Results 1 
3 of
3
Probabilistic Limit Identification up to "Small" Sets?
"... In this paper we study limit identification of total recursive functions in the case when "small" sets of errors are allowed. Here the notion of "small" sets we formalize in a very general way, i.e.we define a notion of measure for subsets of natural numbers, and we consider as being small those set ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
In this paper we study limit identification of total recursive functions in the case when "small" sets of errors are allowed. Here the notion of "small" sets we formalize in a very general way, i.e.we define a notion of measure for subsets of natural numbers, and we consider as being small those sets, which are subsets of sets with zero measure. We study relations between classes of functions identifiable up to "small" sets for different choices of measure. In particular, we focus our attention on properties of probabilistic limit identification. We show that regardless of particular measure we always can identify a strictly larger class of functions with probability 1=(n + 1) than with probability 1=n. Besides that, for computable measures we show that, if there do not exist sets with an arbitrary small non zero measure, then identifiability of a set of functions with probability larger than 1=(n+1) implies also identifiability of the same set with probability 1=n. Otherwise (in the case when there exist sets with an arbitrary small non zero measure), we always can identify a strictly larger class of functions with probability (n+1)=(2n+1) than with probability n=(2n; 1), and identifiability with probability larger than (n +1)=(2n + 1) implies also identi ability with probability n=(2n; 1).
Learning Recursive Functions: A Survey
, 2008
"... Studying the learnability of classes of recursive functions has attracted considerable interest for at least four decades. Starting with Gold’s (1967) model of learning in the limit, many variations, modifications and extensions have been proposed. These models differ in some of the following: the m ..."
Abstract
 Add to MetaCart
Studying the learnability of classes of recursive functions has attracted considerable interest for at least four decades. Starting with Gold’s (1967) model of learning in the limit, many variations, modifications and extensions have been proposed. These models differ in some of the following: the mode of convergence, the requirements intermediate hypotheses have to fulfill, the set of allowed learning strategies, the source of information available to the learner during the learning process, the set of admissible hypothesis spaces, and the learning goals. A considerable amount of work done in this field has been devoted to the characterization of function classes that can be learned in a given model, the influence of natural, intuitive postulates on the resulting learning power, the incorporation of randomness into the learning process, the complexity of learning, among others. On the occasion of Rolf Wiehagen’s 60th birthday, the last four decades of research in that area are surveyed, with a special focus on Rolf Wiehagen’s work, which has made him one of the most influential scientists in the theory of learning recursive functions.