Combinatorial results on the complexity of teaching and learning

Abstract

Some recent work in computational learning theory has focused on the complexity of teaching by examples. In this paper we study two combinatorial measures expressing the number of examples needed to teach any consistent learner, called teaching dimension and universal teaching dimension. We give a general lower bound on the teaching dimension that improves previous results, relate the teaching complexity measures to some learning complexity measures and combinatorial parameters, and compute bounds on the teaching dimension(s) of natural Boolean concept classes. We also observe an analogy between the teaching model and some problems in the fault detection research, and make use of some results achieved within that framework.