Learning DNF in time

Using techniques from learning theory, we show that any s-term DNF over n variables can be computed by a polynomial threshold function of degree O(n1/3 log s). This upper bound matches, up to a logarithmic factor, the longstanding lower bound given by Minsky and Papert in their 1968 book { Perceptrons}. As a consequence of this upper bound we obtain the fastest known algorithm for learning polynomial size DNF, one of the central problems in computational learning theory.