Related papers: How much could we cover a set by c.e sets?

Conventional theoretical machine learning studies generally assume explicitly or implicitly that there are enough or even infinitely supplied computational resources. In real practice, however, computational resources are usually limited,…

Covering-based rough set theory is an extension to classical rough set. The main purpose of this paper is to study covering rough sets from a topological point of view. The relationship among upper approximations based on topological spaces…

Transfinite set theory including the axiom of choice supplies the following basic theorems: (1) Mappings between infinite sets can always be completed, such that at least one of the sets is exhausted. (2) The real numbers can be well…

The set splittability problem is the following: given a finite collection of finite sets, does there exits a single set that contains exactly half the elements from each set in the collection? (If a set has odd size, we allow the floor or…

The goal of this paper is to announce there is a single orbit of the c.e. sets with inclusion, $\E$, such that the question of membership in this orbit is $\Sigma^1_1$-complete. This result and proof have a number of nice corollaries: the…

We study the complexity of the classification problem for countable models of set theory (ZFC). We prove that the classification of arbitrary countable models of ZFC is Borel complete, meaning that it is as complex as it can conceivably be.…

Covering theory is an important tool in representation theory of algebras, however, the results and the proofs are scattered in the literature. We give an introduction to covering theory at a level as elementary as possible.

We propose a definition of quantum computable functions as mappings between superpositions of natural numbers to probability distributions of natural numbers. Each function is obtained as a limit of an infinite computation of a quantum…

In this article we define a new reducibility based on the enumeration orders of r.e. sets.

We will explore the nature of when certain finite groups have an equal covering, and when finite groups do not. Not to be confused with the concept of a cover group, a covering of a group is a collection of proper subgroups whose…

We define E-theory for separable C*-algebras over second countable topological spaces and establish its basic properties. This includes an approximation theorem that relates the E-theory over a general space to the E-theories over finite…

The concept of ``countable set'' is attributed to Georg Cantor, who set the boundary between countable and uncountable sets in 1874. The concept of ``computable set'' arose in the study of computing models in the 1930s by the founders of…

In this paper we present a new bound obtained with the probabilistic method for the solution of the Set Covering problem with unit costs. The bound is valid for problems of fixed dimension, thus extending previous similar asymptotic…

We introduce a notion of computable randomness for infinite sequences that generalises the classical version in two important ways. First, our definition of computable randomness is associated with imprecise probability models, in the sense…

Many tasks aim to measure machine reading comprehension (MRC), often focusing on question types presumed to be difficult. Rarely, however, do task designers start by considering what systems should in fact comprehend. In this paper we make…

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…

Here it is shown that standard set theory can be interpreted in a theory about order. The ordering here is about non-extensional flat classes, i.e. classes that are not elements of classes. So, stipulating a nearly well order over all those…

We study a variant of Set Cover where each element of the universe has some demand that determines how many times the element needs to be covered. Moreover, we examine two generalizations of this problem when a set can be included multiple…

We present a new fragment of axiomatic set theory for pure sets and for the iteration of power sets within given transitive sets. It turns out that this formal system admits an interesting hierarchy of models with true membership relation…

An open (resp., closed) subset A of a topological space (X, T ) is called C-open (resp., C-closed) set if cl(A) \ A (resp., A \ int(A)) is a countable set. This paper aims to present the concept of C-open and C-closed sets. We first…