On the Uniform Learnability of Approximations to Non-Recursive Functions

Abstract. Blum and Blum (1975) showed that a class B of suitable recursive approximations to the halting problem is reliably EX-learnable. These investigations are carried on by showing that B is neither in NUM nor robustly EX-learnable. Since the definition of the class B is quite natural and does not contain any self-referential coding, B serves as an example that the notion of robustness for learning is quite more restrictive than intended. Moreover, variants of this problem obtained by approximating any given recursively enumerable set A instead of the halting problem K are studied. All corresponding function classes U(A) are still EX-inferable but may fail to be reliably EX-learnable, for example if A is non-high and hypersimple. Additionally, it is proved that U(A) is neither in NUM nor robustly EX-learnable provided A is part of a recursively inseparable pair, A is simple but not hypersimple or A is neither recursive nor high. These results provide more evidence that there is s...

• Type: Conference
• Year: 1999
• Where: ALT
• Authors: Frank Stephan, Thomas Zeugmann
• Keywords: ALT 1999, Halting Problem, Machine Learning, Recursively Enumerable Set, Suitable Recursive Approximations