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The Complexity of Tensor Rank

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arxiv 1612.04338 v3 pith:YCZ276KK submitted 2016-12-13 cs.CC

Marcus Schaefer , Daniel Stefankovic This is my paper · ORCID
classification cs.CC
keywords complexityfieldimpliesranktensoralgebraiccitedeciding
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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.

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  1. Optimal Curve Straightening is $\exists\mathbb{R}$-Complete

    cs.CG 2019-08 conditional novelty 6.0 of 10

    Optimal curve straightening to a target vertex count is ∃R-complete, and isotopy realization spaces of curves are universal up to homotopy equivalence.

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