Related papers: Proof Systems Based on Structured Circuits
Understanding how neural networks arrive at their predictions is essential for debugging, auditing, and deployment. Mechanistic interpretability pursues this goal by identifying circuits - minimal subnetworks responsible for specific…
Decision \textsc{dnnf} (a.k.a. $\wedge_d$-\textsc{fbdd}) is an important special case of Decomposable Negation Normal Form (\textsc{dnnf}), a landmark knowledge compilation model. Like other known \textsc{dnnf} restrictions, Decision…
Binary Decision Diagrams (BDDs) are a widely used data structure for efficient Boolean function representation. Context-Free-Language Ordered Binary Decision Diagrams (CFLOBDDs) are a recently introduced hierarchical data structure that…
Nonlinear system identification often involves a fundamental trade-off between interpretability and flexibility, often requiring the incorporation of physical constraints. We propose a unified data-driven framework that combines the…
This paper presents the first in a series of results that allow us to develop a theory providing finer control over the complexity of normalisation, and in particular of cut elimination. By considering atoms as self-dual non-commutative…
Probabilistic sentential decision diagrams are a class of structured-decomposable probabilistic circuits especially designed to embed logical constraints. To adapt the classical LearnSPN scheme to learn the structure of these models, we…
In this paper, we consider bounded width circuits and nondeterministic circuits in three somewhat new directions. In the first part of this paper, we mainly consider bounded width circuits. The main purpose of this part is to prove that…
This paper proposes new methods for set-based state estimation and active fault diagnosis (AFD) of linear descriptor systems (LDS). Unlike intervals, ellipsoids, and zonotopes, constrained zonotopes (CZs) can directly incorporate linear…
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…
We study -- within the framework of propositional proof complexity -- the problem of certifying unsatisfiability of CNF formulas under the promise that any satisfiable formula has many satisfying assignments, where ``many'' stands for an…
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…
Chain reduction enables reduced ordered binary decision diagrams (BDDs) and zero-suppressed binary decision diagrams (ZDDs) to each take advantage of the others' ability to symbolically represent Boolean functions in compact form. For any…
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…
Modeling and analysis of soft errors in electronic circuits has traditionally been done using computer simulations. Computer simulations cannot guarantee correctness of analysis because they utilize approximate real number representations…
A prominent challenge to the safe and optimal operation of the modern power grid arises due to growing uncertainties in loads and renewables. Stochastic optimal power flow (SOPF) formulations provide a mechanism to handle these…
Decision Diagrams(DDs) are one of the most popular representations for boolean functions. They are widely used in the design and verification of circuits. Different types of DDs have been proven to represent important functions in…
The best current methods for exactly computing the number of satisfying assignments, or the satisfying probability, of Boolean formulas can be seen, either directly or indirectly, as building 'decision-DNNF' (decision decomposable negation…
We consider a variant of the Boolean satisfiability problem where a subset E of the propositional variables appearing in formula Fsat encode a symmetric, transitive, binary relation over N elements. Each of these relational variables,…
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…
In recent years, deep neural network (DNN) compression systems have proved to be highly effective for designing source codes for many natural sources. However, like many other machine learning systems, these compressors suffer from…