2 Search Results for "Rieg, Lionel"


Document
Swarms of Mobile Robots: Towards Versatility with Safety

Authors: Pierre Courtieu, Lionel Rieg, Sébastien Tixeuil, and Xavier Urbain

Published in: LITES, Volume 8, Issue 2 (2022): Special Issue on Distributed Hybrid Systems. Leibniz Transactions on Embedded Systems, Volume 8, Issue 2


Abstract
We present Pactole, a formal framework to design and prove the correctness of protocols (or the impossibility of their existence) that target mobile robotic swarms. Unlike previous approaches, our methodology unifies in a single formalism the execution model, the problem specification, the protocol, and its proof of correctness. The Pactole framework makes use of the Coq proof assistant, and is specially targeted at protocol designers and problem specifiers, so that a common unambiguous language is used from the very early stages of protocol development. We stress the underlying framework design principles to enable high expressivity and modularity, and provide concrete examples about how the Pactole framework can be used to tackle actual problems, some previously addressed by the Distributed Computing community, but also new problems, while being certified correct.

Cite as

Pierre Courtieu, Lionel Rieg, Sébastien Tixeuil, and Xavier Urbain. Swarms of Mobile Robots: Towards Versatility with Safety. In LITES, Volume 8, Issue 2 (2022): Special Issue on Distributed Hybrid Systems. Leibniz Transactions on Embedded Systems, Volume 8, Issue 2, pp. 02:1-02:36, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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@Article{courtieu_et_al:LITES.8.2.2,
  author =	{Courtieu, Pierre and Rieg, Lionel and Tixeuil, S\'{e}bastien and Urbain, Xavier},
  title =	{{Swarms of Mobile Robots: Towards Versatility with Safety}},
  journal =	{Leibniz Transactions on Embedded Systems},
  pages =	{02:1--02:36},
  ISSN =	{2199-2002},
  year =	{2022},
  volume =	{8},
  number =	{2},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LITES.8.2.2},
  doi =		{10.4230/LITES.8.2.2},
  annote =	{Keywords: distributed algorithm, mobile autonomous robots, formal proof}
}
Document
Extracting Herbrand trees in classical realizability using forcing

Authors: Lionel Rieg

Published in: LIPIcs, Volume 23, Computer Science Logic 2013 (CSL 2013)


Abstract
Krivine presented in [Krivine, 2011] a methodology to combine Cohen's forcing with the theory of classical realizability and showed that the forcing condition can be seen as a reference that is not subject to backtracks. The underlying classical program transformation was then analyzed by Miquel [Miquel, 2011] in a fully typed setting in classical higher-order arithmetic (PA-omega^+). As a case study of this methodology, we present a method to extract a Herbrand tree from a classical realizer of inconsistency, following the ideas underlying the completeness theorem and the proof of Herbrand's theorem. Unlike the traditional proof based on König's lemma (using a fixed enumeration of atomic formulas), our method is based on the introduction of a particular Cohen real. It is formalized as a proof in PA-omega^+, making explicit the construction of generic sets in this framework in the particular case where the set of forcing conditions is arithmetical. We then analyze the algorithmic content of this proof.

Cite as

Lionel Rieg. Extracting Herbrand trees in classical realizability using forcing. In Computer Science Logic 2013 (CSL 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 23, pp. 597-614, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)


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@InProceedings{rieg:LIPIcs.CSL.2013.597,
  author =	{Rieg, Lionel},
  title =	{{Extracting Herbrand trees in classical realizability using forcing}},
  booktitle =	{Computer Science Logic 2013 (CSL 2013)},
  pages =	{597--614},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-60-6},
  ISSN =	{1868-8969},
  year =	{2013},
  volume =	{23},
  editor =	{Ronchi Della Rocca, Simona},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2013.597},
  URN =		{urn:nbn:de:0030-drops-42212},
  doi =		{10.4230/LIPIcs.CSL.2013.597},
  annote =	{Keywords: classical realizability, forcing, Curry-Howard correspondence, Herbrand trees}
}
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