Christian Cachin, Klaus Kursawe, et al.
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
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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