Related papers: Functions Definable by Numerical Set-Expressions
The present work proposes and discusses the category of supported sets which provides a uniform foundation for nominal sets of various kinds, such as those for equality symmetry, for the order symmetry, and renaming sets. We show that all…
The paper presents two equivalent definitions of answer sets for logic programs with aggregates. These definitions build on the notion of unfolding of aggregates, and they are aimed at creating methodologies to translate logic programs with…
Let $\cal R$ be either the Grothendieck semiring (semiring with multiplication) of complex algebraic varieties, or the Grothendieck ring of these varieties, or the Grothendieck ring localized by the class of the complex affine line. We…
Recursive relational specifications are commonly used to describe the computational structure of formal systems. Recent research in proof theory has identified two features that facilitate direct, logic-based reasoning about such…
We study the degrees of selector functions related to the degrees in which a rigid computable structure is relatively computably categorical. It is proved that for some structures such degrees can be represented as the unions of upper cones…
Boolean functions and binary arithmetic operations are central to standard computing paradigms. Accordingly, many advances in computing have focused upon how to make these operations more efficient as well as exploring what they can…
Classification of Non-linear Boolean functions is a long-standing problem in the area of theoretical computer science. In this paper, effort has been made to achieve a systematic classification of all n-variable Boolean functions, where…
The functional interpretation is a systematic, syntactic method for transforming certain non-constructive proofs into constructive proofs with explicit bounds. We illustrate the interpretation by working through a concrete, fairly simple…
In Combinatorics Stirling numbers may be defined in several ways. One such definition is given in [1], where an extensive consideration of Stirling numbers is presented. In this paper an alternative definition of Stirling numbers of both…
Representations of quantum computations are almost always based on a tensor product $\otimes$-structure. This coincides with what we are able to execute in our experiments, as well as what we observe in Nature, but it makes certain familiar…
For a given function from a set to itself, we can define a directed graph called the functional graph, where the vertices are the elements of the set, and the edges are all the pairs of inputs and outputs for the function. In this article…
In this paper we introduce an enclosure of the numerical range of a class of rational operator functions. In contrast to the numerical range the presented enclosure can be computed exactly in the infinite dimensional case as well as in the…
This paper proposes a new approach to defining and expressing algorithms: the notion of {\it task logical} algorithms. This notion allows the user to define an algorithm for a task $T$ as a set of agents who can collectively perform $T$.…
Our goal is to define an algebraic language for reasoning about non-deterministic computations. Towards this goal, we introduce an algebra of string-to-string transductions. Specifically, it is an algebra of partial functions on words over…
The number of ordered factorizations and the number of recursive divisors are two related arithmetic functions that are recursively defined. But it is hard to construct explicit representations of these functions. Taking advantage of their…
The question of obtaining well-defined criteria for multiple criteria decision making problems is well-known. One of the approaches dealing with this question is the concept of nonessential objective function. A certain objective function…
It is known that any rational abstract numeration system is faithfully, and effectively, represented by an N-rational series. A simple proof of this result is given which yields a representation of this series which in turn allows a simple…
We call a finite family of activation functions superexpressive if any multivariate continuous function can be approximated by a neural network that uses these activations and has a fixed architecture only depending on the number of input…
Grainy numbers are defined as tuples of bits. They form a lattice where the meet and the join operations are an addition and a multiplication. They may be substituted for the real numbers in the definition of fuzzy sets. The aim is to…
An integer additive set-indexer is defined as an injective function $f:V(G)\rightarrow 2^{\mathbb{N}_0}$ such that the induced function $g_f:E(G) \rightarrow 2^{\mathbb{N}_0}$ defined by $g_f (uv) = f(u)+ f(v)$ is also injective. An integer…