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Using the cavity equations of \cite{mezard:parisi:zecchina:02,mezard:zecchina:02}, we derive the various threshold values for the number of clauses per variable of the random $K$-satisfiability problem, generalizing the previous results to…

Computational Complexity · Computer Science 2007-05-23 Stephan Mertens , Marc Mezard , Riccardo Zecchina

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

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 problem of estimating the proportion of satisfiable instances of a given CSP (constraint satisfaction problem) can be tackled through weighting. It consists in putting onto each solution a non-negative real value based on its…

Discrete Mathematics · Computer Science 2015-03-17 Yacine Boufkhad , Thomas Hugel

A constraint satisfaction problem (CSP) is a computational problem where the input consists of a finite set of variables and a finite set of constraints, and where the task is to decide whether there exists a satisfying assignment of values…

Computational Complexity · Computer Science 2019-04-23 Manuel Bodirsky

We determine under which conditions certain natural models of random constraint satisfaction problems have sharp thresholds of satisfiability. These models include graph and hypergraph homomorphism, the $(d,k,t)$-model, and binary…

Combinatorics · Mathematics 2009-03-17 Hamed Hatami , Michael Molloy

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

For a constraint satisfaction problem (CSP), a robust satisfaction algorithm is one that outputs an assignment satisfying most of the constraints on instances that are near-satisfiable. It is known that the CSPs that admit efficient robust…

Data Structures and Algorithms · Computer Science 2025-09-09 Joshua Brakensiek , Venkatesan Guruswami , Sai Sandeep

Constraint satisfaction problems (CSPs) are an important formal framework for the uniform treatment of various prominent AI tasks, e.g., coloring or scheduling problems. Solving CSPs is, in general, known to be NP-complete and…

Computational Complexity · Computer Science 2020-07-29 Hubie Chen , Georg Gottlob , Matthias Lanzinger , Reinhard Pichler

An active topic in the study of random constraint satisfaction problems (CSPs) is the geometry of the space of satisfying or almost satisfying assignments as the function of the density, for which a precise landscape of predictions has been…

Data Structures and Algorithms · Computer Science 2021-06-25 Jun-Ting Hsieh , Sidhanth Mohanty , Jeff Xu

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 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

We compute the probability of satisfiability of a class of random Horn-SAT formulae, motivated by a connection with the nonemptiness problem of finite tree automata. In particular, when the maximum clause length is 3, this model displays a…

Probability · Mathematics 2007-05-23 Cristopher Moore , Gabriel Istrate , Demetrios Demopoulos , Moshe Y. Vardi

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

A Constraint Satisfaction Problem (CSP) is a computational problem where we are given variables and constraints about them; the question is whether the variables can be assigned values such that all constraints are satisfied. We give an…

Logic in Computer Science · Computer Science 2022-04-01 Michael Pinsker

The constraint satisfaction problem (CSP) involves deciding, given a set of variables and a set of constraints on the variables, whether or not there is an assignment to the variables satisfying all of the constraints. One formulation of…

Computational Complexity · Computer Science 2017-01-09 Hubie Chen , Benoit Larose

The exponential-time hypothesis (ETH) states that 3-SAT is not solvable in subexponential time, i.e. not solvable in O(c^n) time for arbitrary c > 1, where n denotes the number of variables. Problems like k-SAT can be viewed as special…

Computational Complexity · Computer Science 2017-06-20 Peter Jonsson , Victor Lagerkvist , Biman Roy

We study the satisfiability threshold and solution-space geometry of random constraint satisfaction problems defined over uniquely extendable (UE) constraints. Motivated by a conjecture of Connamacher and Molloy, we consider random $k$-ary…

Combinatorics · Mathematics 2026-01-27 Pu Gao , Theodore Morrison

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 first analyzes the resolution complexity of two random CSP models (i.e. Model RB/RD) for which we can establish the existence of phase transitions and identify the threshold points exactly. By encoding CSPs into CNF formulas, it…

Computational Complexity · Computer Science 2007-05-23 Ke Xu , Wei Li