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arXiv · 2011.02303

Belief Propagation on the random $k$-SAT model

Amin Coja-Oghlan·Noëla Müller·Jean B. Ravelomanana
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Abstract

Corroborating a prediction from statistical physics, we prove that the Belief Propagation message passing algorithm approximates the partition function of the random $k$-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 $k$-SAT model at low temperature for clause/variable densities below but close to the satisfiability threshold.

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BibTeXRIS

Amin Coja-Oghlan, Noëla Müller, Jean B. Ravelomanana. 2020-11-04. Belief Propagation on the random $k$-SAT model. https://arxiv.org/abs/2011.02303

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