License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CCC.2020.38
URN: urn:nbn:de:0030-drops-125900
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Potechin, Aaron

Sum of Squares Bounds for the Ordering Principle

LIPIcs-CCC-2020-38.pdf (0.6 MB)


In this paper, we analyze the sum of squares hierarchy (SOS) on the ordering principle on n elements (which has N = Θ(n²) variables). We prove that degree O(√nlog(n)) SOS can prove the ordering principle. We then show that this upper bound is essentially tight by proving that for any ε > 0, SOS requires degree Ω(n^(1/2 - ε)) to prove the ordering principle.

BibTeX - Entry

  author =	{Aaron Potechin},
  title =	{{Sum of Squares Bounds for the Ordering Principle}},
  booktitle =	{35th Computational Complexity Conference (CCC 2020)},
  pages =	{38:1--38:37},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-156-6},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{169},
  editor =	{Shubhangi Saraf},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-125900},
  doi =		{10.4230/LIPIcs.CCC.2020.38},
  annote =	{Keywords: sum of squares hierarchy, proof complexity, ordering principle}

Keywords: sum of squares hierarchy, proof complexity, ordering principle
Collection: 35th Computational Complexity Conference (CCC 2020)
Issue Date: 2020
Date of publication: 17.07.2020

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