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The Promise Constraint Satisfaction Problem (PCSP) is a generalization of the Constraint Satisfaction Problem (CSP) that includes approximation variants of satisfiability and graph coloring problems. Barto [LICS '19] has shown that a…

Computational Complexity · Computer Science 2025-06-09 Kristina Asimi , Libor Barto

In the weighted flow-time problem on a single machine, we are given a set of n jobs, where each job has a processing requirement p_j, release date r_j and weight w_j. The goal is to find a preemptive schedule which minimizes the sum of…

Data Structures and Algorithms · Computer Science 2018-08-21 Jatin Batra , Naveen Garg , Amit Kumar

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

The constraint satisfaction problem asks to decide if a set of constraints over a relational structure $\mathcal{A}$ is satisfiable (CSP$(\mathcal{A})$). We consider CSP$(\mathcal{A} \cup \mathcal{B})$ where $\mathcal{A}$ is a structure and…

Computational Complexity · Computer Science 2024-08-28 Peter Jonsson , Victor Lagerkvist , George Osipov

This work focuses on effectively generating diverse solutions for satisfiability modulo theories (SMT) formulas, targeting the theories of bit-vectors, arrays, and uninterpreted functions, which is a critical task in software and hardware…

Software Engineering · Computer Science 2025-11-14 Shuangyu Lyu , Chuan Luo , Ruizhi Shi , Wei Wu , Chanjuan Liu , Chunming Hu

Parameterized complexity theory offers a framework for a refined analysis of hard algorithmic problems. Instead of expressing the running time of an algorithm as a function of the input size only, running times are expressed with respect to…

Distributed, Parallel, and Cluster Computing · Computer Science 2021-02-18 Sebastian Siebertz , Alexandre Vigny

We study the complexity of the parameterised counting constraint satisfaction problem: given a set of constraints over a set of variables and a positive integer $k$, how many ways are there to assign $k$ variables to 1 (and the others to 0)…

Computational Complexity · Computer Science 2026-04-29 Panagiotis Aivasiliotis , Andreas Göbel , Marc Roth

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

Recent work has shown that many problems of satisfiability and resiliency in workflows may be viewed as special cases of the authorization policy existence problem (APEP), which returns an authorization policy if one exists and 'No'…

Data Structures and Algorithms · Computer Science 2021-07-15 Jason Crampton , Eduard Eiben , Gregory Gutin , Daniel Karapetyan , Diptapriyo Majumdar

We study a model of constraint satisfaction problems geared towards instances with few variables but with domain of unbounded size (udCSP). Our model is inspired by recent work on FPT algorithms for MinCSP where frequently both upper and…

Data Structures and Algorithms · Computer Science 2025-08-25 Peter Jonsson , Victor Lagerkvist , Jorke M. de Vlas , Magnus Wahlström

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

The Constraint Satisfaction Problem (CSP) is ubiquitous in various areas of mathematics and computer science. Many of its variations have been studied including the Counting CSP, where the goal is to find the number of solutions to a CSP…

Computational Complexity · Computer Science 2025-01-24 Amirhossein Kazeminia , Andrei A. Bulatov

Constraints such as separation-of-duty are widely used to specify requirements that supplement basic authorization policies. However, the existence of constraints (and authorization policies) may mean that a user is unable to fulfill…

Cryptography and Security · Computer Science 2016-12-20 Pierre Bergé , Jason Crampton , Gregory Gutin , Rémi Watrigant

User alignment is crucial for adapting general-purpose language models (LMs) to downstream tasks, but human annotations are often not available for all types of instructions, especially those with customized constraints. We observe that…

Computation and Language · Computer Science 2024-03-12 Fei Wang , Chao Shang , Sarthak Jain , Shuai Wang , Qiang Ning , Bonan Min , Vittorio Castelli , Yassine Benajiba , Dan Roth

CSP sparsification, introduced by Kogan and Krauthgamer (ITCS 2015), considers the following question: how much can an instance of a constraint satisfaction problem be sparsified (by retaining a reweighted subset of the constraints) while…

Data Structures and Algorithms · Computer Science 2024-11-07 Sanjeev Khanna , Aaron L. Putterman , Madhu Sudan

The fixed template Promise Constraint Satisfaction Problem (PCSP) is a recently proposed significant generalization of the fixed template CSP, which includes approximation variants of satisfiability and graph coloring problems. All the…

Computational Complexity · Computer Science 2019-09-12 Libor Barto

Constraint satisfaction problems (CSPs) are ubiquitous in theoretical computer science. We study the problem of StrongCSPs, i.e. instances where a large induced sub-instance has a satisfying assignment. More formally, given a CSP instance…

Data Structures and Algorithms · Computer Science 2022-05-24 Suprovat Ghoshal , Anand Louis

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

We explore the problem of step-wise explaining how to solve constraint satisfaction problems, with a use case on logic grid puzzles. More specifically, we study the problem of explaining the inference steps that one can take during…

Logic in Computer Science · Computer Science 2021-07-06 Bart Bogaerts , Emilio Gamba , Tias Guns

Through legislation and technical advances users gain more control over how their data is processed, and they expect online services to respect their privacy choices and preferences. However, data may be processed for many different…

Databases · Computer Science 2024-03-19 Dorota Filipczuk , Enrico H. Gerding , George Konstantinidis
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