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

For large clause-to-variable ratios, 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 andVilenchik (2006 Complete convergence of message passing algorithms for some satisfiability problems Proc. Random 2006 pp 339-50), 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.