Learning DNF in Time 2^{O(n^{1/3})}.
A. Klivans and R. Servedio.
Journal of Computer and System Sciences 68(2), 2004, pp. 303-318 (special issue for STOC 2001).
Preliminary version in 33rd Annual Symposium on Theory of Computing (STOC), 2001, pp. 258-265.
Best Student Paper award, STOC 2001.

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 $O(n^{1/3} \log s)$. This upper bound matches, up to a logarithmic factor, the longstanding lower bound given by Minsky and Papert in their 1968 book {\em 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.

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Postscript or pdf of journal version