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Belief Propagation Guided Decimation on Random k-XORSAT

Authors Arnab Chatterjee, Amin Coja-Oghlan , Mihyun Kang , Lena Krieg, Maurice Rolvien, Gregory B. Sorkin

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ACM Subject Classification
  • Mathematics of computing → Probability and statistics
  • Mathematics of computing → Combinatoric problems
  • Mathematics of computing → Combinatorics
  • Mathematics of computing → Probabilistic algorithms
Keywords
  • random k-XORSAT
  • belief propagation
  • decimation process
  • random matrices

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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].

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Arnab Chatterjee, Amin Coja-Oghlan, Mihyun Kang, Lena Krieg, Maurice Rolvien, and Gregory B. Sorkin. Belief Propagation Guided Decimation on Random k-XORSAT. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 47:1-47:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.ICALP.2025.47

Author Details

Arnab Chatterjee
  • Faculty of Computer Science, TU Dortmund, Germany
Amin Coja-Oghlan
  • Faculty of Computer Science, TU Dortmund, Germany
Mihyun Kang
  • Institute of Discrete Mathematics, TU Graz, Austria
Lena Krieg
  • Faculty of Computer Science, TU Dortmund, Germany
Maurice Rolvien
  • Department of Informatics, University of Hamburg, Germany
Gregory B. Sorkin
  • Department of Mathematics, The London School of Economics and Political Science, UK

Funding

  • Coja-Oghlan, Amin: supported by DFG CO 646/3, DFG CO 646/5 and DFG CO 646/6.
  • Kang, Mihyun: supported by Austrian Science Fund (FWF) 10.55776/I6502.
  • Krieg, Lena: supported by DFG CO 646/3.
  • Rolvien, Maurice: supported by DFG Research Group ADYN (FOR 2975) under grant DFG 411362735.

References

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