Characterizing propagation methods for boolean satisfiability

Abstract. Iterative algorithms such as Belief Propagation and Survey Propagation can handle some of the largest randomly-generated satisfiability problems (SAT) created to this point. But they can make inaccurate estimates or fail to converge on instances whose underlying constraint graphs contain small loops–a particularly strong concern with structured problems. More generally, their behavior is only wellunderstood in terms of statistical physics on a specific underlying model. Our alternative characterization of propagation algorithms presents them as value and variable ordering heuristics whose operation can be codified in terms of the Expectation Maximization (EM) method. Besides explaining failure to converge in the general case, understanding the equivalence between Propagation and EM yields new versions of such algorithms. When these are applied to SAT, such an understanding even yields a slight modification that guarantees convergence.