Belief Propagation Guided Decimation on Random k-XORSAT
Abstract
We analyse the performance of Belief Propagation Guided Decimation, a physics-inspired message passing algorithm, on the random -XORSAT problem. Specifically, we derive an explicit threshold up to which the algorithm succeeds with a strictly positive probability that we compute explicitly, but beyond which the algorithm with high probability fails to find a satisfying assignment. In addition, we analyse a thought experiment called the decimation process for which we identify a (non-) reconstruction and a condensation phase transition. The main results of the present work confirm physics predictions from [RTS: J. Stat. Mech. 2009] that link the phase transitions of the decimation process with the performance of the algorithm, and improve over partial results from a recent article [Yung: Proc. ICALP 2024].
Keywords
Cite
@article{arxiv.2501.17657,
title = {Belief Propagation Guided Decimation on Random k-XORSAT},
author = {Arnab Chatterjee and Amin Coja-Oghlan and Mihyun Kang and Lena Krieg and Maurice Rolvien and Gregory B. Sorkin},
journal= {arXiv preprint arXiv:2501.17657},
year = {2025}
}