P-Sufficient Statistics for PAC Learning k-term-DNF Formulas through Enumeration

Working in the framework of PAC-learning theory, we present special statistics for accomplishing in polynomial time proper learning of DNF boolean formulas having a fixed number of monomials. Our statistics turn out to be near sufficient for a large family of distribution laws—that we call butterfly distributions. We develop a theory of most powerful learning for analyzing the performance of learning algorithms, with particular reference to trade-offs between power and computational costs. Focusing attention on sample and time complexity, we prove that our algorithm works as efficiently as the best algorithms existing in the literature — while the latter only take care of subclasses of our family of distributions. Abbreviated title. P-sufficient statistics for learning k-term DNF.