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Revisiting the cavity-method threshold for random 3-SAT
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
2019 (English)In: Physical review. E, ISSN 2470-0045, E-ISSN 2470-0053, Vol. 99, no 2, article id 022106Article in journal (Refereed) Published
Abstract [en]

A detailed Monte Carlo study of the satisfiability threshold for random 3-SAT has been undertaken. In combination with a monotonicity assumption we find that the threshold for random 3-SAT satisfies α3≤4.262. If the assumption is correct, this means that the actual threshold value for k=3 is lower than that given by the cavity method. In contrast the latter has recently been shown to give the correct value for large k. Our result thus indicate that there are distinct behaviors for k above and below some critical kc, and the cavity method may provide a correct mean-field picture for the range above kc.

Place, publisher, year, edition, pages
American Physical Society, 2019. Vol. 99, no 2, article id 022106
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:umu:diva-162509DOI: 10.1103/PhysRevE.99.022106ISI: 000458140700001PubMedID: 30934345OAI: oai:DiVA.org:umu-162509DiVA, id: diva2:1344685
Available from: 2019-08-21 Created: 2019-08-21 Last updated: 2019-08-21Bibliographically approved

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Lundow, Per-HåkanMarkström, Klas

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