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42nd IEEE symposium on Foundations of Computer Science (FOCS?01)
Lower Bounds for Matrix Product
Las Vegas, Nevada
October 14-October 17
ISBN: 0-7695-1390-5
| ASCII Text | x | ||
| A. Shpilka, "Lower Bounds for Matrix Product," Foundations of Computer Science, IEEE Annual Symposium on, pp. 358, 42nd IEEE symposium on Foundations of Computer Science (FOCS?01), 2001. | |||
| BibTex | x | ||
| @article{ 10.1109/SFCS.2001.959910, author = {A. Shpilka}, title = {Lower Bounds for Matrix Product}, journal ={Foundations of Computer Science, IEEE Annual Symposium on}, volume = {0}, year = {2001}, isbn = {0-7695-1390-5}, pages = {358}, doi = {http://doi.ieeecomputersociety.org/10.1109/SFCS.2001.959910}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, } | |||
| RefWorks Procite/RefMan/Endnote | x | ||
| TY - CONF JO - Foundations of Computer Science, IEEE Annual Symposium on TI - Lower Bounds for Matrix Product SN - 0-7695-1390-5 SP EP A1 - A. Shpilka, PY - 2001 VL - 0 JA - Foundations of Computer Science, IEEE Annual Symposium on ER - | |||
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 3n^2 - o(n^2 ). 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 + \frac{{1.5}}{{p^3 - 1}})n^2 - o(n^2). These results improve the former results of [3, 1] who proved lower bounds of 2.5n^2 - o(n^2).
Citation:
A. Shpilka, "Lower Bounds for Matrix Product," focs, pp.358, 42nd IEEE symposium on Foundations of Computer Science (FOCS?01), 2001
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