Survey propagation is a powerful technique from statistical physics that has
been applied to solve the 3-SAT problem both in principle and in practice. We
give, using only probability arguments, a common derivation of survey
propagation, belief propagation and several interesting hybrid methods. We then
present numerical experiments which use WSAT (a widely used random-walk based
SAT solver) to quantify the complexity of the 3-SAT formulae as a function of
their parameters, both as randomly generated and after simplification, guided
by survey propagation. Some properties of WSAT which have not previously been
reported make it an ideal tool for this purpose -- its mean cost is
proportional to the number of variables in the formula (at a fixed ratio of
clauses to variables) in the easy-SAT regime and slightly beyond, and its
behavior in the hard-SAT regime appears to reflect the underlying structure of
the solution space that has been predicted by replica symmetry-breaking
arguments. An analysis of the tradeoffs between the various methods of search
for satisfying assignments shows WSAT to be far more powerful that has been
appreciated, and suggests some interesting new directions for practical
algorithm development.Comment: 8 pages, 5 figure