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This paper presents the foundation for a decomposition theory for Boolean networks, a type of discrete dynamical system that has found a wide range of applications in the life sciences, engineering, and physics. Given a Boolean network…

Dynamical Systems · Mathematics 2022-06-10 Claus Kadelka , Reinhard Laubenbacher , David Murrugarra , Alan Veliz-Cuba , Matthew Wheeler

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

We study the complexity of local search for the Boolean constraint satisfaction problem (CSP), in the following form: given a CSP instance, that is, a collection of constraints, and a solution to it, the question is whether there is a…

Data Structures and Algorithms · Computer Science 2017-11-13 Andrei Krokhin , Dániel Marx

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

The concept of control is crucial for effectively understanding and applying biological network models. Key structural features relate to control functions through gene regulation, signaling, or metabolic mechanisms, and computational…

Molecular Networks · Quantitative Biology 2024-11-05 David Murrugarra , Alan Veliz-Cuba , Elena Dimitrova , Claus Kadelka , Matthew Wheeler , Reinhard Laubenbacher

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

In the Constraint Satisfaction Problem (CSP for short) the goal is to decide the existence of a homomorphism from a given relational structure $G$ to a given relational structure $H$. If the structure $H$ is fixed and $G$ is the only input,…

Logic in Computer Science · Computer Science 2025-10-14 Andrei A. Bulatov , Amirhossein Kazeminia

This paper focuses on the branching process for solving any constraint satisfaction problem (CSP). A parametrised schema is proposed that (with suitable instantiations of the parameters) can solve CSP's on both finite and infinite domains.…

Programming Languages · Computer Science 2007-05-23 Antonio J. Fernandez , Patricia M. Hill

We investigate the computational complexity of the problem of counting the maximal satisfying assignments of a Constraint Satisfaction Problem (CSP) over the Boolean domain {0,1}. A satisfying assignment is maximal if any new assignment…

Computational Complexity · Computer Science 2016-05-17 Leslie Ann Goldberg , Mark Jerrum

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

We initiate a systematic study of the computational complexity of the Constraint Satisfaction Problem (CSP) over finite structures that may contain both relations and operations. We show the close connection between this problem and a…

Logic in Computer Science · Computer Science 2021-12-02 Libor Barto , William DeMeo , Antoine Mottet

Many biochemical and industrial applications involve complicated networks of simultaneously occurring chemical reactions. Under the assumption of mass action kinetics, the dynamics of these chemical reaction networks are governed by systems…

Dynamical Systems · Mathematics 2014-07-15 Matthew D. Johnston

The CSP of a first-order theory $T$ is the problem of deciding for a given finite set $S$ of atomic formulas whether $T \cup S$ is satisfiable. Let $T_1$ and $T_2$ be two theories with countably infinite models and disjoint signatures.…

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

This paper describes a new approach on optimization of constraint satisfaction problems (CSPs) by means of substituting sub-CSPs with locally consistent regular membership constraints. The purpose of this approach is to reduce the number of…

Artificial Intelligence · Computer Science 2019-08-19 Sven Löffler , Ke Liu , Petra Hofstedt

Thermodynamic constraints on reactions directions are inherent in the structure of a given biochemical network. However, concrete procedures for determining feasible reaction directions for large-scale metabolic networks are not well…

Molecular Networks · Quantitative Biology 2007-05-23 Feng Yang , Feng Qi , Daniel A. Beard

Methods of modeling cellular regulatory networks as diverse as differential equations and Boolean networks co-exist, however, without any closer correspondence to each other. With the example system of the fission yeast cell cycle control…

Molecular Networks · Quantitative Biology 2015-03-13 Maria Davidich , Stefan Bornholdt

The binary Constraint Satisfaction Problem (CSP) is to decide whether there exists an assignment to a set of variables which satisfies specified constraints between pairs of variables. A binary CSP instance can be presented as a labelled…

Computational Complexity · Computer Science 2019-06-28 David A. Cohen , Martin C. Cooper , Peter G. Jeavons , Stanislav Zivny

We study constraint satisfaction problems (CSPs) where the constraint languages are defined by finite automata, giving rise to automata-based CSPs. The key notion is the concept of Automatic Constraint Satisfaction Problem ($AutCSP$), where…

Logic in Computer Science · Computer Science 2026-04-22 Andrei Bulatov , Xiaoyang Gong , Bakh Khoussainov , Xinyao Wang

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

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