Belief Propagation guided decimation on random 1 k-XORSAT

We analyse the performance of Belief Propagation Guided Decimation, a physics-inspired message 18 passing algorithm, on the random k-XORSAT problem. Specifically, we derive an explicit threshold 19 up to which the algorithm succeeds with a strictly positive probability Ω(1) that we compute 20 explicitly, but beyond which the algorithm with high probability fails to find a satisfying assignment. 21 In addition, we analyse a thought experiment called the decimation process for which we identify a 22 (non-) reconstruction and a condensation phase transition. The main results of the present work 23 confirm physics predictions from [Ricci-Tersenghi and Semerjian: J. Stat. Mech. 2009] that link the 24 phase transitions of the decimation process with the performance of the algorithm, and improve 25 over partial results from a recent article [Yung: Proc. ICALP 2024].