Related papers: A New Look at BDDs for Pseudo-Boolean Constraints
In the field of Boolean satisfiability problems (SAT), at-most-k constraints, which suppress the number of true target variables at most k, are often used to describe objective problems. At-most-k constraints are used not only for…
Current pseudo-Boolean solvers implement different variants of the cutting planes proof system to infer new constraints during conflict analysis. One of these variants is generalized resolution, which allows to infer strong constraints, but…
The Pseudo-Boolean Optimization (PBO) and Maximum Satisfiability (MaxSAT) problems are natural optimization extensions of Boolean Satisfiability (SAT). In the recent past, different algorithms have been proposed for PBO and for MaxSAT,…
Binary Decision Diagrams (BDDs) are widely used for the representation of Boolean functions. Context-Free-Language Ordered Decision Diagrams (CFLOBDDs) are a plug-compatible replacement for BDDs -- roughly, they are BDDs augmented with a…
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…
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 the article, within the framework of the Boolean Satisfiability problem (SAT), the problem of estimating the hardness of specific Boolean formulas w.r.t. a specific complete SAT solving algorithm is considered. Based on the well-known…
Two-level logic minimization is a central problem in logic synthesis, and has applications in reliability analysis and automated reasoning. This paper represents a method of minimizing Boolean sum of products function with binary decision…
Understanding the characteristics of neural networks is important but difficult due to their complex structures and behaviors. Some previous work proposes to transform neural networks into equivalent Boolean expressions and apply…
In this paper we present a new approach to modeling finite set domain constraint problems using Reduced Ordered Binary Decision Diagrams (ROBDDs). We show that it is possible to construct an efficient set domain propagator which compactly…
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…
In this paper, we study the problem of minimizing a polynomial function with literals over all binary points, often referred to as pseudo-Boolean optimization. We investigate the fundamental limits of computation for this problem by…
Constrained coding plays a key role in optimizing performance and mitigating errors in applications such as storage and communication, where specific constraints on codewords are required. While non-parametric constraints have been…
In this paper we propose, implement, and test the first practical decomposition algorithms for the width parameters treecut width and treedepth. These two parameters have recently gained a lot of attention in the theoretical research…
We introduce partial differential encodings of Boolean functions as a way of measuring the complexity of Boolean functions. These encodings enable us to derive from group actions non-trivial bounds on the Chow-Rank of polynomials used to…
Pseudo-Labeling is a simple and effective approach to semi-supervised learning. It requires criteria that guide the selection of pseudo-labeled data. The latter have been shown to crucially affect pseudo-labeling's generalization…
Symmetries are intrinsic to many combinatorial problems including Boolean Satisfiability (SAT) and Constraint Programming (CP). In SAT, the identification of symmetry breaking predicates (SBPs) is a well-known, often effective, technique…
We consider the problem of finding and enumerating polyominos that can be folded into multiple non-isomorphic boxes. While several computational approaches have been proposed, including SAT, randomized algorithms, and decision diagrams,…
The growing interest in explainable artificial intelligence (XAI) for critical decision making motivates the need for interpretable machine learning (ML) models. In fact, due to their structure (especially with small sizes), these models…
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…