Related papers: How much could we cover a set by c.e sets?
In this thesis, we develop various techniques for working with sets in machine learning. Each input or output is not an image or a sequence, but a set: an unordered collection of multiple objects, each object described by a feature vector.…
We initiate a rigorous study of computational entanglement theory, inspired by the emerging usefulness of ideas from quantum information theory in computational complexity. We define new operational computational measures of entanglement --…
In this talk we introduce several topics in combinatorial number theory which are related to groups; the topics include combinatorial aspects of covers of groups by cosets, and also restricted sumsets and zero-sum problems on abelian…
In this work we study the set size distribution estimation problem, where elements are randomly sampled from a collection of non-overlapping sets and we seek to recover the original set size distribution from the samples. This problem has…
This paper examines the completion of an w-ordered sequence of recursive definitions which on the one hand defines an increasing sequence of nested set and on the other redefines successively a numeric variable as the cardinal of the…
In most prediction and estimation situations, scientists consider various statistical models for the same problem, and naturally want to select amongst the best. Hansen et al. (2011) provide a powerful solution to this problem by the…
The potential harms of algorithmic decisions have ignited algorithmic fairness as a central topic in computer science. One of the fundamental problems in computer science is Set Cover, which has numerous applications with societal impacts,…
The purpose of this thesis is to make an analysis of the concept of Hypercomputation and of some hypermachines. This thesis is separated in three main parts. We start in the first chapter with an analysis of the concept of Classical…
Many techniques for handling missing data have been proposed in the literature. Most of these techniques are overly complex. This paper explores an imputation technique based on rough set computations. In this paper, characteristic…
Over the past two decades the field of computational science and engineering (CSE) has penetrated both basic and applied research in academia, industry, and laboratories to advance discovery, optimize systems, support decision-makers, and…
Reachability analysis, in general, is a fundamental method that supports formally-correct synthesis, robust model predictive control, set-based observers, fault detection, invariant computation, and conformance checking, to name but a few.…
Richter, Stephan, and Zhang asked whether every nonrecursive many-one degree contains a least finite-one degree. We solve this question in the negative, already within the class of computably enumerable many-one degrees. Positive answers…
In this paper we introduce the notion of $e$-computability as a method of finding the Waring rank of forms. We use this notion to find infinitely many new examples which satisfy Strassen's Conjecture.
A variant of the well-known Set Covering Problem is studied in this paper, where subsets of a collection have to be selected, and pairwise conflicts among subsets of items exist. The selection of each subset has a cost, and the inclusion of…
In this first of two papers, strong limits on the accuracy of physical computation are established. First it is proven that there cannot be a physical computer C to which one can pose any and all computational tasks concerning the physical…
In many instances in first order logic or computable algebra, classical theorems show that many problems are undecidable for general structures, but become decidable if some rigidity is imposed on the structure. For example, the set of…
For $r \in [0,1]$ we say that a set $A \subseteq \omega$ is \emph{coarsely computable at density} $r$ if there is a computable set $C$ such that $\{n : C(n) = A(n)\}$ has lower density at least $r$. Let $\gamma(A) = \sup \{r : A \hbox{ is…
In this paper, we present a novel approach for conformal prediction (CP), in which we aim to identify a set of promising prediction candidates -- in place of a single prediction. This set is guaranteed to contain a correct answer with high…
This article shows that PSPACE not equal EXP. A simple but novel proof technique has been used to separate these two classes. Whether an arbitrary Turing machine accepts an input when the running time is limited has been computed in this…
Rough set theory is a new mathematical approach to imperfect knowledge. The notion of rough sets is generalized by using an arbitrary binary relation on attribute values in information systems, instead of the trivial equality relation. The…