Erich Kaltofen, Victor Shoup
Mathematics of Computation
Paper
Lower bounds for polynomial evaluation and interpolation problems
Abstract
We show that there is a set of points p1, p2, . . . , pn such that any arithmetic circuit of depth d for polynomial evaluation (or interpolation) at these points has size Ω (n log n/log(2 + d/log n)). Moreover, for circuits of sub-logarithmic depth d, we obtain a lower bound of Ω(dn1+1/d) on its size.
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