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

We define and study a statistical mechanics ensemble that characterizes connected solutions in constraint satisfaction problems (CSPs). Built around a well-known local entropy bias, it allows us to better identify hardness transitions in…

Disordered Systems and Neural Networks · Physics 2026-04-17 Damien Barbier

Phase transitions in combinatorial problems have recently been shown to be useful in locating "hard" instances of combinatorial problems. The connection between computational complexity and the existence of phase transitions has been…

Computational Complexity · Computer Science 2016-11-17 Gabriel Istrate

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

Random instances of constraint satisfaction problems such as k-SAT provide challenging benchmarks. If there are m constraints over n variables there is typically a large range of densities r=m/n where solutions are known to exist with…

Discrete Mathematics · Computer Science 2009-11-13 Amin Coja-Oghlan

This thesis investigates the extent to which the optimal value of a constraint satisfaction problem (CSP) can be approximated by some sentence of fixed point logic with counting (FPC). It is known that, assuming $\mathsf{P} \neq…

Logic in Computer Science · Computer Science 2020-08-10 Jamie Tucker-Foltz

In this work, we focus on the Partial Constraint Satisfaction Problem (PCSP) over control-flow graphs (CFGs) of programs. PCSP serves as a generalization of the well-known Constraint Satisfaction Problem (CSP). In the CSP framework, we…

Computation and Language · Computer Science 2026-02-04 Xuran Cai , Amir Goharshady

Raghavendra (STOC 2008) gave an elegant and surprising result: if Khot's Unique Games Conjecture (STOC 2002) is true, then for every constraint satisfaction problem (CSP), the best approximation ratio is attained by a certain simple…

Data Structures and Algorithms · Computer Science 2010-11-01 Yuichi Yoshida

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

The degree of a CSP instance is the maximum number of times that a variable may appear in the scope of constraints. We consider the approximate counting problem for Boolean CSPs with bounded-degree instances, for constraint languages…

Computational Complexity · Computer Science 2010-02-03 Martin E. Dyer , Leslie Ann Goldberg , Markus Jalsenius , David Richerby

Constraint Satisfaction Problem (CSP) is a framework for modeling and solving a variety of real-world problems. Once the problem is expressed as a finite set of constraints, the goal is to find the variables' values satisfying them. Even…

Discrete Mathematics · Computer Science 2019-05-23 Rachid Oucheikh , Ismail Berrada , Outman El Hichami

Constraint satisfaction problems (or CSPs) have been extensively studied in, for instance, artificial intelligence, database theory, graph theory, and statistical physics. From a practical viewpoint, it is beneficial to approximately solve…

Computational Complexity · Computer Science 2012-10-17 Tomoyuki Yamakami

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 finite domain to the variables so…

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

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

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

The degree of a CSP instance is the maximum number of times that any variable appears in the scopes of constraints. We consider the approximate counting problem for Boolean CSP with bounded-degree instances, for constraint languages…

Computational Complexity · Computer Science 2011-09-19 Martin Dyer , Leslie Ann Goldberg , Markus Jalsenius , David Richerby

In this paper, we try to further demonstrate that the models of random CSP instances proposed by [Xu and Li, 2000; 2003] are of theoretical and practical interest. Indeed, these models, called RB and RD, present several nice features.…

Artificial Intelligence · Computer Science 2016-08-31 Ke Xu , Frederic Boussemart , Fred Hemery , Christophe Lecoutre

The Constraint Satisfaction Problem (CSP) is a central and generic computational problem which provides a common framework for many theoretical and practical applications. A central line of research is concerned with the identification of…

Data Structures and Algorithms · Computer Science 2015-07-21 Robert Ganian , M. S. Ramanujan , Stefan Szeider

We give a trichotomy theorem for the complexity of approximately counting the number of satisfying assignments of a Boolean CSP instance. Such problems are parameterised by a constraint language specifying the relations that may be used in…

Computational Complexity · Computer Science 2009-07-23 Martin Dyer , Leslie Ann Goldberg , Mark Jerrum