Learning DNFs and Circuits Using Teaching Assistants

In this paper we consider the complexity of learning monotone DNF formulae and Boolean circuits in an exact learning model called the teaching assistant model. This model, introduced in one of our earlier works, uses teaching assistant classes for classifying learning problems. Teaching assistant classes are a learning-theoretic analog of complexity classes. We show that monotone DNFs are learnable using a teaching assistant in the class SPP. On the other hand, Boolean circuits and general DNFs are not learnable using an SPP teaching assistant unless \(\mbox{\rm NP}\subseteq \mbox{\rm SPP}\). We also show that learnability of Boolean circuits with an assistant in the class NP will improve the Karp-Lipton collapse result to PNP.

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