Related papers: Classifying the Arithmetical Complexity of Teachin…

We relate the computational complexity of finite strings to universal representations of their underlying symmetries. First, Boolean functions are classified using the universal covering topologies of the circuits which enumerate them. A…

This paper takes a computational learning theory approach to a problem of linear systems identification. It is assumed that input signals have only a finite number k of frequency components, and systems to be identified have dimension no…

The influence of class orderings in the evaluation of incremental learning has received very little attention. In this paper, we investigate the impact of class orderings for incrementally learned classifiers. We propose a method to compute…

This chapter presents a brief review of complexity research in mathematics education. We argue how research on complexity, as it pertains to mathematics education, can be viewed as an epistemological discourse, an historical discourse, a…

We introduce a new framework for a descriptive complexity approach to arithmetic computations. We define a hierarchy of classes based on the idea of counting assignments to free function variables in first-order formulae. We completely…

We use algebraic geometry to study matrix rigidity, and more generally, the complexity of computing a matrix-vector product, continuing a study initiated by Kumar, et. al. We (i) exhibit many non-obvious equations testing for (border)…

We compute the degree complexity of a family of birational mappings of the plane with high order singularities.

We study the classical and parameterized complexity of computing the positive non-clashing teaching dimension of a set of concepts, that is, the smallest number of examples per concept required to successfully teach an intelligent learner…

We study the complexity of the model checking problem, for fixed model A, over certain fragments L of first-order logic. These are sometimes known as the expression complexities of L. We obtain various complexity classification theorems for…

This contribution investigates the computational complexity of simulating linear ordinary differential equations (ODEs) on digital computers. We provide an exact characterization of the complexity blowup for a class of ODEs of arbitrary…

Theories of classification distinguish classes with some good structure theorem from those for which none is possible. Some classes (dense linear orders, for instance) are non-classifiable in general, but are classifiable when we consider…

Most classical results in circuit complexity theory concern circuits over the Boolean domain. Besides their simplicity and the ease of comparing different languages, the actual architecture of computers is also an important motivating…

Decomposition and abstraction is an essential component of computational thinking, yet it is not always emphasized in introductory programming courses. In addition, as generative AI further reduces the focus on syntax and increases the…

In this paper, we study three matching problems all of which came up quite recently in the field of machine teaching. The cost of a matching is defined in such a way that, for some formal model of teaching, it equals (or bounds) the number…

We prove that every online learnable class of functions of Littlestone dimension $d$ admits a learning algorithm with finite information complexity. Towards this end, we use the notion of a globally stable algorithm. Generally, the…

We present consistent algorithms for multiclass learning with complex performance metrics and constraints, where the objective and constraints are defined by arbitrary functions of the confusion matrix. This setting includes many common…

Classification of ordinal data is one of the most important tasks of relation learning. In this thesis a novel framework for ordered classes is proposed. The technique reduces the problem of classifying ordered classes to the standard…

In this paper, based on results of exact learning, test theory, and rough set theory, we study arbitrary infinite families of concepts each of which consists of an infinite set of elements and an infinite set of subsets of this set called…

The nature of concept learning is a core question in cognitive science. Theories must account for the relative difficulty of acquiring different concepts by supervised learners. For a canonical set of six category types, two distinct…

Defect prediction is crucial for software quality assurance and has been extensively researched over recent decades. However, prior studies rarely focus on data complexity in defect prediction tasks, and even less on understanding the…