Complete analysis of BP and SP guided decimation on random k-SAT

Complete the rigorous analysis of Belief Propagation Guided Decimation and Survey Propagation Guided Decimation on random k-SAT for every clause length k≥3, in analogy with the established results for random k-XORSAT.

Background

The paper rigorously analyzes Belief Propagation Guided Decimation on random k-XORSAT, exploiting the half-integrality of its messages and the equivalence between Belief Propagation and Warning Propagation. The authors explain that these structural features are absent for random k-SAT, where messages are generally not half-integral and the phase-transition formulas become infinite-dimensional variational problems.

They note that rigorous results are available for random k-SAT only when k is sufficiently large, and that Survey Propagation Guided Decimation has been proposed as a potentially stronger alternative. Although a negative result is known beyond the shattering threshold for sufficiently large k, a complete treatment for all k≥3 remains unresolved.