Weizmann Logo
ECCC
Electronic Colloquium on Computational Complexity

Under the auspices of the Computational Complexity Foundation (CCF)

Login | Register | Classic Style



REPORTS > DETAIL:

Paper:

TR01-060 | 23rd August 2001 00:00

Lower bounds for matrix product

RSS-Feed




TR01-060
Authors: Amir Shpilka
Publication: 3rd September 2001 11:46
Downloads: 1127
Keywords: 


Abstract:

We prove lower bounds on the number of product gates in bilinear
and quadratic circuits that
compute the product of two $n \times n$ matrices over finite fields.
In particular we obtain the following results:

1. We show that the number of product gates in any bilinear
(or quadratic) circuit
that computes the product of two $n \times n$ matrices over $GF(2)$ is at
least $3 n^2 - o(n^2)$.

2. We show that the number of product gates in any bilinear circuit
that computes the product of two $n \times n$ matrices over $GF(p)$ is at
least $(2.5 + \frac{1.5}{p^3 -1})n^2 -o(n^2)$.

These results improve the former results of Bshouty (89) and Blaser
(99) who proved lower bounds of $2.5 n^2 - o(n^2)$.



ISSN 1433-8092 | Imprint