License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.STACS.2021.58
URN: urn:nbn:de:0030-drops-137038
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2021/13703/
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Schweitzer, Pascal ; Seebach, Constantin

Resolution with Symmetry Rule Applied to Linear Equations

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LIPIcs-STACS-2021-58.pdf (0.8 MB)

Abstract

This paper considers the length of resolution proofs when using Krishnamurthy’s classic symmetry rules. We show that inconsistent linear equation systems of bounded width over a fixed finite field ?_p with p a prime have, in their standard encoding as CNFs, polynomial length resolutions when using the local symmetry rule (SRC-II).
As a consequence it follows that the multipede instances for the graph isomorphism problem encoded as CNF formula have polynomial length resolution proofs. This contrasts exponential lower bounds for individualization-refinement algorithms on these graphs.
For the Cai-Fürer-Immerman graphs, for which Torán showed exponential lower bounds for resolution proofs (SAT 2013), we also show that already the global symmetry rule (SRC-I) suffices to allow for polynomial length proofs.

BibTeX - Entry

@InProceedings{schweitzer_et_al:LIPIcs.STACS.2021.58,
  author =	{Schweitzer, Pascal and Seebach, Constantin},
  title =	{{Resolution with Symmetry Rule Applied to Linear Equations}},
  booktitle =	{38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021)},
  pages =	{58:1--58:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-180-1},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{187},
  editor =	{Bl\"{a}ser, Markus and Monmege, Benjamin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/13703},
  URN =		{urn:nbn:de:0030-drops-137038},
  doi =		{10.4230/LIPIcs.STACS.2021.58},
  annote =	{Keywords: Logical Resolution, Symmetry Rule, Linear Equation System}
}

Keywords: Logical Resolution, Symmetry Rule, Linear Equation System
Collection: 38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021)
Issue Date: 2021
Date of publication: 10.03.2021

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