  We study the behavior of ASAT, a heuristic for solving satisfiability
problems by stochastic local search near the SAT/UNSAT transition. The
heuristic is focused, i.e. only variables in unsatisfied clauses are updated in
each step, and is significantly simpler, while similar to, walksat or Focused
Metropolis Search. We show that ASAT solves instances as large as one million
variables in linear time, on average, up to 4.21 clauses per variable for
random 3SAT. For K higher than 3, ASAT appears to solve instances at the ``FRSB
threshold'' in linear time, up to K=7.
