Can rare SAT formulas be easily recognized? On the efficiency of message passing algorithms for K-SAT at large clause-to-variable ratios
Abstract
For large clause-to-variable ratio, typical K-SAT instances drawn from the uniform distribution have no solution. We argue, based on statistical mechanics calculations using the replica and cavity methods, that rare satisfiable instances from the uniform distribution are very similar to typical instances drawn from the so-called planted distribution, where instances are chosen uniformly between the ones that admit a given solution. It then follows, from a recent article by Feige, Mossel and Vilenchik, that these rare instances can be easily recognized (in O(log N) time and with probability close to 1) by a simple message-passing algorithm.
Cite
@article{arxiv.cs/0609101,
title = {Can rare SAT formulas be easily recognized? On the efficiency of message passing algorithms for K-SAT at large clause-to-variable ratios},
author = {Fabrizio Altarelli and Remi Monasson and Francesco Zamponi},
journal= {arXiv preprint arXiv:cs/0609101},
year = {2015}
}
Comments
8 pages of text and 7 of appendices; updated to take into account comments received on the first version; to be published on J.Phys.A:Math.Gen