Related papers: Derivative structure enumeration using binary deci…
Deep neural networks (DNNs) and decision trees (DTs) are both state-of-the-art classifiers. DNNs perform well due to their representational learning capabilities, while DTs are computationally efficient as they perform inference along one…
Combinatorics of biopolymer structures, especially enumeration of various RNA secondary structures and protein contact maps, is of significant interest for communities of both combinatorics and computational biology. However, most of the…
Binary decision diagrams (BDDs) are widely used to mitigate the state-explosion problem in model checking. A variation of BDDs are Zero-suppressed Decision Diagrams (ZDDs) which omit variables that must be false, instead of omitting…
Decision Diagrams (DDs) have emerged as a powerful tool for discrete optimization, with rapidly growing adoption. DDs are directed acyclic layered graphs; restricted DDs are a generalized greedy heuristic for finding feasible solutions, and…
The structural design of functional molecules, also called molecular optimization, is an essential chemical science and engineering task with important applications, such as drug discovery. Deep generative models and combinatorial…
Existing methods for differentiable structure learning in discrete data typically assume that the data are generated from specific structural equation models. However, these assumptions may not align with the true data-generating process,…
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…
Ordered Binary Decision Diagrams (OBDDs) are a data structure that is used in an increasing number of fields of Computer Science (e.g., logic synthesis, program verification, data mining, bioinformatics, and data protection) for…
We introduce a dynamic data structure for the compact representation of binary relations $\mathcal{R} \subseteq A \times B$. The data structure is a dynamic variant of the k$^2$-tree, a static compact representation that takes advantage of…
A decision tree looks like a simple directed acyclic computational graph, where only the leaf nodes specify the output values and the non-terminals specify their tests or split conditions. From the numerical perspective, we express decision…
In this paper, we propose a fast method for exactly enumerating a very large number of all lower cost solutions for various combinatorial problems. Our method is based on backtracking for a given decision diagram which represents all the…
Symbolic variants of clause distribution using decision diagrams to eliminate variables in SAT were shown to perform well on hard combinatorial instances. In this paper we revisit both existing ZDD and BDD variants of this approach. We…
Ordered binary decision diagrams (OBDDs) are a fundamental data structure for the manipulation of Boolean functions, with strong applications to finite-state symbolic model checking. OBDDs allow for efficient algorithms using top-down…
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…
Classical planners can effectively solve very large deterministic MDPs represented in STRIPS or PDDL where states are sets of atoms over objects and relations, and lifted action schemas add or delete these atoms. This compact representation…
Data sets in the form of binary matrices are ubiquitous across scientific domains, and researchers are often interested in identifying and quantifying noteworthy structure. One approach is to compare the observed data to that which might be…
Here we present an approximate analytical theory for the relationship between a protein structure's contact matrix and the shape of its energy spectrum in amino acid sequence space. We demonstrate a dependence of the number of sequences of…
We propose a novel probabilistic dimensionality reduction framework that can naturally integrate the generative model and the locality information of data. Based on this framework, we present a new model, which is able to learn a smooth…
Representing a proof tree by a combinator term that reduces to the tree lets subtle forms of duplication within the tree materialize as duplicated subterms of the combinator term. In a DAG representation of the combinator term these…
An algebraic structure related to discrete zero curvature equations is established. It is used to give an approach for generating master symmetries of first degree for systems of discrete evolution equations and an answer to why there exist…