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We show that a DNF with terms of size at most <italic>d</italic> can be approximated by a function with at most <italic>d<supscrpt>O(d log 1/ε)</supscrpt>)</italic>non zero Fourier coefficients such that the expected error squared, with respect to the uniform distribution, is at most ε. This property is used to derive a learning algorithm for DNF, under the uniform distribution.The learning algorithm uses queries and learns, with respect to the uniform distribution, a DNF with terms of size at most <italic>d</italic> in time polynomial in <italic>n</italic> and <italic>d<supscrpt>O(d log 1/egr;)</supscrpt></italic>. The interesting implications are for the case when ε is constant. In this case our algorithm learns a DNF with a polynomial number of terms in time <italic>n<supscrpt>O(log log n)</supscrpt></italic>, and a DNF with terms of size at most <italic>O(log n/log log n)</italic> in polynomial time.

An O(n log log n ) learning algorithm for DNF under the uniform distribution

An O(n ^{log log n} ) learning algorithm for DNF under the uniform distribution