Impossibility of Gathering, a Certification

Abstract : Recent advances in Distributed Computing highlight models and algorithms for autonomous swarms of mobile robots that self-organise and cooperate to solve global objectives. The overwhelming majority of works so far considers handmade algorithms and proofs of correctness. This paper builds upon a previously proposed formal framework to certify the correctness of impossibility results regarding distributed algorithms that are dedicated to autonomous mobile robots evolving in a continuous space. As a case study, we consider the problem of gathering all robots at a particular location, not known beforehand. A fundamental (but not yet formally certified) result, due to Suzuki and Yamashita, states that this simple task is impossible for two robots executing deterministic code and initially located at distinct positions. Not only do we obtain a certified proof of the original impossibility result, we also get the more general impossibility of gathering with an even number of robots, when any two robots are possibly initially at the same exact location.
Document type :
Reports
Complete list of metadatas

Cited literature [14 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-00995126
Contributor : Xavier Urbain <>
Submitted on : Thursday, May 22, 2014 - 5:29:12 PM
Last modification on : Tuesday, May 14, 2019 - 10:15:14 AM
Long-term archiving on : Friday, August 22, 2014 - 1:30:38 PM

Files

rrcedric.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-00995126, version 1
  • ARXIV : 1405.5902

Citation

Pierre Courtieu, Lionel Rieg, Xavier Urbain, Sébastien Tixeuil. Impossibility of Gathering, a Certification. [Technical Report] CEDRIC-14-3016, CEDRIC laboratory, CNAM-Paris, France. 2014, pp.10. ⟨hal-00995126⟩

Share

Metrics

Record views

552

Files downloads

268