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The decimation process in random k-SAT (1102.3145v1)
Published 15 Feb 2011 in math.CO, cs.DM, and math.PR
Abstract: 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.