The Number of Solutions for Random Regular NAE-SAT

Allan Sly, Nike Sun, Yumeng Zhang

Research output: Chapter in Book/Report/Conference proceedingConference contribution

5 Scopus citations

Abstract

Recent 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.

Original languageEnglish (US)
Title of host publicationProceedings - 57th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2016
PublisherIEEE Computer Society
Pages724-731
Number of pages8
ISBN (Electronic)9781509039333
DOIs
StatePublished - Dec 14 2016
Externally publishedYes
Event57th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2016 - New Brunswick, United States
Duration: Oct 9 2016Oct 11 2016

Publication series

NameProceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS
Volume2016-December
ISSN (Print)0272-5428

Other

Other57th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2016
CountryUnited States
CityNew Brunswick
Period10/9/1610/11/16

All Science Journal Classification (ASJC) codes

  • Computer Science(all)

Keywords

  • Condensation transition
  • Free energy
  • One-step replica symmetry breaking
  • Random constraint satisfaction problem
  • Replica symmetry
  • Satisfiability threshold

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  • Cite this

    Sly, A., Sun, N., & Zhang, Y. (2016). The Number of Solutions for Random Regular NAE-SAT. In Proceedings - 57th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2016 (pp. 724-731). [7782987] (Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS; Vol. 2016-December). IEEE Computer Society. https://doi.org/10.1109/FOCS.2016.82