Belief Propagation on the random $k$-SAT model
Probability
2020-11-24 v2 Discrete Mathematics
Combinatorics
Abstract
Corroborating a prediction from statistical physics, we prove that the Belief Propagation message passing algorithm approximates the partition function of the random -SAT model well for all clause/variable densities and all inverse temperatures for which a modest absence of long-range correlations condition is satisfied. This condition is known as "replica symmetry" in physics language. From this result we deduce that a replica symmetry breaking phase transition occurs in the random -SAT model at low temperature for clause/variable densities below but close to the satisfiability threshold.
Cite
@article{arxiv.2011.02303,
title = {Belief Propagation on the random $k$-SAT model},
author = {Amin Coja-Oghlan and Noëla Müller and Jean B. Ravelomanana},
journal= {arXiv preprint arXiv:2011.02303},
year = {2020}
}