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arXiv · 1712.04888

Revisiting the cavity-method threshold for random 3-SAT

P. H. Lundow·K. Markström
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Abstract

A detailed Monte Carlo-study of the satisfiability threshold for random 3-SAT has been undertaken. In combination with a monotonicity assumption we find that the threshold for random 3-SAT satisfies $α_3 \leq 4.262$. If the assumption is correct, this means that the actual threshold value for $k=3$ is lower than that given by the cavity method. In contrast the latter has recently been shown to give the correct value for large $k$. Our result thus indicate that there are distinct behaviors for $k$ above and below some critical $k_c$, and the cavity method may provide a correct mean-field picture for the range above $k_c$.

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BibTeXRIS

P. H. Lundow, K. Markström. 2018-12-20. Revisiting the cavity-method threshold for random 3-SAT. https://doi.org/10.1103/physreve.99.022106

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