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Automatic Analysis of Expected Termination Time for Population Protocols

Authors Michael Blondin , Javier Esparza , Antonín Kucera



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Author Details

Michael Blondin
  • TU Munich, Germany
Javier Esparza
  • TU Munich, Germany
Antonín Kucera
  • Masaryk University, Brno, Czech Republic

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Michael Blondin, Javier Esparza, and Antonín Kucera. Automatic Analysis of Expected Termination Time for Population Protocols. In 29th International Conference on Concurrency Theory (CONCUR 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 118, pp. 33:1-33:16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2018)
https://doi.org/10.4230/LIPIcs.CONCUR.2018.33

Abstract

Population protocols are a formal model of sensor networks consisting of identical mobile devices. Two devices can interact and thereby change their states. Computations are infinite sequences of interactions in which the interacting devices are chosen uniformly at random. In well designed population protocols, for every initial configuration of devices, and for every computation starting at this configuration, all devices eventually agree on a consensus value. We address the problem of automatically computing a parametric bound on the expected time the protocol needs to reach this consensus. We present the first algorithm that, when successful, outputs a function f(n) such that the expected time to consensus is bound by O(f(n)), where n is the number of devices executing the protocol. We experimentally show that our algorithm terminates and provides good bounds for many of the protocols found in the literature.

Subject Classification

ACM Subject Classification
  • Theory of computation → Distributed computing models
  • Theory of computation → Probabilistic computation
  • Theory of computation → Logic and verification
Keywords
  • population protocols
  • performance analysis
  • expected termination time

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