On vanishing sums of roots of unity in polynomial calculus and sum-of-squares-Reference-Cited by-同舟云学术

On vanishing sums of roots of unity in polynomial calculus and sum-of-squares

Published:2023-11-12 Issue:2 Volume:32 Page:
ISSN:1016-3328
Container-title:computational complexity
language:en
Short-container-title:comput. complex.

Author:

Bonacina Ilario^ORCID,Galesi Nicola^ORCID,Lauria Massimo^ORCID

Abstract

AbstractWe introduce a novel take on sum-of-squares that is able to reason with complex numbers and still make use of polynomial inequalities. This proof system might be of independent interest since it allows to represent multivalued domains both with Boolean and Fourier encoding. We show degree and size lower bounds in this system for a natural generalization of knapsack: the vanishing sums of roots of unity. These lower bounds naturally apply to polynomial calculus as-well.

Funder

Universitat Politècnica de Catalunya

Publisher

Springer Science and Business Media LLC

Subject

Computational Mathematics,Computational Theory and Mathematics,General Mathematics,Theoretical Computer Science

Link

https://link.springer.com/content/pdf/10.1007/s00037-023-00242-z.pdf

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