The Log-Rank conjecture and low degree polynomials

Authors:
Paul Valiant
Affiliations:
Stanford University, P.O. Box 17308, Stanford, CA
Venue:
Information Processing Letters
Year:
2004

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Abstract

We formulate several questions concerning the intersections of sets of Boolean roots of low degree polynomials. Two of these questions we show to be equivalent to the Log-Rank Conjecture from communication complexity. We further exhibit a slightly stronger formulation which we prove to be false, and a weaker formulation which we prove to be true. These results suggest a possible new approach to the Log-Rank Conjecture.