License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.MFCS.2022.23
URN: urn:nbn:de:0030-drops-168211
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2022/16821/
Go to the corresponding LIPIcs Volume Portal

Bonacina, Ilario ; Galesi, Nicola ; Lauria, Massimo

On Vanishing Sums of Roots of Unity in Polynomial Calculus and Sum-Of-Squares

pdf-format:
LIPIcs-MFCS-2022-23.pdf (0.7 MB)

Abstract

Vanishing sums of roots of unity can be seen as a natural generalization of knapsack from Boolean variables to variables taking values over the roots of unity. We show that these sums are hard to prove for polynomial calculus and for sum-of-squares, both in terms of degree and size.

BibTeX - Entry

@InProceedings{bonacina_et_al:LIPIcs.MFCS.2022.23,
  author =	{Bonacina, Ilario and Galesi, Nicola and Lauria, Massimo},
  title =	{{On Vanishing Sums of Roots of Unity in Polynomial Calculus and Sum-Of-Squares}},
  booktitle =	{47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)},
  pages =	{23:1--23:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-256-3},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{241},
  editor =	{Szeider, Stefan and Ganian, Robert and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2022/16821},
  URN =		{urn:nbn:de:0030-drops-168211},
  doi =		{10.4230/LIPIcs.MFCS.2022.23},
  annote =	{Keywords: polynomial calculus, sum-of-squares, roots of unity, knapsack}
}

Keywords: polynomial calculus, sum-of-squares, roots of unity, knapsack
Collection: 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)
Issue Date: 2022
Date of publication: 22.08.2022

DROPS-Home | Fulltext Search | Imprint | Privacy Published by LZI