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Electronic Colloquium on Computational Complexity

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Reports tagged with tensor:
TR09-007 | 9th January 2009
Eli Ben-Sasson, Michael Viderman

Tensor Products of Weakly Smooth Codes are Robust

We continue the study of {\em robust} tensor codes and expand the
class of base codes that can be used as a starting point for the
construction of locally testable codes via robust two-wise tensor
products. In particular, we show that all unique-neighbor expander
codes and all locally correctable codes, ... more >>>

TR12-068 | 25th May 2012
Manuel Arora, Gábor Ivanyos, Marek Karpinski, Nitin Saxena

Deterministic Polynomial Factoring and Association Schemes

The problem of finding a nontrivial factor of a polynomial $f(x)$ over a finite field $\mathbb{F}_q$ has many known efficient, but randomized, algorithms. The deterministic complexity of this problem is a famous open question even assuming the generalized Riemann hypothesis (GRH). In this work we improve the state of the ... more >>>

TR18-086 | 23rd April 2018
Joseph Swernofsky

Tensor Rank is Hard to Approximate

Revisions: 1

We prove that approximating the rank of a 3-tensor to within a factor of $1 + 1/1852 - \delta$, for any $\delta > 0$, is NP-hard over any finite field. We do this via reduction from bounded occurrence 2-SAT.

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