English
Related papers

Related papers: On the CNF encoding of cardinality constraints and…

200 papers

Linear integer constraints are one of the most important constraints in combinatorial problems since they are commonly found in many practical applications. Typically, encodings to Boolean satisfiability (SAT) format of conjunctive normal…

Logic in Computer Science · Computer Science 2020-05-06 Ignasi Abío , Valentin Mayer-Eichberger , Peter Stuckey

With the continue development of Convolutional Neural Networks (CNNs), there is a growing concern regarding representations that they encode internally. Analyzing these internal representations is referred to as model interpretation. While…

Computer Vision and Pattern Recognition · Computer Science 2023-05-18 Hamed Behzadi-Khormouji , José Oramas

The minimum number of clauses in a CNF representation of the parity function $x_1 \oplus x_2 \oplus \dotsb \oplus x_n$ is $2^{n-1}$. One can obtain a more compact CNF encoding by using non-deterministic variables (also known as guess or…

Computational Complexity · Computer Science 2022-05-17 Gregory Emdin , Alexander S. Kulikov , Ivan Mihajlin , Nikita Slezkin

A monotone CNF formula is a Boolean formula in conjunctive normal form where each variable appears positively. We design a deterministic fully polynomial-time approximation scheme (FPTAS) for counting the number of satisfying assignments…

Data Structures and Algorithms · Computer Science 2014-04-03 Jingcheng Liu , Pinyan Lu

Cardinality constraints are important in many Sat problems; previous studies provide contradictory conclusions about the best encoding to use. Here, three encodings are compared: Sinz's sequential-counter, Bailleux and Boufkhad's…

Logic in Computer Science · Computer Science 2018-11-01 Ed Wynn

BoolVar/PB is an open source java library dedicated to the translation of pseudo-Boolean constraints into CNF formulae. Input constraints can be categorized with tags. Several encoding schemes are implemented in a way that each input…

Artificial Intelligence · Computer Science 2011-03-22 Olivier Bailleux

We show that some common and important global constraints like ALL-DIFFERENT and GCC can be decomposed into simple arithmetic constraints on which we achieve bound or range consistency, and in some cases even greater pruning. These…

Artificial Intelligence · Computer Science 2009-05-26 Christian Bessiere , George Katsirelos , Nina Narodytska , Claude-Guy Quimper , Toby Walsh

We provide a formula for the lower bound in the form of $|F| \ge K$, in such a way that the decision version of unweighted non-bipartite matching can be solved in polynomial time. ~The parameter $K$ can vary from instance to instance. We…

Logic in Computer Science · Computer Science 2014-10-24 Prabhu Manyem

Verifying and explaining the behavior of neural networks is becoming increasingly important, especially when they are deployed in safety-critical applications. In this paper, we study verification problems for Binarized Neural Networks…

Machine Learning · Computer Science 2021-03-15 Yedi Zhang , Zhe Zhao , Guangke Chen , Fu Song , Taolue Chen

We mainly investigate model of set theory with restricted choice, e.g., ZF + DC + "the family of countable subsets of lambda is well ordered for every lambda" (really local version for a given lambda). In this frame much of pcf theory can…

Logic · Mathematics 2019-01-29 Saharon Shelah

We construct Boolean Algebras answering questions of Monk on cardinal invariants. The results are proved in ZFC (rather than giving consistency results). We deal with the existence of superatomic Boolean Algebras with ``few automorphisms'',…

Logic · Mathematics 2007-05-23 Saharon Shelah

Chart constraints, which specify at which string positions a constituent may begin or end, have been shown to speed up chart parsers for PCFGs. We generalize chart constraints to more expressive grammar formalisms and describe a neural…

Computation and Language · Computer Science 2018-06-29 Stefan Grünewald , Sophie Henning , Alexander Koller

Beyond identifying genetic variants, we introduce a set of Boolean relations that allows for a comprehensive classification of the relations for every pair of variants by taking all minimal alignments into account. We present an efficient…

Genomics · Quantitative Biology 2023-01-04 Jonathan K. Vis , Mark A. Santcroos , Walter A. Kosters , Jeroen F. J. Laros

The success of Constraint Programming relies partly on the global constraints and implementation of the associated filtering algorithms. Recently, new ideas emerged to improve these implementations in practice, especially regarding the all…

Artificial Intelligence · Computer Science 2025-02-06 Margaux Schmied , Jean-Charles Regin

High\-cardinality categorical variables pose significant challenges in machine learning, particularly in terms of computational efficiency and model interpretability. Traditional one\-hot encoding often results in high\-dimensional sparse…

Machine Learning · Computer Science 2025-01-13 Zixuan Liang

We use the implicitization procedure to generate polynomial equality constraints on the set of distributions induced by local interventions on variables governed by a causal Bayesian network with hidden variables. We show how we may reduce…

Artificial Intelligence · Computer Science 2012-06-26 Changsung Kang , Jin Tian

Computational learning theory states that many classes of boolean formulas are learnable in polynomial time. This paper addresses the understudied subject of how, in practice, such formulas can be learned by deep neural networks.…

Machine Learning · Computer Science 2025-09-17 Marcio Nicolau , Anderson R. Tavares , Zhiwei Zhang , Pedro Avelar , João M. Flach , Luis C. Lamb , Moshe Y. Vardi

In this paper we present a rule based formalism for filtering variables domains of constraints. This formalism is well adapted for solving dynamic CSP. We take diagnosis as an instance problem to illustrate the use of these rules. A…

Artificial Intelligence · Computer Science 2007-05-23 S. Piechowiak , J. Rodriguez

We show unconditional parameterized lower bounds in the area of knowledge compilation, more specifically on the size of circuits in decomposable negation normal form (DNNF) that encode CNF-formulas restricted by several graph width…

Artificial Intelligence · Computer Science 2016-04-25 Stefan Mengel

We investigate weakly constrained codes, in which specific patterns occur with prescribed frequencies rather than being strictly forbidden as in conventional constrained coding. We propose a capacity-achieving construction of a weakly…

Information Theory · Computer Science 2026-05-22 Prachi Mishra , Sidharth Jaggi , Navin Kashyap , Michael Langberg