TCS-TR-A-10-49

Date: Fri Dec 17 21:02:47 2010

Title: On the Amount of Nonconstructivity in the Inductive Inference of Recursive Functions

Authors: Rūsiņš Freivalds and Thomas Zeugmann

Contact:

First name: Thomas
Last name: Zeugmann
Address: Division of Computer Science Hokkaido University N-14, W-9 Sapporo 060-0814, Japan
Email: thomas@ist.hokudai.ac.jp

Abstract. Nonconstructive proofs are a powerful mechanism in mathematics. Furthermore, nonconstructive computations by various types of machines and automata have been considered by e.g., Karp and Lipton (1982) and Freivalds (2009). They allow to regard more complicated algorithms from the viewpoint of much more primitive computational devices. The amount of nonconstructivity is a quantitative characterization of the distance between types of computational devices with respect to solving a specific problem.

In the present paper, the amount of nonconstructivity in learning of recursive functions is studied. Different learning types are compared with respect to the amount of nonconstructivity needed to learn whole class of general recursive functions. Upper and lower bounds for the amount of nonconstructivity needed are proved.