Certified Impossibility Results for Byzantine-Tolerant Mobile Robots

  • Cédric Auger
  • Zohir Bouzid
  • Pierre Courtieu
  • Sébastien Tixeuil
  • Xavier Urbain
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8255)

Abstract

We propose a framework to build formal developments for robot networks using the Coq proof assistant, to state and prove formally various properties. We focus in this paper on impossibility proofs, as it is natural to take advantage of the Coq higher order calculus to reason about algorithms as abstract objects. We present in particular formal proofs of two impossibility results for convergence of oblivious mobile robots if respectively more than one half and more than one third of the robots exhibit Byzantine failures, starting from the original theorems by Bouzid et al.. Thanks to our formalisation, the corresponding Coq developments are quite compact. To our knowledge, these are the first certified (in the sense of formally proved) impossibility results for robot networks.

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Copyright information

© Springer International Publishing Switzerland 2013

Authors and Affiliations

  • Cédric Auger
    • 1
  • Zohir Bouzid
    • 4
  • Pierre Courtieu
    • 2
  • Sébastien Tixeuil
    • 4
    • 5
  • Xavier Urbain
    • 1
    • 3
  1. 1.École Nat. Sup. d’Informatique pour l’Industrie et l’Entreprise (ENSIIE)EvryFrance
  2. 2.CÉDRIC – Conservatoire national des arts et métiersParisFrance
  3. 3.LRI, CNRS UMR 8623Université Paris-SudOrsayFrance
  4. 4.UPMC Sorbonne UniversitésFrance
  5. 5.Institut Universitaire de FranceFrance

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