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Expressive Power of Broadcast Consensus Protocols

Authors Michael Blondin, Javier Esparza, Stefan Jaax

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  • 16 pages

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Author Details

Michael Blondin
  • Département d'informatique, Université de Sherbrooke, Sherbrooke, Canada
Javier Esparza
  • Fakultät für Informatik, Technische Universität München, Garching bei München, Germany
Stefan Jaax
  • Fakultät für Informatik, Technische Universität München, Garching bei München, Germany


Part of this work was realized while Stefan Jaax was visiting the Université de Sherbrooke. We warmly thank the anonymous reviewers for their helpful comments and suggestions.

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Michael Blondin, Javier Esparza, and Stefan Jaax. Expressive Power of Broadcast Consensus Protocols. In 30th International Conference on Concurrency Theory (CONCUR 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 140, pp. 31:1-31:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


Population protocols are a formal model of computation by identical, anonymous mobile agents interacting in pairs. Their computational power is rather limited: Angluin et al. have shown that they can only compute the predicates over N^k expressible in Presburger arithmetic. For this reason, several extensions of the model have been proposed, including the addition of devices called cover-time services, absence detectors, and clocks. All these extensions increase the expressive power to the class of predicates over N^k lying in the complexity class NL when the input is given in unary. However, these devices are difficult to implement, since they require that an agent atomically receives messages from all other agents in a population of unknown size; moreover, the agent must know that they have all been received. Inspired by the work of the verification community on Emerson and Namjoshi’s broadcast protocols, we show that NL-power is also achieved by extending population protocols with reliable broadcasts, a simpler, standard communication primitive.

Subject Classification

ACM Subject Classification
  • Theory of computation → Distributed computing models
  • Theory of computation → Complexity classes
  • Theory of computation → Automata over infinite objects
  • population protocols
  • complexity theory
  • counter machines
  • distributed computing


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