Learning monotone DNF from a teacher that almost does not answer membership queries

Abstract

We present results concerning the learning of Monotone DNF (MDNF) from Incomplete Membership Queries and Equivalence Queries. Our main result is a new algorithm that allows efficient learning of MDNF using Equivalence Queries and Incomplete Membership Queries with probability of p = 1 - 1/poly(n, t) of failing. Our algorithm is expected to make O((tn/1 - p)2) queries, when learning a MDNF formula with t terms over n variables. Note that this is polynomial for any failure probability p = 1 - 1/poly(n, t). The algorithm's running time is also polynomial in t, n, and 1/(1 - p). In a sense this is the best possible, as learning with p = 1 - 1/ω(poly(n, t)) would imply learning MDNF, and thus also DNF, from equivalence queries alone.