Verification of Population Protocols with Unordered Data

Authors Steffen van Bergerem , Roland Guttenberg , Sandra Kiefer , Corto Mascle, Nicolas Waldburger , Chana Weil-Kennedy

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Author Details

Steffen van Bergerem
  • Humboldt-Universität zu Berlin, Germany
Roland Guttenberg
  • Technische Universität München, Germany
Sandra Kiefer
  • University of Oxford, UK
Corto Mascle
  • LaBRI, Université de Bordeaux, France
Nicolas Waldburger
  • IRISA, Université de Rennes, France
Chana Weil-Kennedy
  • IMDEA Software Institute, Madrid, Spain


This project started at and has benefitted substantially from the research camp Autobóz 2023 in Kassel, Germany. We would like to thank the host, sponsors, and organisers of the research camp for bringing us together.

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Steffen van Bergerem, Roland Guttenberg, Sandra Kiefer, Corto Mascle, Nicolas Waldburger, and Chana Weil-Kennedy. Verification of Population Protocols with Unordered Data. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 156:1-156:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


Population protocols are a well-studied model of distributed computation in which a group of anonymous finite-state agents communicates via pairwise interactions. Together they decide whether their initial configuration, i. e., the initial distribution of agents in the states, satisfies a property. As an extension in order to express properties of multisets over an infinite data domain, Blondin and Ladouceur (ICALP'23) introduced population protocols with unordered data (PPUD). In PPUD, each agent carries a fixed data value, and the interactions between agents depend on whether their data are equal or not. Blondin and Ladouceur also identified the interesting subclass of immediate observation PPUD (IOPPUD), where in every transition one of the two agents remains passive and does not move, and they characterised its expressive power. We study the decidability and complexity of formally verifying these protocols. The main verification problem for population protocols is well-specification, that is, checking whether the given PPUD computes some function. We show that well-specification is undecidable in general. By contrast, for IOPPUD, we exhibit a large yet natural class of problems, which includes well-specification among other classic problems, and establish that these problems are in ExpSpace. We also provide a lower complexity bound, namely coNExpTime-hardness.

Subject Classification

ACM Subject Classification
  • Theory of computation → Verification by model checking
  • Theory of computation → Distributed computing models
  • Population protocols
  • Parameterized verification
  • Distributed computing
  • Well-specification


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