Abstract

We show that the class of all circuits is exactly learnable in randomized expected polynomial time using weak subset and weak superset queries. This is a consequence of the following result which we consider to be of independent interest: circuits are exactly learnable in randomized expected polynomial time with equivalence queries and the aid of an NP-oracle. We also show that circuits are exactly learnable in deterministic polynomial time with equivalence queries and a \Sigma 3 -oracle. The hypothesis class for the above learning algorithms is the class of circuits of larger---but polynomially related---size. Also, the algorithms can be adapted to learn the class of DNF formulas with hypothesis class consisting of depth-3 -- formulas (by the work of Angluin [A90], this is optimal in the sense that the hypothesis class cannot be reduced to DNF formulas, i.e. depth-2 - formulas).

Citations