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.2020.3
URN: urn:nbn:de:0030-drops-125552
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Scheder, Dominik ; Talebanfard, Navid

Super Strong ETH Is True for PPSZ with Small Resolution Width

LIPIcs-CCC-2020-3.pdf (0.6 MB)


We construct k-CNFs with m variables on which the strong version of PPSZ k-SAT algorithm, which uses resolution of width bounded by O(√{log log m}), has success probability at most 2^{-(1-(1 + ε)2/k)m} for every ε > 0. Previously such a bound was known only for the weak PPSZ algorithm which exhaustively searches through small subformulas of the CNF to see if any of them forces the value of a given variable, and for strong PPSZ the best known previous upper bound was 2^{-(1-O(log(k)/k))m} (Pudlák et al., ICALP 2017).

BibTeX - Entry

  author =	{Dominik Scheder and Navid Talebanfard},
  title =	{{Super Strong ETH Is True for PPSZ with Small Resolution Width}},
  booktitle =	{35th Computational Complexity Conference (CCC 2020)},
  pages =	{3:1--3:12},
  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 =		{},
  URN =		{urn:nbn:de:0030-drops-125552},
  doi =		{10.4230/LIPIcs.CCC.2020.3},
  annote =	{Keywords: k-SAT, PPSZ, Resolution}

Keywords: k-SAT, PPSZ, Resolution
Collection: 35th Computational Complexity Conference (CCC 2020)
Issue Date: 2020
Date of publication: 17.07.2020

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