@inproceedings{be123e90fd174f048222c184a33c45db,
title = "Satisfiability threshold for random regular nae-sat",
abstract = "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 Krzaka{\l}a 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.",
keywords = "Condensation, Constraint satisfaction problem, Replica symmetry breaking, Satisfiability threshold, Survey propagation",
author = "Jian Ding and Allan Sly and Nike Sun",
year = "2014",
doi = "10.1145/2591796.2591862",
language = "English (US)",
isbn = "9781450327107",
series = "Proceedings of the Annual ACM Symposium on Theory of Computing",
publisher = "Association for Computing Machinery",
pages = "814--822",
booktitle = "STOC 2014 - Proceedings of the 2014 ACM Symposium on Theory of Computing",
note = "4th Annual ACM Symposium on Theory of Computing, STOC 2014 ; Conference date: 31-05-2014 Through 03-06-2014",
}