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The Condensation Phase Transition in the Regular k-SAT Model

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Abstract

Much of the recent work on phase transitions in discrete structures has been inspired by ingenious but non-rigorous approaches from physics. The physics predictions typically come in the form of distributional fixed point problems that mimic Belief Propagation, a message passing algorithm. In this paper we show how the Belief Propagation calculation can be turned into a rigorous proof of such a prediction, namely the existence and location of a condensation phase transition in the regular k-SAT model.

BibTeX - Entry

@InProceedings{bapst_et_al:LIPIcs:2016:6645,
  author =	{Victor Bapst and Amin Coja-Oghlan},
  title =	{{The Condensation Phase Transition in the Regular k-SAT Model}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2016)},
  pages =	{22:1--22:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-018-7},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{60},
  editor =	{Klaus Jansen and Claire Mathieu and Jos{\'e} D. P. Rolim and Chris Umans},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2016/6645},
  URN =		{urn:nbn:de:0030-drops-66452},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2016.22},
  annote =	{Keywords: random k-SAT, phase transitions, Belief Propagation, condensation}
}

Keywords: random k-SAT, phase transitions, Belief Propagation, condensation
Seminar: Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2016)
Issue date: 2016
Date of publication: 2016


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