### On the inductive inference of recursive real-valued functions

**Authors: Kalvis Apsitis, Setsuo Arikawa, Rusins Freivalds, Eiju Hirowatari and
Carl H. Smith**

**Source: ***Theoretical Computer Science* Vol. **219**, No. 1/2,
1999, 3 - 17.

**Abstract.**
We combine traditional studies of inductive inference and classical continuous
mathematics to produce a study of learning real-valued functions. We consider two
possible ways to model the learning by example of functions with domain and range
the real numbers. The first approach considers functions as represented by
computable analytic functions. The second considers arbitrary computable functions
of recursive real numbers. In each case we find natural examples of learnable
classes of functions and unlearnable classes of functions.

©Copyright 1999, Elsevier Science.