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.2020.19
URN: urn:nbn:de:0030-drops-125712
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/12571/
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Göös, Mika ; Kamath, Pritish ; Sotiraki, Katerina ; Zampetakis, Manolis

On the Complexity of Modulo-q Arguments and the Chevalley - Warning Theorem

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LIPIcs-CCC-2020-19.pdf (0.9 MB)

Abstract

We study the search problem class PPA_q defined as a modulo-q analog of the well-known polynomial parity argument class PPA introduced by Papadimitriou (JCSS 1994). Our first result shows that this class can be characterized in terms of PPA_p for prime p.
Our main result is to establish that an explicit version of a search problem associated to the Chevalley - Warning theorem is complete for PPA_p for prime p. This problem is natural in that it does not explicitly involve circuits as part of the input. It is the first such complete problem for PPA_p when p ≥ 3.
Finally we discuss connections between Chevalley-Warning theorem and the well-studied short integer solution problem and survey the structural properties of PPA_q.

BibTeX - Entry

@InProceedings{gs_et_al:LIPIcs:2020:12571,
  author =	{Mika G{\"o}{\"o}s and Pritish Kamath and Katerina Sotiraki and Manolis Zampetakis},
  title =	{{On the Complexity of Modulo-q Arguments and the Chevalley - Warning Theorem}},
  booktitle =	{35th Computational Complexity Conference (CCC 2020)},
  pages =	{19:1--19:42},
  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 =		{https://drops.dagstuhl.de/opus/volltexte/2020/12571},
  URN =		{urn:nbn:de:0030-drops-125712},
  doi =		{10.4230/LIPIcs.CCC.2020.19},
  annote =	{Keywords: Total NP Search Problems, Modulo-q arguments, Chevalley - Warning Theorem}
}

Keywords: Total NP Search Problems, Modulo-q arguments, Chevalley - Warning Theorem
Collection: 35th Computational Complexity Conference (CCC 2020)
Issue Date: 2020
Date of publication: 17.07.2020

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