  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.
