On the computational equivalence of co-NP refutations of a matrix being a P-matrix
Abstract
A P-matrix is a square matrix such that all principal submatrices of have positive determinant. Such matrices appear naturally in instances of the linear complementarity problem, where these are precisely the matrices for which the corresponding linear complementarity problem has a unique solution for any input vector. Testing whether or not a square matrix is a P-matrix is co-NP complete, so while it is possible to exhibit polynomially-sized witnesses for the fact that a matrix is not a P-matrix, it is believed that there is no efficient way to prove that a given matrix is a P-matrix. We will show that several well known witnesses for the fact that a matrix is not a P-matrix are computationally equivalent, so that we are able to convert between them in polynomial time, answering a question raised in arXiv:1811.03841 .
Cite
@article{arxiv.2110.05644,
title = {On the computational equivalence of co-NP refutations of a matrix being a P-matrix},
author = {Spencer Gordon and Kevin Shu},
journal= {arXiv preprint arXiv:2110.05644},
year = {2021}
}