Binary Determinantal Complexity
Computational Complexity
2017-04-11 v2
Abstract
We prove that for writing the 3 by 3 permanent polynomial as a determinant of a matrix consisting only of zeros, ones, and variables as entries, a 7 by 7 matrix is required. Our proof is computer based and uses the enumeration of bipartite graphs. Furthermore, we analyze sequences of polynomials that are determinants of polynomially sized matrices consisting only of zeros, ones, and variables. We show that these are exactly the sequences in the complexity class of constant free polynomially sized (weakly) skew circuits.
Keywords
Cite
@article{arxiv.1410.8202,
title = {Binary Determinantal Complexity},
author = {Jesko Hüttenhain and Christian Ikenmeyer},
journal= {arXiv preprint arXiv:1410.8202},
year = {2017}
}
Comments
10 pages, C source code for the computation available as ancillary files