Learning Read-Once Functions Using Subcube Identity Queries (1007.1073v1)

Abstract: We consider the problem of exact identification for read-once functions over arbitrary Boolean bases. We introduce a new type of queries (subcube identity ones), discuss its connection to previously known ones, and study the complexity of the problem in question. Besides these new queries, learning algorithms are allowed to use classic membership ones. We present a technique of modeling an equivalence query with a polynomial number of membership and subcube identity ones, thus establishing (under certain conditions) a polynomial upper bound on the complexity of the problem. We show that in some circumstances, though, equivalence queries cannot be modeled with a polynomial number of subcube identity and membership ones. We construct an example of an infinite Boolean basis with an exponential lower bound on the number of membership and subcube identity queries required for exact identification. We prove that for any finite subset of this basis, the problem remains polynomial.