Lower bounds for matrix product

Amir Shpilka*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-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(q) is at least (2.5 + 1.5/q3-1)n2-o(n2). These results improve the former results of [N. H. Bshouty, SIAM J. Comput., 18 (1989), pp. 759-765; M. Bläser, Proceedings of the 40th Annual IEEE Symposium on Foundations of Computer Science, IEEE Computer Society, Los Alamitos, CA, 1999, pp. 45-50], who proved lower bounds of 2.5n2 - o(n2).

Original languageEnglish
Pages (from-to)1185-1200
Number of pages16
JournalSIAM Journal on Computing
Volume32
Issue number5
DOIs
StatePublished - Aug 2003
Externally publishedYes

Keywords

  • Linear codes
  • Lower bounds
  • Matrix product

Fingerprint

Dive into the research topics of 'Lower bounds for matrix product'. Together they form a unique fingerprint.

Cite this