The decimation process in random k-SAT

Let Φ be a uniformly distributed random k-SAT formula with n variables and m clauses. Nonrigorous statistical mechanics ideas have inspired a message passing algorithm called belief propagation guided decimation for finding satisfying assignments of Φ. 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.