A nonlinear lower bound for constant depth arithmetical circuits via the discrete uncertainty principle

Abstract

We prove a super-linear lower bound on the size of a bounded depth bilinear arithmetical circuit computing cyclic convolution. Our proof uses the strengthening of the Donoho-Stark uncertainty principle [DS89] given by Tao [Tao05], and a combinatorial lemma by Raz and Shpilka [RS03]. This combination and an observation on ranks of circulant matrices, which… (More)
DOI: 10.1016/j.tcs.2008.09.029

Topics

Cite this paper

@article{Jansen2008ANL, title={A nonlinear lower bound for constant depth arithmetical circuits via the discrete uncertainty principle}, author={Maurice J. Jansen and Kenneth W. Regan}, journal={Theor. Comput. Sci.}, year={2008}, volume={409}, pages={617-622} }