Certified Impossibility Results for Byzantine-Tolerant Mobile Robots

Cédric Auger (1) , Zohir Bouzid (2) , Pierre Courtieu (3) , Sébastien Tixeuil (4, 5, 2) , Xavier Urbain (3, 6)

1 Chercheur indépendant
2 NPA - Networks and Performance Analysis
3 CEDRIC - Centre d'études et de recherche en informatique et communications
4 LINCS - Laboratory of Information, Network and Communication Sciences
5 IUF - Institut universitaire de France
6 LRI - Laboratoire de Recherche en Informatique

We propose a framework to build formal developments for robot networks using the COQ proof assistant, to state and to 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 forconvergence 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 formalization, 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.

Mots clés: proof certification; Mobile autonomous robots; gathering; Byzantine tolerance; impossibility results

Domaines: Logique en informatique [cs.LO]

Cédric Auger, Zohir Bouzid, Pierre Courtieu, Sébastien Tixeuil, Xavier Urbain. Certified Impossibility Results for Byzantine-Tolerant Mobile Robots. [Research Report] 1560, LRI - CNRS, University Paris-Sud. 2013. ⟨hal-00834633⟩