Related papers: Compilation and Fast Model Counting beyond CNF
Since their introduction by Atserias, Kolaitis, and Vardi in 2004, proof systems where each line is represented by an ordered binary decision diagram (OBDD) have been intensively studied as they allow to compactly represent Boolean…
Feature models are commonly used to specify the valid configurations of a product line. In industry, feature models are often complex due to a large number of features and constraints. Thus, a multitude of automated analyses have been…
Model counting is the problem of computing the number of satisfying assignments of a given propositional formula. Although exact model counters can be naturally furnished by most of the knowledge compilation (KC) methods, in practice, they…
Structured $d$-DNNFs and SDDs are restricted negation normal form circuits used in knowledge compilation as target languages into which propositional theories are compiled. Structuredness is imposed by so-called vtrees. By definition SDDs…
Deep Neural Networks (DNNs) deliver impressive performance but their black-box nature limits deployment in high-stakes domains requiring transparency. We introduce Compositional Function Networks (CFNs), a novel framework that builds…
A knowledge compilation map analyzes tractable operations in Boolean function representations and compares their succinctness. This enables the selection of appropriate representations for different applications. In the knowledge…
We consider the problem EnumIP of enumerating prime implicants of Boolean functions represented by decision decomposable negation normal form (dec-DNNF) circuits. We study EnumIP from dec-DNNF within the framework of enumeration complexity…
Density functional theory (DFT) offers a desirable balance between quantitative accuracy and computational efficiency in practical many-electron calculations. Its central component, the exchange-correlation energy functional, has been…
Model counting is a fundamental problem in many practical applications, including query evaluation in probabilistic databases and failure-probability estimation of networks. In this work, we focus on a variant of this problem where the…
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…
We develop a representation suitable for the unconstrained recognition of words in natural images: the general case of no fixed lexicon and unknown length. To this end we propose a convolutional neural network (CNN) based architecture which…
The Normalizing Flow (NF) models a general probability density by estimating an invertible transformation applied on samples drawn from a known distribution. We introduce a new type of NF, called Deep Diffeomorphic Normalizing Flow (DDNF).…
Conventional matrix completion methods approximate the missing values by assuming the matrix to be low-rank, which leads to a linear approximation of missing values. It has been shown that enhanced performance could be attained by using…
A classical question of propositional logic is one of the shortest proof of a tautology. A related fundamental problem is to determine the relative efficiency of standard proof systems, where the relative complexity is measured using the…
Selman and Kautz's work on ``knowledge compilation'' established how approximation (strengthening and/or weakening) of a propositional knowledge-base can be used to speed up query processing, at the expense of completeness. In this…
Calculating perturbation response properties of materials from first principles provides a vital link between theory and experiment, but is bottlenecked by the high computational cost. Here a general framework is proposed to perform density…
Deep learning has delivered its powerfulness in many application domains, especially in image and speech recognition. As the backbone of deep learning, deep neural networks (DNNs) consist of multiple layers of various types with hundreds to…
Boolean circuits in d-DNNF form enable tractable probabilistic inference. However, as a key insight of this work, we show that commonly used d-DNNF compilation approaches introduce irrelevant subcircuits. We call these subcircuits Tseitin…
In this article, we study the problem of enumerating the models of DNF formulas. The aim is to provide enumeration algorithms with a delay that depends polynomially on the size of each model and not on the size of the formula, which can be…
Knowledge compilation (KC) languages find a growing number of practical uses, including in Constraint Programming (CP) and in Machine Learning (ML). In most applications, one natural question is how to explain the decisions made by models…