Implementation of linear maps with circulant matrices via modulo 2 rectifier circuits of bounded depth
Data Structures and Algorithms
2013-05-21 v1
Abstract
In the present note we show that for any positive integer k an arbitrary Boolean circulant matrix can be implemented via modulo 2 rectifier circuit of depth 2k-1 and complexity O(n^{1+1/k}), and also via circuit of depth 2k and complexity O(n^{1+1/k} log^{-1/k} n).
Cite
@article{arxiv.1305.4389,
title = {Implementation of linear maps with circulant matrices via modulo 2 rectifier circuits of bounded depth},
author = {Igor S. Sergeev},
journal= {arXiv preprint arXiv:1305.4389},
year = {2013}
}
Comments
3 pages, in English; 4 pages, in Russian