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Lower bounds for matrix product

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1 Author(s)
Shpilka, A. ; Inst. of Comput. Sci., Hebrew Univ., Jerusalem, Israel

We prove lower bounds on the number of product gates in bilinear and quadratic circuits that compute the product of two n × 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 × n matrices over GF(2) is at least 3n2 o(n2). 2. We show that the number of product gates in any bilinear circuit that computes the product of two n × n matrices over GF(p) is at least (2.5 + 1.5/p3-1)n2 - o(n2). These results improve the former results of N.H. Bshouty (1997) and M. Blaser (1999) who proved lower bounds of 2.5n2 o(n2).

Published in:

Foundations of Computer Science, 2001. Proceedings. 42nd IEEE Symposium on

Date of Conference:

8-11 Oct. 2001

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