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.ICALP.2016.57
URN: urn:nbn:de:0030-drops-62266
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2016/6226/
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Berkholz, Christoph ; Nordström, Jakob

Supercritical Space-Width Trade-Offs for Resolution

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LIPIcs-ICALP-2016-57.pdf (0.5 MB)

Abstract

We show that there are CNF formulas which can be refuted in resolution in both small space and small width, but for which any small-width resolution proof must have space exceeding by far the linear worst-case upper bound. This significantly strengthens the space-width trade-offs in [Ben-Sasson 2009], and provides one more example of trade-offs in the "supercritical" regime above worst case recently identified by [Razborov 2016]. We obtain our results by using Razborov’s new hardness condensation technique and combining it with the space lower bounds in [Ben-Sasson and Nordström 2008].

BibTeX - Entry

@InProceedings{berkholz_et_al:LIPIcs:2016:6226,
  author =	{Christoph Berkholz and Jakob Nordstr{\"o}m},
  title =	{{Supercritical Space-Width Trade-Offs for Resolution}},
  booktitle =	{43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)},
  pages =	{57:1--57:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-013-2},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{55},
  editor =	{Ioannis Chatzigiannakis and Michael Mitzenmacher and Yuval Rabani and Davide Sangiorgi},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2016/6226},
  URN =		{urn:nbn:de:0030-drops-62266},
  doi =		{10.4230/LIPIcs.ICALP.2016.57},
  annote =	{Keywords: Proof complexity, resolution, space, width, trade-offs, supercritical}
}

Keywords: Proof complexity, resolution, space, width, trade-offs, supercritical
Collection: 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)
Issue Date: 2016
Date of publication: 23.08.2016

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