The decimation process in random k-SAT
  Let F be a uniformly distributed random k-SAT formula with n variables and m clauses. Non-rigorous statistical mechanics ideas have inspired a message passing algorithm called Belief Propagation Guided Decimation for finding satisfying assignments of F. This algorithm can be viewed as an attempt at implementing a certain thought experiment that we call the Decimation Process. In this paper we identify a variety of phase transitions in the decimation process and link these phase transitions to the performance of the algorithm. 
Amin Coja-Oghlan, Angelica Y. Pachon-Pinzon
math.CO cs.DM math.PR