Satisfiability threshold for random regular nae-sat

Jian Ding, Allan Sly, Nike Sun

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

19 Scopus citations


We consider the random regular κ-nae-sat problem with n variables each appearing in exactly d clauses. For all κ exceeding an absolute constant κ0, we establish explicitly the satisfiability threshold d* ≡ d*pkq. We prove that for d < d* the problem is satisfiable with high probability while for d < d* the problem is unsatisfiable with high probability. If the threshold d* lands exactly on an integer, we show that the problem is satisfiable with probability bounded away from both zero and one. This is the first result to locate the exact satisfiability threshold in a random constraint satisfaction problem exhibiting the condensation phenomenon identified by Krzakała et al. (2007). Our proof verifies the onestep replica symmetry breaking formalism for this model. We expect our methods to be applicable to a broad range of random constraint satisfaction problems and combinatorial problems on random graphs.

Original languageEnglish (US)
Title of host publicationSTOC 2014 - Proceedings of the 2014 ACM Symposium on Theory of Computing
PublisherAssociation for Computing Machinery
Number of pages9
ISBN (Print)9781450327107
StatePublished - 2014
Externally publishedYes
Event4th Annual ACM Symposium on Theory of Computing, STOC 2014 - New York, NY, United States
Duration: May 31 2014Jun 3 2014

Publication series

NameProceedings of the Annual ACM Symposium on Theory of Computing
ISSN (Print)0737-8017


Other4th Annual ACM Symposium on Theory of Computing, STOC 2014
Country/TerritoryUnited States
CityNew York, NY

All Science Journal Classification (ASJC) codes

  • Software


  • Condensation
  • Constraint satisfaction problem
  • Replica symmetry breaking
  • Satisfiability threshold
  • Survey propagation


Dive into the research topics of 'Satisfiability threshold for random regular nae-sat'. Together they form a unique fingerprint.

Cite this