### Learnability of Enumerable Classes of Recursive Functions from ``Typical'' Examples

**Author: Jochen Nessel**.

**Source: ***Lecture Notes in Artificial Intelligence* Vol. 1720,
1999, 264 - 275.

The paper investigates whether it is possible to learn every
enumerable classes of recursive functions from ``typical''
examples. ``Typical'' means, there is a computable
family of finite sets, such that
for each function in the class there is *one* set of examples
that can be used in *any* suitable hypothesis space for
this class of functions.
As it will turn out, there are enumerable classes of recursive functions
that are not learnable from ``typical'' examples.
The learnable classes are characterized.

The results are proved within an abstract model of learning from
examples, introduced by Freivalds, Kinber and Wiehagen. Finally, the
results are interpreted and possible connections of this
theoretical work to the situation in real life classrooms are
pointed out.

©Copyright 1999 Springer-Verlag