Abstract
We show that randomly generated c log(n)-DNF formula can be learned exactly in probabilistic polynomial time using randomly generated examples. Our notion of randomly generated is with respect to a uniform distribution.To prove this we extend the concept of well behaved c log(n)-Monotone DNF formulae to c log(n)-DNF formulae, and show that almost every DNF formula is well-behaved, and that there exists a probabilistic polynomial time algorithm that exactly learns all well behaved c log(n)-DNF formula. This is the first algorithm that properly learns (non-monotone) DNF with a polynomial number of terms from random examples alone.
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