Work

The random $k$-SAT Gibbs uniqueness threshold revisited

Year: 2025

Type: preprint

Abstract: We prove that for any $k\geq3$ for clause/variable ratios up to the Gibbs uniqueness threshold of the corresponding Galton-Watson tree, the number of satisfying assignments of random $k$-SAT formulas is given by the `replica symmetric solution' predicted by physics methods [Monasson, Zecchina: Phys. Rev. Lett. (1996)]. Furthermore, while the Gibbs uniqueness threshold is still not known precisely for any $k\geq3$, we derive new lower bounds on this threshold that improve over prior work [Montanari and Shah: SODA (2007)].The improvement is significant particularly for small $k$.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2506.01359

Authors: Chatterjee, Arnab, Coja-Oghlan, Amin, Greenhill, Catherine, Pfenninger, Vincent, Rolvien, Maurice, Zakharov, Pavel, Zampetakis, Kostas

Language: English

Topic: Constraint Satisfaction and Optimization

Subfield: Computer Networks and Communications

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funders: Deutsche Forschungsgemeinschaft, Austrian Science Fund, Australian Research Council

Awards: G2464290484, G5514198786, Probabilistic methods for complex discrete structures, G7401965855

OpenAlex ID: W4414896337

Cites:

Cited by:

Related to: