Abstract

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 Papertin 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.

Citations