Belief Propagation Guided Decimation on random 1 k-XORSAT

Chatterjee, Arnab, Coja-oghlan, Amin, Kang, Mihyun, Krieg, Lena, Rolvien, Maurice and Sorkin, Gregory B. ORCID: 0000-0003-4935-7820 (2025) Belief Propagation Guided Decimation on random 1 k-XORSAT. In: Censor-Hillel, Keren, Grandoni, Fabrizio, Ouaknine, Joël and Puppis, Gabriele, (eds.) 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs) (334). Schloss Dagstuhl - Leibniz-Zentrum für Informatik. ISBN 9783959773720

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Abstract

We analyse the performance of Belief Propagation Guided Decimation, a physics-inspired message passing algorithm, on the random k-XORSAT problem. Specifically, we derive an explicit threshold up to which the algorithm succeeds with a strictly positive probability Ω(1) 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 [Ricci-Tersenghi and Semerjian: 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].

Item Type:	Book Section
Additional Information:	© 2025 The Author(s)
Divisions:	Mathematics
Subjects:	Q Science > QA Mathematics
Date Deposited:	03 Jun 2025 13:51
Last Modified:	15 Jul 2025 13:21
URI:	http://eprints.lse.ac.uk/id/eprint/128298

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