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.2019.18
URN: urn:nbn:de:0030-drops-108403
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2019/10840/
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de Rezende, Susanna F. ; Nordström, Jakob ; Meir, Or ; Robere, Robert

Nullstellensatz Size-Degree Trade-offs from Reversible Pebbling

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LIPIcs-CCC-2019-18.pdf (0.5 MB)

Abstract

We establish an exactly tight relation between reversible pebblings of graphs and Nullstellensatz refutations of pebbling formulas, showing that a graph G can be reversibly pebbled in time t and space s if and only if there is a Nullstellensatz refutation of the pebbling formula over G in size t+1 and degree s (independently of the field in which the Nullstellensatz refutation is made). We use this correspondence to prove a number of strong size-degree trade-offs for Nullstellensatz, which to the best of our knowledge are the first such results for this proof system.

BibTeX - Entry

@InProceedings{derezende_et_al:LIPIcs:2019:10840,
  author =	{Susanna F. de Rezende and Jakob Nordstr{\"o}m and Or Meir and Robert Robere},
  title =	{{Nullstellensatz Size-Degree Trade-offs from Reversible Pebbling}},
  booktitle =	{34th Computational Complexity Conference (CCC 2019)},
  pages =	{18:1--18:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-116-0},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{137},
  editor =	{Amir Shpilka},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2019/10840},
  URN =		{urn:nbn:de:0030-drops-108403},
  doi =		{10.4230/LIPIcs.CCC.2019.18},
  annote =	{Keywords: proof complexity, Nullstellensatz, pebble games, trade-offs, size, degree}
}

Keywords: proof complexity, Nullstellensatz, pebble games, trade-offs, size, degree
Collection: 34th Computational Complexity Conference (CCC 2019)
Issue Date: 2019
Date of publication: 16.07.2019

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