Oracles and queries that are sufficient for exact learning (extended abstract)
Nader H. Bshouty, Richard Cleve, Sampath Kannan, Christino Tamon · 1994
We show that the class of all circuits is exactly learnable in randomized expected polynomial-time using subset and 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 Σ3p-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 Λ-V-Λ formulas (by the work of Angluin, this is optimal in the sense that the hypothesis class cannot be reduced to depth-2 DNF formulas.