相关论文: Revisiting Decision Diagrams for SAT

We present a SAT framework which allows to investigate properties of simple drawings of the complete graph $K_n$ using the power of AI. In contrast to classic imperative programming, where a program is operated step by step, our framework…

This paper introduces new technique for efficient calculation of different Shannon information measures which operates Binary Decision Diagrams (BDDs). We offer an algorithm of BDD reordering which demonstrates the improvement of the…

To enhance the scalability and performance of the traditional finite-difference time-domain (FDTD) methods, a three-dimensional summation-by-parts simultaneous approximation term (SBP-SAT) FDTD method is developed to solve complex…

The literature on Multiple Criteria Decision Analysis (MCDA) proposes several methods in order to sort alternatives evaluated on several attributes into ordered classes. Non Compensatory Sorting models (NCS) assign alternatives to classes…

Many problems in robotics involve both continuous and discrete components, and modeling them together for estimation tasks has been a long standing and difficult problem. Hybrid Factor Graphs give us a mathematical framework to model these…

Decision diagrams are an increasingly important tool in cutting-edge solvers for discrete optimization. However, the field of decision diagrams is relatively new, and is still incorporating the library of techniques that conventional…

We offer a new understanding of some aspects of practical SAT-solvers that are based on DPLL with unit-clause propagation, clause-learning, and restarts. We do so by analyzing a concrete algorithm which we claim is faithful to what…

We propose a method for variable selection in discriminant analysis with mixed categorical and continuous variables. This method is based on a criterion that permits to reduce the variable selection problem to a problem of estimating…

We introduce a novel framework, termed $\lambda$DD, that revisits Binary Decision Diagrams from a purely functional point of view. The framework allows to classify the already existing variants, including the most recent ones like Chain-DD…

The boolean satisfiability (SAT) problem asks whether there exists an assignment of boolean values to the variables of an arbitrary boolean formula making the formula evaluate to True. It is well-known that all NP-problems can be coded as…

We propose a neurosymbolic approach to the explanation of complex sequences of decisions that combines the strengths of decision procedures and Large Language Models (LLMs). We demonstrate this approach by producing explanations for the…

Instances of logical cryptanalysis, circuit verification, and bounded model checking can often be succinctly represented as a combined satisfiability (SAT) problem where an instance is a combination of traditional clauses and parity…

The "bisimulation problem" for equational graphs of finite out-degree is shown to be decidable. We reduce this problem to the bisimulation problem for deterministic rational (vectors of) boolean series on the alphabet of a dpda M. We then…

We propose a general algorithm of constructing an extended formulation for any given set of linear constraints with integer coefficients. Our algorithm consists of two phases: first construct a decision diagram $(V,E)$ that somehow…

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…

This paper studies a difference between Binary Decision Diagrams (BDDs) and Zero-suppressed BDDs (ZDDs) from a conceptual point of view. It is commonly understood that a BDD is a representation of a Boolean function, whereas a ZDD is a…

We follow up on the idea of Lars Arge to rephrase the Reduce and Apply procedures of Binary Decision Diagrams (BDDs) as iterative I/O-efficient algorithms. We identify multiple avenues to simplify and improve the performance of his proposed…

Boolean Satisfiability (SAT) problems are expressed as mathematical formulas. This paper presents a matrix representation for these SAT problems. It shows how to use this matrix representation to get the full set of valid satisfying…

Generating diverse solutions to the Boolean Satisfiability Problem (SAT) is a hard computational problem with practical applications for testing and functional verification of software and hardware designs. We explore the way to generate…

The goal of this brief pedagogical article is to show that Binary Decision Diagrams are a special kind of Bayesian Net. This observation is obvious to workers in these two fields, but it might not be too obvious to others.