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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 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

Functional verification plays a central role in ensuring the correctness of modern integrated circuit designs, where constrained-random verification is widely adopted to generate diverse stimuli under high-level constraints. In industrial…

Hardware Architecture · Computer Science 2026-04-07 Nanbing Li , Weijie Peng , Jin Luo , Shuai Wang , Yihui Li , Jun Fang , Yun Liang

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 \emph{Sandwich Problem} (SP) for a graph class $\calC$ is the following computational problem. The input is a pair of graphs $(V,E_1)$ and $(V,E_2)$ where $E_1\subseteq E_2$, and the task is to decide whether there is an edge set $E$…

Discrete Mathematics · Computer Science 2025-10-13 Manuel Bodirsky , Santiago Guzmán-Pro

Constraint satisfaction problems have been studied in numerous fields with practical and theoretical interests. In recent years, major breakthroughs have been made in a study of counting constraint satisfaction problems (or #CSPs). In…

Computational Complexity · Computer Science 2012-10-23 Tomoyuki Yamakami

Many fundamental problems in artificial intelligence, knowledge representation, and verification involve reasoning about sets and relations between sets and can be modeled as set constraint satisfaction problems (set CSPs). Such problems…

Artificial Intelligence · Computer Science 2012-07-19 Manuel Bodirsky , Martin Hils , Alex Krimkevich

Constraint satisfaction problems are computational problems that naturally appear in many areas of theoretical computer science. One of the central themes is their computational complexity, and in particular the border between…

Computational Complexity · Computer Science 2026-04-28 Manuel Bodirsky

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

Many real world problems naturally appear as constraints satisfaction problems (CSP), for which very efficient algorithms are known. Most of these involve the combination of two techniques: some direct propagation of constraints between…

Artificial Intelligence · Computer Science 2013-04-12 Denis Berthier

Neural Networks are used today in numerous security- and safety-relevant domains and are, as such, a popular target of attacks that subvert their classification capabilities, by manipulating the network parameters. Prior work has introduced…

Machine Learning · Computer Science 2021-09-10 Amel Nestor Docena , Thomas Wahl , Trevor Pearce , Yunsi Fei

Recurrent models are a popular choice for video enhancement tasks such as video denoising or super-resolution. In this work, we focus on their stability as dynamical systems and show that they tend to fail catastrophically at inference time…

Computer Vision and Pattern Recognition · Computer Science 2023-03-14 Thomas Tanay , Aivar Sootla , Matteo Maggioni , Puneet K. Dokania , Philip Torr , Ales Leonardis , Gregory Slabaugh

In the field of constraint satisfaction problems (CSP), promise CSPs are an exciting new direction of study. In a promise CSP, each constraint comes in two forms: "strict" and "weak," and in the associated decision problem one must…

Data Structures and Algorithms · Computer Science 2020-12-03 Joshua Brakensiek , Venkatesan Guruswami , Marcin Wrochna , Stanislav Živný

Recent results show that a constraint satisfaction problem (CSP) defined over rational numbers with their natural ordering has a solution if and only if it has a definable solution. The proof uses advanced results from topology and modern…

Logic in Computer Science · Computer Science 2020-03-31 Michał R. Przybyłek

In many real world applications of machine learning, models have to meet certain domain-based requirements that can be expressed as constraints (e.g., safety-critical constraints in autonomous driving systems). Such constraints are often…

Machine Learning · Computer Science 2022-06-20 Kshitij Goyal , Sebastijan Dumancic , Hendrik Blockeel

In this contribution, we provide a comprehensive evaluation of graph neural networks applied to Boolean satisfiability problems, accompanied by an intuitive explanation of the mechanisms enabling the model to generalize to different…

Machine Learning · Computer Science 2025-04-03 David Mojžíšek , Jan Hůla , Ziwei Li , Ziyu Zhou , Mikoláš Janota

Symbolic execution is a powerful systematic software analysis technique, but suffers from the high cost of constraint solving, which is the key supporting technology that affects the effectiveness of symbolic execution. Techniques like…

Software Engineering · Computer Science 2020-03-19 Junye Wen , Mujahid Khan , Meiru Che , Yan Yan , Guowei Yang

Although the CSP (constraint satisfaction problem) is NP-complete, even in the case when all constraints are binary, certain classes of instances are tractable. We study classes of instances defined by excluding subproblems. This approach…

Artificial Intelligence · Computer Science 2012-01-19 Martin C. Cooper , Guillaume Escamocher

Although convolutional neural networks (CNNs) showed remarkable results in many vision tasks, they are still strained by simple yet challenging visual reasoning problems. Inspired by the recent success of the Transformer network in computer…

Computer Vision and Pattern Recognition · Computer Science 2021-11-30 Nicola Messina , Giuseppe Amato , Fabio Carrara , Claudio Gennaro , Fabrizio Falchi

The complexity and approximability of the constraint satisfaction problem (CSP) has been actively studied over the last 20 years. A new version of the CSP, the promise CSP (PCSP) has recently been proposed, motivated by open questions about…

Computational Complexity · Computer Science 2021-07-19 Libor Barto , Jakub Bulín , Andrei Krokhin , Jakub Opršal
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