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.2020.53
URN: urn:nbn:de:0030-drops-124603
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/12460/
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Galanis, Andreas ; Goldberg, Leslie Ann ; Guo, Heng ; Yang, Kuan

Counting Solutions to Random CNF Formulas

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LIPIcs-ICALP-2020-53.pdf (0.5 MB)

Abstract

We give the first efficient algorithm to approximately count the number of solutions in the random k-SAT model when the density of the formula scales exponentially with k. The best previous counting algorithm was due to Montanari and Shah and was based on the correlation decay method, which works up to densities (1+o_k(1))(2log k)/k, the Gibbs uniqueness threshold for the model. Instead, our algorithm harnesses a recent technique by Moitra to work for random formulas with much higher densities. The main challenge in our setting is to account for the presence of high-degree variables whose marginal distributions are hard to control and which cause significant correlations within the formula.

BibTeX - Entry

@InProceedings{galanis_et_al:LIPIcs:2020:12460,
  author =	{Andreas Galanis and Leslie Ann Goldberg and Heng Guo and Kuan Yang},
  title =	{{Counting Solutions to Random CNF Formulas}},
  booktitle =	{47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)},
  pages =	{53:1--53:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-138-2},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{168},
  editor =	{Artur Czumaj and Anuj Dawar and Emanuela Merelli},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/12460},
  URN =		{urn:nbn:de:0030-drops-124603},
  doi =		{10.4230/LIPIcs.ICALP.2020.53},
  annote =	{Keywords: random CNF formulas, approximate counting}
}

Keywords: random CNF formulas, approximate counting
Collection: 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)
Issue Date: 2020
Date of publication: 29.06.2020

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