Lower bounds for matrix product

Research output: Contribution to journalConference articlepeer-review

Abstract

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 [3, 1] who proved lower bounds of 2.5n2 - o(n2).

Original languageEnglish
Pages (from-to)358-367
Number of pages10
JournalAnnual Symposium on Foundations of Computer Science - Proceedings
DOIs
StatePublished - 2001
Externally publishedYes
Event42nd Annual Symposium on Foundations of Computer Science - Las Vegas, NV, United States
Duration: 14 Oct 200117 Oct 2001

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