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Track A: Algorithms, Complexity and Games

DOI: 10.4230/LIPIcs.ICALP.2025.47

Belief Propagation Guided Decimation on Random k-XORSAT

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

Published in: LIPIcs, Volume 334, 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)

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)

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@InProceedings{chatterjee_et_al:LIPIcs.ICALP.2025.47,
  author =	{Chatterjee, Arnab and Coja-Oghlan, Amin and Kang, Mihyun and Krieg, Lena and Rolvien, Maurice and Sorkin, Gregory B.},
  title =	{{Belief Propagation Guided Decimation on Random k-XORSAT}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{47:1--47:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2025.47},
  URN =		{urn:nbn:de:0030-drops-234248},
  doi =		{10.4230/LIPIcs.ICALP.2025.47},
  annote =	{Keywords: random k-XORSAT, belief propagation, decimation process, random matrices}
}

@InProceedings{chatterjee_et_al:LIPIcs.ICALP.2025.47,
  author =	{Chatterjee, Arnab and Coja-Oghlan, Amin and Kang, Mihyun and Krieg, Lena and Rolvien, Maurice and Sorkin, Gregory B.},
  title =	{{Belief Propagation Guided Decimation on Random k-XORSAT}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{47:1--47:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2025.47},
  URN =		{urn:nbn:de:0030-drops-234248},
  doi =		{10.4230/LIPIcs.ICALP.2025.47},
  annote =	{Keywords: random k-XORSAT, belief propagation, decimation process, random matrices}
}

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Belief Propagation Guided Decimation on Random k-XORSAT

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