On the Inductive Inference of Real Valued Functions

Introduction The starting point for studies in inductive inference is the model of learning by example introduced by Gold [Gol67]. This is a simple model of learning algorithms that input examples of some function and produce programs that are intended to compute the function generating the examples. Learning takes place as the "correct " program must be produced after the learning algorithm has seen only finitely many examples. The functions used as input are typically (partial) recursive functions. Using traditional encoding techniques, this class of functions is rich enough to model a wide range of phenomena [AS83]. Researchers in inductive inference have used the basic model of Gold to study the effects of other parameters of the learning process such as errors tolerance, plurality of approaches, probability of success, learning via queries, etc. Herein we combine traditional studies of inductive inference and classical continuous mathematics to produce a study of learnin