The Complexity of Tensor Rank
Computational Complexity
2024-01-11 v3
Abstract
We show that determining the rank of a tensor over a field has the same complexity as deciding the existential theory of that field. This implies earlier NP-hardness results by H{\aa}stad~\cite{H90}. The hardness proof also implies an algebraic universality result.
Cite
@article{arxiv.1612.04338,
title = {The Complexity of Tensor Rank},
author = {Marcus Schaefer and Daniel Stefankovic},
journal= {arXiv preprint arXiv:1612.04338},
year = {2024}
}
Comments
fixed error in Section 3.3