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For large clause-to-variable ratio, typical K-SAT instances drawn from theuniform distribution have no solution. We argue, based on statistical mechanicscalculations using the replica and cavity methods, that rare satisfiableinstances from the uniform distribution are very similar to typical instancesdrawn from the so-called planted distribution, where instances are chosenuniformly between the ones that admit a given solution. It then follows, from arecent article by Feige, Mossel and Vilenchik, that these rare instances can beeasily recognized (in O(log N) time and with probability close to 1) by asimple message-passing algorithm.Comment: 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.Ge

Can rare SAT formulae be easily recognized? On the efficiency of message-passing algorithms forK-SAT at large clause-to-variable ratios