Prior work of Gavryushkin, Khoussainov, Jain and Stephan investigated what algebraic structures can be realised in worlds given by a positive (= recursively enumerable) equivalence relation which partitions the natural numbers into infinitely many classes. The present investigates infinite one-one numbered enumerable (r.e.) families such relations asks how choice impacts learnability properties...

Learnability has always been one of the most central problems in learning theory. Most previous studies on this issue were based on the assumption that the samples are drawn independently and identically according to an underlying (unknown) distribution. The i.i.d. assumption, however, does not hold in many real applications. In this paper, we study the learnability of problems where the sample...

This work continues the study of the relationship between sample compression schemes and statistical learning, which has been mostly investigated within the framework of binary classification. The central theme of this work is establishing equivalences between learnability and compressibility, and utilizing these equivalences in the study of statistical learning theory. We begin with the settin...

The learnability of quantum neural network, which includes its convergence behavior in optimization and the ability to efficiently learn classes computationally hard concepts is investigated, providing theoretical guidance for developing advanced protocols NISQ era.

The problem of learning the solution space of an unknown formula has been studied in multiple embodiments in computational learning theory. In this article, we study a family of such learning problems; this family contains, for each relational structure, the problem of learning the solution space of an unknown conjunctive query evaluated on the structure. A progression of results aimed to class...

We investigate upper bounds on the sample-size sufficient for ‘solid’ learnability with respect to a probability distribution. We obtain a sufficient condition for feasible (polynomially bounded) sample-size bounds for distributionspecific (solid) learnability.

The ability to predict, or at least recognize, the state of the world that an action brings about, is a central feature of autonomous agents. We propose, herein, a formal framework within which we investigate whether this ability can be autonomously learned. The framework makes explicit certain premises that we contend are central in such a learning task: (i) slow sensors may prevent the sensin...

This paper investigates the learnability by positive examples in the sense of Gold of Pregroup Grammars. In a first part, Pregroup Grammars are presented and a new parsing strategy is proposed. Then, theoretical learnability and non-learnability results for subclasses of Pregroup Grammars are proved. In the last two parts, we focus on learning Pregroup Grammars from a special kind of input call...