Learning decision lists and trees with equivalence-queries

Abstract

This paper is concerned with the model of learning with equivalence-queries which was introduced by Angluin in [2]. We show that decision lists and decision trees of bounded rank are polynomially learnable in this model. If there are N base functions, then N ² queries are sufficient for learning lists. For learning trees of rank r, (1+o(1))N ^2r queries are sufficient. We also investigate the problem of learning a shortest representation of a target decision list. Let k-DL denote the class of decision lists with boolean terms of maximal length k as base functions. We show that shortest representations for lists from 1-DL can be learned efficiently. The corresponding questions for k≥2 are open, although we are able to show some related (but weaker) results. For instance, we present an algorithm which efficiently learns shortest representations of boolean 2-CNF or 2-DNF formulas.