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DOI: 10.4230/LIPIcs.CCC.2020.19
On the Complexity of Modulo-q Arguments and the Chevalley - Warning Theorem

Authors: Mika Göös, Pritish Kamath, Katerina Sotiraki, and Manolis Zampetakis

Published in: LIPIcs, Volume 169, 35th Computational Complexity Conference (CCC 2020)

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.
Cite as

Mika Göös, Pritish Kamath, Katerina Sotiraki, and Manolis Zampetakis. On the Complexity of Modulo-q Arguments and the Chevalley - Warning Theorem. In 35th Computational Complexity Conference (CCC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 169, pp. 19:1-19:42, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{goos_et_al:LIPIcs.CCC.2020.19,
  author =	{G\"{o}\"{o}s, Mika and Kamath, Pritish and Sotiraki, Katerina and Zampetakis, Manolis},
  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 =	{Saraf, Shubhangi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2020.19},
  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}
}
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