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.2020.28
URN: urn:nbn:de:0030-drops-125804
URL: https://drops.dagstuhl.de/opus/volltexte/2020/12580/
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de Rezende, Susanna F. ; Nordström, Jakob ; Risse, Kilian ; Sokolov, Dmitry

Exponential Resolution Lower Bounds for Weak Pigeonhole Principle and Perfect Matching Formulas over Sparse Graphs

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LIPIcs-CCC-2020-28.pdf (0.6 MB)


Abstract

We show exponential lower bounds on resolution proof length for pigeonhole principle (PHP) formulas and perfect matching formulas over highly unbalanced, sparse expander graphs, thus answering the challenge to establish strong lower bounds in the regime between balanced constant-degree expanders as in [Ben-Sasson and Wigderson '01] and highly unbalanced, dense graphs as in [Raz '04] and [Razborov '03, '04]. We obtain our results by revisiting Razborov’s pseudo-width method for PHP formulas over dense graphs and extending it to sparse graphs. This further demonstrates the power of the pseudo-width method, and we believe it could potentially be useful for attacking also other longstanding open problems for resolution and other proof systems.

BibTeX - Entry

@InProceedings{derezende_et_al:LIPIcs:2020:12580,
  author =	{Susanna F. de Rezende and Jakob Nordstr{\"o}m and Kilian Risse and Dmitry Sokolov},
  title =	{{Exponential Resolution Lower Bounds for Weak Pigeonhole Principle and Perfect Matching Formulas over Sparse Graphs}},
  booktitle =	{35th Computational Complexity Conference (CCC 2020)},
  pages =	{28:1--28:24},
  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/2020/12580},
  URN =		{urn:nbn:de:0030-drops-125804},
  doi =		{10.4230/LIPIcs.CCC.2020.28},
  annote =	{Keywords: proof complexity, resolution, weak pigeonhole principle, perfect matching, sparse graphs}
}

Keywords: proof complexity, resolution, weak pigeonhole principle, perfect matching, sparse graphs
Collection: 35th Computational Complexity Conference (CCC 2020)
Issue Date: 2020
Date of publication: 17.07.2020


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