Learning recursive functions: A survey

Authors: Thomas Zeugmann and Sandra Zilles

Source: Theoretical Computer Science, Vol. 397, Issues 1-3, 2008, 4-56.
(Special Issue Forty Years of Inductive Inference: Dedicated to the 60th Birthday of Rolf Wiehagen)

Abstract. 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.


Keywords: Inductive inference; Recursive functions; Recursion theory; Complexity theory; Computable numberings; Algorithmic learning


©Copyright 2008, Elsevier Science B.V.