Population Protocols with Unordered Data

Authors Michael Blondin , François Ladouceur

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Author Details

Michael Blondin
  • Department of Computer Science, Université de Sherbrooke, Canada
François Ladouceur
  • Department of Computer Science, Université de Sherbrooke, Canada


We thank Manuel Lafond for his ideas and feedback in the early phase of our research. We further thank the anonymous reviewers for their comments and insightful suggestions.

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Michael Blondin and François Ladouceur. Population Protocols with Unordered Data. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 115:1-115:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


Population protocols form a well-established model of computation of passively mobile anonymous agents with constant-size memory. It is well known that population protocols compute Presburger-definable predicates, such as absolute majority and counting predicates. In this work, we initiate the study of population protocols operating over arbitrarily large data domains. More precisely, we introduce population protocols with unordered data as a formalism to reason about anonymous crowd computing over unordered sequences of data. We first show that it is possible to determine whether an unordered sequence from an infinite data domain has a datum with absolute majority. We then establish the expressive power of the "immediate observation" restriction of our model, namely where, in each interaction, an agent observes another agent who is unaware of the interaction.

Subject Classification

ACM Subject Classification
  • Theory of computation → Distributed computing models
  • Theory of computation → Automata over infinite objects
  • Population protocols
  • unordered data
  • colored Petri nets


