TCS-TR-A-13-68

Date: Thu Oct 24 01:33:31 2013

Title: Active Learning of Classes of Recursive Functions by Ultrametric Algorithms

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. We study active learning of classes of recursive functions by asking value queries about the target function ƒ, where ƒ is from the target class. That is, the query is a natural number x, and the answer to the query is ƒ(x). The complexity measure in this paper is the worst-case number of queries asked. We prove that for some classes of recursive functions ultrametric active learning algorithms can achieve the learning goal by asking significantly fewer queries than deterministic, probabilistic, and even nondeterministic active learning algorithms. This is the first ever example of a problem, where ultrametric algorithms have advantages over nondeterministic algorithms.