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/ w (poly( n,t )) would imply learning MDNF, and thus also DNF, from equivalence queries alone. An early version of this paper appeared as Bshouty and Eiron (2001). [abs] [pdf] [ps.gz] [ps]