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Random constraint satisfaction problems (CSPs) have been widely studied both in AI and complexity theory. Empirically and theoretically, many random CSPs have been shown to exhibit a phase transition. As the ratio of constraints to…

Discrete Mathematics · Computer Science 2017-01-24 Colin Wei , Stefano Ermon

The algebraic dichotomy conjecture for Constraint Satisfaction Problems (CSPs) of reducts of (infinite) finitely bounded homogeneous structures states that such CSPs are polynomial-time tractable when the model-complete core of the template…

Logic in Computer Science · Computer Science 2020-07-22 Manuel Bodirsky , Antoine Mottet , Miroslav Olšák , Jakub Opršal , Michael Pinsker , Ross Willard

We review the understanding of the random constraint satisfaction problems, focusing on the q-coloring of large random graphs, that has been achieved using the cavity method of the physicists. We also discuss the properties of the phase…

Computational Complexity · Computer Science 2008-02-04 Florent Krzakala , Lenka Zdeborová

A variational approach to finite connectivity spin-glass-like models is developed and applied to describe the structure of optimal solutions in random satisfiability problems. Our variational scheme accurately reproduces the known replica…

Disordered Systems and Neural Networks · Physics 2009-10-31 Giulio Biroli , Remi Monasson , Martin Weigt

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 Problem (CSP) framework offers a simple and sound basis for representing and solving simple decision problems, without uncertainty. This paper is devoted to an extension of the CSP framework enabling us to deal…

Artificial Intelligence · Computer Science 2013-02-21 Helene Fargier , Jerome Lang , Roger Martin-Clouaire , Thomas Schiex

We introduce and study the random "locked" constraint satisfaction problems. When increasing the density of constraints, they display a broad "clustered" phase in which the space of solutions is divided into many isolated points. While the…

Statistical Mechanics · Physics 2008-09-05 Lenka Zdeborová , Marc Mézard

The so-called algebraic approach to the constraint satisfaction problem (CSP) has been a prevalent method of the study of complexity of these problems since early 2000's. The core of this approach is the notion of polymorphisms which…

Logic in Computer Science · Computer Science 2026-05-15 Maximilian Hadek , Tomáš Jakl , Jakub Opršal

The XOR-satisfiability (XORSAT) problem requires finding an assignment of $n$ Boolean variables that satisfy $m$ exclusive OR (XOR) clauses, whereby each clause constrains a subset of the variables. We consider random XORSAT instances,…

Discrete Mathematics · Computer Science 2015-09-10 Morteza Ibrahimi , Yash Kanoria , Matt Kraning , Andrea Montanari

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

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

The Constraint Satisfaction Problem (CSP) and its counting counterpart appears under different guises in many areas of mathematics, computer science, and elsewhere. Its structural and algorithmic properties have demonstrated to play a…

Combinatorics · Mathematics 2020-07-15 Raimundo Briceño , Andrei Bulatov , Victor Dalmau , Benoit Larose

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 CSP (constraint satisfaction problems) is a class of problems deciding whether there exists a homomorphism from an instance relational structure to a target one. The CSP dichotomy is a profound result recently proved by Zhuk (2020, J.…

Logic · Mathematics 2023-01-13 Azza Gaysin

The solution space of many classical optimization problems breaks up into clusters which are extensively distant from one another in the Hamming metric. Here, we show that an analogous quantum clustering phenomenon takes place in the ground…

Quantum Physics · Physics 2017-10-25 S. C. Morampudi , B. Hsu , S. L. Sondhi , R. Moessner , C. R. Laumann

We determine the exact freezing threshold, r^f, for a family of models of random boolean constraint satisfaction problems, including NAE-SAT and hypergraph 2-colouring, when the constraint size is sufficiently large. If the…

Discrete Mathematics · Computer Science 2012-09-24 Michael Molloy , Ricardo Restrepo

A discrete temporal constraint satisfaction problem is a constraint satisfaction problem (CSP) whose constraint language consists of relations that are first-order definable over $(\Bbb Z,<)$. Our main result says that every distance CSP is…

Logic · Mathematics 2016-04-27 Manuel Bodirsky , Barnaby Martin , Antoine Mottet

The second moment method has always been an effective tool to lower bound the satisfiability threshold of many random constraint satisfaction problems. However, the calculation is usually hard to carry out and as a result, only some loose…

Combinatorics · Mathematics 2020-11-06 Jun Liu , Ke Xu , Guangyan Zhou

The constraint satisfaction problem (CSP) is concerned with homomorphisms between two structures. For CSPs with restricted left-hand side structures, the results of Dalmau, Kolaitis, and Vardi [CP'02], Grohe [FOCS'03/JACM'07], and Atserias,…

Computational Complexity · Computer Science 2022-02-02 Clement Carbonnel , Miguel Romero , Stanislav Zivny

There has been great interest in identifying tractable subclasses of NP complete problems and designing efficient algorithms for these tractable classes. Constraint satisfaction and Bayesian network inference are two examples of such…

Artificial Intelligence · Computer Science 2012-12-12 Yong Gao