Monotone separations for constant degree polynomials

Authors:
Pavel Hrubeš;Amir Yehudayoff
Affiliations:
School of Mathematics, Institute for Advanced Study, Princeton, NJ, United States;School of Mathematics, Institute for Advanced Study, Princeton, NJ, United States
Venue:
Information Processing Letters
Year:
2009

Citing 3
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Abstract

We prove a separation between monotone and general arithmetic formulas for polynomials of constant degree. We give an example of a polynomial C in n variables and degree k which is computable by a homogeneous arithmetic formula of size O(k^2n^2), but every monotone formula computing C requires size (n/k^c)^@W^(^l^o^g^k^), with c@?(0,1). Since the upper bound is achieved by a homogeneous arithmetic formula, we also obtain a separation between monotone and homogeneous formulas, for polynomials of constant degree.