Uncertainty principles and signal recovery
SIAM Journal on Applied Mathematics
Lower bounds for polynomial evaluation and interpolation problems
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Note on a Lower Bound on the Linear Complexity of the Fast Fourier Transform
Journal of the ACM (JACM)
Lower Bounds for Matrix Product in Bounded Depth Circuits with Arbitrary Gates
SIAM Journal on Computing
Superconcentrators, generalizers and generalized connectors with limited depth
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
On the Complexity of Matrix Product
SIAM Journal on Computing
Lower bounds on the bounded coefficient complexity of bilinear maps
Journal of the ACM (JACM)
| Hi-index | 5.23 |
We prove a superlinear 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 [D.L. Donoho, P.B. Stark, Uncertainty principles and signal recovery, SIAM Journal of Applied Mathematics 49 (1989) 906-931] given by Tao [T. Tao, An uncertainty principle for cyclic groups of prime order, Mathematical Research Letters 12 (2005) 121-127], and a combinatorial lemma by Raz and Shpilka [R. Raz, A. Shpilka, Lower bounds for matrix product, in arbitrary circuits with bounded gates, SIAM Journal of Computing 32 (2003) 488-513]. This combination and an observation on ranks of circulant matrices, which we use to give a much shorter proof of the Donoho-Stark principle, may have other applications.