Simulation of complicated queries by membership queries

Abstract

In this paper, we consider the following type of learning: a teacher has some set, which is called a (target) concept, in his mind, and a learner tries to obtain the representation of the concept by asking queries on it to the teacher. This type of learning is called learning via queries or query learning. The main issue in the query learning is to develop an efficient learner's strategy -- a query learning algorithm -- for a given concept class. Recently researchers have proposed polynomial time query learning algorithms for several concept classes [Ang87, Ang88, BR87, Ish90, Sak88]. Most of those learning algorithms are using complicated queries such as "equivalence query" or "superset query"; however, in some applications, we may not be able to assume a teacher who can answer to such complicated queries and thus need a learning algorithm that asks only simple queries such as "membership query". In this paper we will show that one can approximately simulate complicated queries in polynomial time by using only membership queries.