Sufficient conditions for convergence of the survey propagation algorithm

Message propagation algorithms are very effective at finding satisfying assignments for SAT instances, and hard regions of a random SAT have become narrower. However, message propagation algorithms do not always converge for some random SAT instances. Unfortunately, a rigorous theoretical proof of this phenomenon is still lacking. The survey propagation (SP) algorithm is very effective at solving SAT instances, and a theoretical analysis of SP is very important in designing other message passing algorithms. Through this study, we derived the sufficient conditions for convergence of SP with extending message [0,~1] to message $(-\infty,\infty)$. Finally, the experiment results show that the conditions for the convergence of SP are very effective in random 3-SAT instances.