Theory of Computing Systems

, Volume 63, Issue 2, pp 200–218 | Cite as

Synchronous Gathering without Multiplicity Detection: a Certified Algorithm

  • Thibaut Balabonski
  • Amélie Delga
  • Lionel Rieg
  • Sébastien TixeuilEmail author
  • Xavier Urbain
Part of the following topical collections:
  1. Special Issue on Stabilization, Safety, and Security of Distributed Systems (SSS 2016)


In mobile robotic swarms, the gathering problem consists in coordinating all the robots so that in finite time they occupy the same location, not known beforehand. Multiplicity detection refers to the ability to detect that more than one robot can occupy a given position. When the robotic swarm operates synchronously, a well-known result by Cohen and Peleg permits to achieve gathering, provided robots are capable of multiplicity detection. We present a new algorithm for synchronous gathering, that does not assume that robots are capable of multiplicity detection, nor make any other extra assumption. Unlike previous approaches, the correctness of our proof is certified in the model where the protocol is defined, using the Coq proof assistant.


Mobile robots Gathering Multiplicity detection Certification Proof assistant 



The authors are grateful to the reviewers who provided constructive comments and helped to improve the presentation of this work.


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© Springer Science+Business Media, LLC, part of Springer Nature 2017

Authors and Affiliations

  1. 1.LRI, Université Paris-Sud, CNRSUniversité Paris-SaclayOrsayFrance
  2. 2.École Nationale Supérieure d’Informatique pour l’Industrie et l’Entreprise (ENSIIE)ÉvryFrance
  3. 3.UPMC Sorbonne UniversitésParisFrance
  4. 4.Collège de FranceParisFrance
  5. 5.Yale UniversityNew HavenUSA
  6. 6.Institut Universitaire de FranceParisFrance
  7. 7.Université Claude Bernard Lyon-1, LIRIS CNRS UMR 5205Université de LyonLyonFrance

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