# Knottedness is in NP, modulo GRH

@article{Kuperberg2011KnottednessII,
title={Knottedness is in NP, modulo GRH},
author={Greg Kuperberg},
journal={ArXiv},
year={2011},
volume={abs/1112.0845}
}
• G. Kuperberg
• Published 5 December 2011
• Mathematics, Computer Science
• ArXiv
Given a tame knot K presented in the form of a knot diagram, we show that the problem of determining whether K is knotted is in the complexity class NP, assuming the generalized Riemann hypothesis (GRH). In other words, there exists a polynomial-length certificate that can be verified in polynomial time to prove that K is non-trivial. GRH is not needed to believe the certificate, but only to find a short certificate. This result complements the result of Hass, Lagarias, and Pippenger that…

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