Related papers: BDDs Naturally Represent Boolean Functions, and ZD…
The concept of boolean autonomous deterministic regular asynchronous system has its origin in switching theory, the theory of modeling the switching circuits from the digital electrical engineering. The attribute boolean vaguely refers to…
Logical models have been successfully used to describe regulatory and signaling networks without requiring quantitative data. However, existing data is insufficient to adequately define a unique model, rendering the parametrization of a…
Boolean Networks (BNs) describe the time evolution of binary states using logic functions on the nodes of a network. They are fundamental models for complex discrete dynamical systems, with applications in various areas of science and…
This paper aims to construct optimal Z-complementary code set (ZCCS) with non-power-of-two (NPT) lengths to enable interference-free multicarrier code-division multiple access (MC-CDMA) systems. The existing ZCCSs with NPT lengths, which…
Relations between the decision tree complexity and various other complexity measures of Boolean functions is a thriving topic of research in computational complexity. It is known that decision tree complexity is bounded above by the cube of…
When using Bayesian networks for modelling the behavior of man-made machinery, it usually happens that a large part of the model is deterministic. For such Bayesian networks deterministic part of the model can be represented as a Boolean…
A set label disagreement function is defined over the number of variables that deviates from the dominant label. The dominant label is the value assumed by the largest number of variables within a set of binary variables. The submodularity…
Equiangular tight frames (ETFs) and biangular tight frames (BTFs) - sets of unit vectors with basis-like properties whose pairwise absolute inner products admit exactly one or two values, respectively - are useful for many applications. A…
We propose a unified view of the polarity of functions, that encompasses all specific definitions, generalizes several well-known properties and provides new results. We show that bipolar sets and bipolar functions are isomorphic lattices.…
Notes on two constructions of zero-difference balanced (ZDB) functions are made in this letter. Then ZDB functions over $\mathbb{Z}_{e}\times \prod_{i=0}^{k}{\mathbb{F}_{q_i}}$ are obtained. And it shows that all the known ZDB functions…
Bayesian network classifiers are used in many fields, and one common class of classifiers are naive Bayes classifiers. In this paper, we introduce an approach for reasoning about Bayesian network classifiers in which we explicitly convert…
We exhibit an adjunction between a category of abstract algebras of partial functions and a category of set quotients. The algebras are those atomic algebras representable as a collection of partial functions closed under relative…
The sets used to construct other mathematical objects are pure sets, which means that all of their elements are sets, which are themselves pure. One set may therefore be within another, not as an element, but as an element of an element, or…
Multidimensional combinatorial substitutions are rules that replace symbols by finite patterns of symbols in $\mathbb Z^d$. We focus on the case where the patterns are not necessarily rectangular, which requires a specific description of…
Linear diagrams are used to visualize set systems by depicting set memberships as horizontal line segments in a matrix, where each set is represented as a row and each element as a column. Each such line segment of a set is shown in a…
This is a survey paper on rainbow sets (another name for ``choice functions''). The main theme is the distinction between two types of choice functions: those having a large (in the sense of belonging to some specified filter, namely closed…
Bounded Derivation Depth property (BDD) and Finite Controllability (FC) are two properties of sets of datalog rules and tuple generating dependencies (known as Datalog +/- programs), which recently attracted some attention. We conjecture…
Abduction is a fundamental and important form of non-monotonic reasoning. Given a knowledge base explaining how the world behaves it aims at finding an explanation for some observed manifestation. In this paper we focus on propositional…
Partitioning a graph into balanced components is important for several applications. For multi-objective problems, it is useful not only to find one solution but also to enumerate all the solutions with good values of objectives. However,…
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…