Date of Original Version

6-2003

Type

Conference Proceeding

Abstract or Description

We give new upper and lower bounds on the degree of real multivariate polynomials which sign-represent Boolean functions. Our upper bounds for Boolean formulas yield the first known subexponential time learning algorithms for formulas of superconstant depth. Our lower bounds for constant-depth circuits and intersections of halfspaces are the first new degree lower bounds since 1968, improving results of Minsky and Papert. The lower bounds are proved constructively; we give explicit dual solutions to the necessary linear programs

DOI

10.1145/780542.780592

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Published In

Proceedings of the Thirty-Fifth Annual ACM Symposium on theory of Computing , 325-334.