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An Exponential Lower Bound for Depth 3 Arithmetic Circuits (1998)
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BibTeX
@INPROCEEDINGS{Grigoriev98anexponential,
author = {Dima Grigoriev and Marek Karpinski},
title = {An Exponential Lower Bound for Depth 3 Arithmetic Circuits},
booktitle = {},
year = {1998},
pages = {577--582},
publisher = {ACM Press}
}
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Abstract
We prove the first exponential lower bound on the size of any depth 3 arithmetic circuit with unbounded fanin computing an explicit function (the determinant) over an arbitrary finite field. This answers an open problem of [N91] and [NW95] for the case of finite fields. We intepret here arithmetic circuits in the algebra of polynomials over the given field. The proof method involves a new argument on the rank of linear functions, and a group symmetry on polynomials vanishing at certain nonsingular matrices, and could be of independent interest.
Keyphrases
arithmetic circuit exponential lower bound superlinear omega ga independent interest arbitrary finite field polynomial interpolation open problem polynomial size new argument unbounded fanin arithmetic circuit unbounded fanin certain nonsingular matrix symmetric function linear function general arithmetic circuit boolean circuit proof method explicit function general arithmetic circuit size finite field group symmetry fundamental problem
