Related papers: Structured d-DNNF Is Not Closed Under Negation

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…

Introduced by Darwiche (2011), sentential decision diagrams (SDDs) are essentially as tractable as ordered binary decision diagrams (OBDDs), but tend to be more succinct in practice. This makes SDDs a prominent representation language, with…

The Sentential Decision Diagram (SDD) is a tractable representation of Boolean functions that subsumes the famous Ordered Binary Decision Diagram (OBDD) as a strict subset. SDDs are attracting much attention because they are more succinct…

We introduced decomposable negation normal form (DNNF) recently as a tractable form of propositional theories, and provided a number of powerful logical operations that can be performed on it in polynomial time. We also presented an…

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…

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…

We consider the compilation of a binary neural network's decision function into tractable representations such as Ordered Binary Decision Diagrams (OBDDs) and Sentential Decision Diagrams (SDDs). Obtaining this function as an OBDD/SDD…

Sentential decision diagrams (SDDs) introduced by Darwiche in 2011 are a promising representation type used in knowledge compilation. The relative succinctness of representation types is an important subject in this area. The aim of the…

Circuits in deterministic decomposable negation normal form (d-DNNF) are representations of Boolean functions that enable linear-time model counting. This paper strengthens our theoretical knowledge of what classes of functions can be…

Decomposable Negation Normal Forms (DNNFs) are Boolean circuits in negation normal form where the subcircuits leading into each AND gate are defined on disjoint sets of variables. We prove a strongly exponential lower bound on the size of…

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…

In many scientific disciplines, we are interested in inferring the nonlinear dynamical system underlying a set of observed time series, a challenging task in the face of chaotic behavior and noise. Previous deep learning approaches toward…

Two major considerations when encoding pseudo-Boolean (PB) constraints into SAT are the size of the encoding and its propagation strength, that is, the guarantee that it has a good behaviour under unit propagation. Several encodings with…

This paper focuses on the expressive power of disjunctive and normal logic programs under the stable model semantics over finite, infinite, or arbitrary structures. A translation from disjunctive logic programs into normal logic programs is…

We study succinctness as a measure of the expressive power of transformers. Succinctness -- how compactly a formalism can describe a language relative to other formalisms -- is a classical notion in logic and automata theory. We prove that…

The community is increasingly exploring linear RNNs (LRNNs) as language models, motivated by their expressive power and parallelizability. While prior work establishes the expressivity benefits of LRNNs over transformers, it is unclear what…

Nested logic programs have recently been introduced in order to allow for arbitrarily nested formulas in the heads and the bodies of logic program rules under the answer sets semantics. Nested expressions can be formed using conjunction,…

The remarkable performance of deep Convolutional neural networks (CNNs) is generally attributed to their deeper and wider architectures, which can come with significant computational costs. Pruning neural networks has thus gained interest…

Configurable systems typically consist of reusable assets that have dependencies between each other. To specify such dependencies, feature models are commonly used. As feature models in practice are often complex, automated reasoning is…

A central task in knowledge compilation is to compile a CNF-SAT instance into a succinct representation format that allows efficient operations such as testing satisfiability, counting, or enumerating all solutions. Useful representation…