# The number of solutions for random regular NAE-SAT

## Author(s): Sly, Allan M.; Sun, Nike; Zhang, Yumeng

To refer to this page use: http://arks.princeton.edu/ark:/88435/pr1k41h
DC FieldValueLanguage
dc.contributor.authorSly, Allan M.-
dc.contributor.authorSun, Nike-
dc.contributor.authorZhang, Yumeng-
dc.date.accessioned2019-04-05T19:48:49Z-
dc.date.available2019-04-05T19:48:49Z-
dc.date.issued2016en_US
dc.identifier.citationSly, Allan, Sun, Nike, Zhang, Yumeng. (2016). The number of solutions for random regular NAE-SAT. 2016 IEEE 57TH ANNUAL SYMPOSIUM ON FOUNDATIONS OF COMPUTER SCIENCE (FOCS), 724 - 731. doi:10.1109/FOCS.2016.82en_US
dc.identifier.issn0272-5428-
dc.identifier.urihttp://arks.princeton.edu/ark:/88435/pr1k41h-
dc.description.abstractRecent work has made substantial progress in understanding the transitions of random constraint satisfaction problems (CSPs). In particular, for several of these models, the exact satisfiability threshold has been rigorously determined, confirming predictions from the statistical physics literature. Here we revisit one of these models, random regular NAE-SAT: knowing the satisfiability threshold, it is natural to study, in the satisfiable regime, the number of solutions in a typical instance. We prove here that these solutions have a well-defined free energy (limiting exponential growth rate), with explicit value matching the one-step replica symmetry breaking prediction. The proof develops new techniques for analyzing a certain “survey propagation model” associated to this problem. We believe that these methods may be applicable in a wide class of related problems.en_US
dc.format.extent724 - 731en_US
dc.language.isoen_USen_US
dc.relation.ispartof2016 IEEE 57TH ANNUAL SYMPOSIUM ON FOUNDATIONS OF COMPUTER SCIENCE (FOCS)en_US
dc.rightsAuthor's manuscripten_US
dc.titleThe number of solutions for random regular NAE-SATen_US
dc.typeConference Articleen_US
dc.identifier.doidoi:10.1109/FOCS.2016.82-
pu.type.symplectichttp://www.symplectic.co.uk/publications/atom-terms/1.0/conference-proceedingen_US

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