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  1. Dana Angluin, James Aspnes, Zoë Diamadi, Michael J. Fischer, and René Peralta. Computation in networks of passively mobile finite-state sensors. Distributed Computing, 18(4):235-253, 2006. URL: https://doi.org/10.1007/s00446-005-0138-3.
  2. Dana Angluin, James Aspnes, David Eisenstat, and Eric Ruppert. The computational power of population protocols. Distributed Computing, 20(4):279-304, 2007. URL: https://doi.org/10.1007/s00446-007-0040-2.
  3. Gregor Bankhamer, Petra Berenbrink, Felix Biermeier, Robert Elsässer, Hamed Hosseinpour, Dominik Kaaser, and Peter Kling. Population protocols for exact plurality consensus: How a small chance of failure helps to eliminate insignificant opinions. In Proc. 41^st ACM Symposium on Principles of Distributed Computing (PODC), pages 224-234, 2022. URL: https://doi.org/10.1145/3519270.3538447.
  4. Petra Berenbrink, Felix Biermeier, Christopher Hahn, and Dominik Kaaser. Loosely-stabilizing phase clocks and the adaptive majority problem. In Proc. 1^st Symposium on Algorithmic Foundations of Dynamic Networks (SAND), pages 7:1-7:17, 2022. Google Scholar
  5. Petra Berenbrink, Robert Elsässer, Tom Friedetzky, Dominik Kaaser, Peter Kling, and Tomasz Radzik. A population protocol for exact majority with O(log^5/3 n) stabilization time and Θ(log n) states. In Proc. 32^nd International Symposium on Distributed Computing (DISC), pages 10:1-10:18, 2018. URL: https://doi.org/10.4230/LIPIcs.DISC.2018.10.
  6. Michael Blondin, Javier Esparza, Blaise Genest, Martin Helfrich, and Stefan Jaax. Succinct population protocols for Presburger arithmetic. In Proc. 37^th International Symposium on Theoretical Aspects of Computer Science (STACS), pages 40:1-40:15, 2020. URL: https://doi.org/10.4230/LIPIcs.STACS.2020.40.
  7. Michael Blondin, Javier Esparza, Stefan Jaax, and Philipp J. Meyer. Towards efficient verification of population protocols. Formal Methods in System Design (FMSD), 57(3):305-342, 2021. URL: https://doi.org/10.1007/s10703-021-00367-3.
  8. Mikołaj Bojańczyk, Claire David, Anca Muscholl, Thomas Schwentick, and Luc Segoufin. Two-variable logic on data words. ACM Transactions on Computational Logic (TOCL), 12(4):27:1-27:26, 2011. URL: https://doi.org/10.1145/1970398.1970403.
  9. Benedikt Bollig, Patricia Bouyer, and Fabian Reiter. Identifiers in registers - describing network algorithms with logic. In Proc. 22^nd International Conference on Foundations of Software Science and Computation Structures (FoSSaCS), pages 115-132, 2019. URL: https://doi.org/10.1007/978-3-030-17127-8_7.
  10. Benedikt Bollig, Fedor Ryabinin, and Arnaud Sangnier. Reachability in distributed memory automata. In Proc. 29^th EACSL Annual Conference on Computer Science Logic (CSL), pages 13:1-13:16, 2021. URL: https://doi.org/10.4230/LIPIcs.CSL.2021.13.
  11. Robert S. Boyer and J. Strother Moore. Mjrty: A fast majority vote algorithm. In Automated Reasoning: Essays in Honor of Woody Bledsoe, 1991. Google Scholar
  12. Philipp Czerner, Roland Guttenberg, Martin Helfrich, and Javier Esparza. Fast and succinct population protocols for Presburger arithmetic. In Proc. 1^st Symposium on Algorithmic Foundations of Dynamic Networks (SAND), pages 11:1-11:17, 2022. URL: https://doi.org/10.4230/LIPIcs.SAND.2022.11.
  13. Giorgio Delzanno, Arnaud Sangnier, and Riccardo Traverso. Adding data registers to parameterized networks with broadcast. Fundamenta Informaticae, 143(3-4):287-316, 2016. URL: https://doi.org/10.3233/FI-2016-1315.
  14. David Doty, Mahsa Eftekhari, Leszek Gasieniec, Eric E. Severson, Przemyslaw Uznanski, and Grzegorz Stachowiak. A time and space optimal stable population protocol solving exact majority. In Proc. 62^nd IEEE Annual Symposium on Foundations of Computer Science (FOCS), pages 1044-1055, 2021. URL: https://doi.org/10.1109/FOCS52979.2021.00104.
  15. Javier Esparza, Pierre Ganty, Jérôme Leroux, and Rupak Majumdar. Verification of population protocols. Acta Informatica, 54(2):191-215, 2017. URL: https://doi.org/10.1007/s00236-016-0272-3.
  16. Leszek Gasieniec, David D. Hamilton, Russell Martin, Paul G. Spirakis, and Grzegorz Stachowiak. Deterministic population protocols for exact majority and plurality. In Proc. 20^th International Conference on Principles of Distributed Systems (OPODIS), pages 14:1-14:14, 2016. URL: https://doi.org/10.4230/LIPIcs.OPODIS.2016.14.
  17. Utkarsh Gupta, Preey Shah, S. Akshay, and Piotr Hofman. Continuous reachability for unordered data Petri nets is in PTime. In Proc. 22^nd International Conference on Foundations of Software Science and Computation Structures (FoSSaCS), pages 260-276, 2019. URL: https://doi.org/10.1007/978-3-030-17127-8_15.
  18. Piotr Hofman, Slawomir Lasota, Ranko Lazic, Jérôme Leroux, Sylvain Schmitz, and Patrick Totzke. Coverability trees for Petri nets with unordered data. In Proc. 19^th International Conference on Foundations of Software Science and Computation Structures (FoSSaCS), pages 445-461, 2016. URL: https://doi.org/10.1007/978-3-662-49630-5_26.
  19. Piotr Hofman, Jérôme Leroux, and Patrick Totzke. Linear combinations of unordered data vectors. In Proc. 32^nd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS), pages 1-11, 2017. URL: https://doi.org/10.1109/LICS.2017.8005065.
  20. Michael Kaminski and Nissim Francez. Finite-memory automata. Theoretical Computer Science, 134(2):329-363, 1994. URL: https://doi.org/10.1016/0304-3975(94)90242-9.
  21. Ahmet Kara, Thomas Schwentick, and Tony Tan. Feasible automata for two-variable logic with successor on data words. In Proc. 6^th International Conference on Language and Automata Theory and Applications (LATA), volume 7183, pages 351-362, 2012. URL: https://doi.org/10.1007/978-3-642-28332-1_30.
  22. Denis Lugiez. Multitree automata that count. Theoretical Computer Science, 333(1-2):225-263, 2005. URL: https://doi.org/10.1016/j.tcs.2004.10.023.
  23. Othon Michail and Paul G. Spirakis. Elements of the theory of dynamic networks. Communications of the ACM, 61(2):72, 2018. URL: https://doi.org/10.1145/3156693.
  24. Ruzica Piskac and Viktor Kuncak. Decision procedures for multisets with cardinality constraints. In Proc. 9^th International Conference on Verification, Model Checking, and Abstract Interpretation (VMCAI), pages 218-232, 2008. URL: https://doi.org/10.1007/978-3-540-78163-9_20.
  25. Zhilin Wu. Commutative data automata. In Proc. 26^th International Workshop/21^st Annual Conference of the EACSL on Computer Science Logic (CSL), volume 16, pages 528-542, 2012. URL: https://doi.org/10.4230/LIPIcs.CSL.2012.528.
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