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.STACS.2016.15
URN: urn:nbn:de:0030-drops-57164
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2016/5716/
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Beyersdorff, Olaf ; Chew, Leroy ; Mahajan, Meena ; Shukla, Anil

Are Short Proofs Narrow? QBF Resolution is not Simple

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Abstract

The groundbreaking paper 'Short proofs are narrow - resolution made simple' by Ben-Sasson and Wigderson (J. ACM 2001) introduces what is today arguably the main technique to obtain resolution lower bounds: to show a lower bound for the width of proofs. Another important measure for resolution is space, and in their fundamental work, Atserias and Dalmau (J. Comput. Syst. Sci. 2008) show that space lower bounds again can be obtained via width lower bounds.

Here we assess whether similar techniques are effective for resolution calculi for quantified Boolean formulas (QBF). A mixed picture emerges. Our main results show that both the relations between size and width as well as between space and width drastically fail in Q-resolution, even in its weaker tree-like version. On the other hand, we obtain positive results for the expansion-based resolution systems Forall-Exp+Res and IR-calc, however only in the weak tree-like models.

Technically, our negative results rely on showing width lower bounds together with simultaneous upper bounds for size and space. For our positive results we exhibit space and width-preserving simulations between QBF resolution calculi.

BibTeX - Entry

@InProceedings{beyersdorff_et_al:LIPIcs:2016:5716,
  author =	{Olaf Beyersdorff and Leroy Chew and Meena Mahajan and Anil Shukla},
  title =	{{Are Short Proofs Narrowl QBF Resolution is not Simple}},
  booktitle =	{33rd Symposium on Theoretical Aspects of Computer Science (STACS 2016)},
  pages =	{15:1--15:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-001-9},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{47},
  editor =	{Nicolas Ollinger and Heribert Vollmer},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2016/5716},
  URN =		{urn:nbn:de:0030-drops-57164},
  doi =		{10.4230/LIPIcs.STACS.2016.15},
  annote =	{Keywords: proof complexity, QBF, resolution, lower bound techniques, simulations}
}

Keywords: proof complexity, QBF, resolution, lower bound techniques, simulations
Collection: 33rd Symposium on Theoretical Aspects of Computer Science (STACS 2016)
Issue Date: 2016
Date of publication: 16.02.2016

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