文章基本信息

标题：Counting Solutions to Random CNF Formulas
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作者：Andreas Galanis ; Leslie Ann Goldberg ; Heng Guo 等
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2020
卷号：168
页码：53:1-53:14
DOI：10.4230/LIPIcs.ICALP.2020.53
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：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.
关键词：random CNF formulas; approximate counting