A Certified Universal Gathering Algorithm for Oblivious Mobile Robots

We present a new algorithm for the problem of universal gathering mobile oblivious robots (that is, starting from any initial configuration that is not bivalent, using any number of robots, the robots reach in a finite number of steps the same position, not known beforehand) without relying on a common chirality. We give very strong guaranties on the correctness of our algorithm by proving formally that it is correct, using the COQ proof assistant. To our knowledge, this is the first certified positive (and constructive) result in the context of oblivious mobile robots. It demonstrates both the effectiveness of the approach to obtain new algorithms that are truly generic, and its managability since the amount of developped code remains human readable

Certified Universal Gathering in R2R^2 for Oblivious Mobile Robots

We present a unified formal framework for expressing mobile robots models, protocols, and proofs, and devise a protocol design/proof methodology dedicated to mobile robots that takes advantage of this formal framework. As a case study, we present the first formally certified protocol for oblivious mobile robots evolving in a two-dimensional Euclidean space. In more details, we provide a new algorithm for the problem of universal gathering mobile oblivious robots (that is, starting from any initial configuration that is not bivalent, using any number of robots, the robots reach in a finite number of steps the same position, not known beforehand) without relying on a common orientation nor chirality. We give very strong guaranties on the correctness of our algorithm by proving formally that it is correct, using the COQ proof assistant. This result demonstrates both the effectiveness of the approach to obtain new algorithms that use as few assumptions as necessary, and its manageability since the amount of developed code remains human readable.Comment: arXiv admin note: substantial text overlap with arXiv:1506.0160

Certified Impossibility Results for Byzantine-Tolerant Mobile Robots

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

Impossibility of Gathering, a Certification

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.Comment: 10

Company-Coq: Taking Proof General one step closer to a real IDE

Company-Coq is a new Emacs package that extends Proof General with a contextual auto-completion engine for Coq proofs and many additional facilities to make writing proofs easier and more efficient. Beyond fuzzy auto-completion of tactics, options, module names, and local definitions, company-coq offers offline in-editor documentation, convenient snippets, and multiple other Coq-specific IDE features. The system will be presented at CoqPL 2016, focusing on a live demo with an emphasis on writing proofs in Emacs more efficiently, and a discussion of desirable features of proof-oriented development environments. https://github.com/cpitclaudel/company-co

Une preuve est une histoire

International audienceLa narration computationnelle est un sous-domaine de l'Intelligence Artificielle, lié notamment aux problèmes de représentation des connaissances et en particulier à la représentation des actions et du changement. On s'y intéresse aux objets narratifs (littéraires, interactifs, cinématographiques) pour les comprendre, les analyser, ou les construire, en proposant des techniques qui peuvent être mises en oeuvre par des programmes et systèmes informatiques. C'est un domaine qui a des applications dans le domaine des jeux vidéos ou jeux utiles par exemple. Nous proposons de revenir dans cet exposé sur la motivation et les fondements d'un travail en cours, qui repose sur une connivence entre la structure des preuves en logique linéaire et la structure d'histoires interactives. Bien qu'ayant déjà donné lieu à une interprétation opérationnelle, cette approche a laissé des pistes inexplorées, surtout en ce qui concerne une normalisation et modularité de preuves/histoires dans un sous-ensemble ad hoc de la logique linéaire. Certaines idées ont été explorées en 2011 à l'aide de Coq et nous aimerions partager et échanger au sujet de nos projets actuels pour approfondir ce travail

Certified Impossibility Results for Byzantine-Tolerant Mobile Robots

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

Comment s'assurer de garder le contact (et nos distances)

International audienceNous étudions le problème du maintien de connexion dans les réseaux de robots mobiles. On considère un robot incontrôlable (la « cible ») et une flotte de robots volumiques autonomes se déplaçant dans le plan réel et munis de capteurs et transmetteurs à portée limitée. Le problème consiste à maintenir à tout moment une connexion entre un point fixe connu au départ et la cible. Cette situation est par exemple instanciée dans le cas d'une équipe de recherche (la cible) en cours d'exploration et qui doit conserver une liaison avec la base des secours (le point fixe). Dans un tel cas où des vies sont en jeu, le problème devient critique : il est impératif d'avoir les plus fortes garanties de correction possibles sur les protocoles candidats. Nous définissons formellement ce problème et proposons une famille de protocoles que nous prouvons correcte grâce à l'assistant de preuve Coq et la bibliothèque PACTOLE. Nous illustrons en particulier l'utilité de cet outil formel ainsi que de la démarche associée, de la réflexion préliminaire sur un problème à la production d'une solution certifiée