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Certified Round Complexity of Self-Stabilizing Algorithms

Authors Karine Altisen , Pierre Corbineau , Stéphane Devismes

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Author Details

Karine Altisen
  • Université Grenoble Alpes, CNRS, Grenoble INP, VERIMAG, 38000 Grenoble, France
Pierre Corbineau
  • Université Grenoble Alpes, CNRS, Grenoble INP, VERIMAG, 38000 Grenoble, France
Stéphane Devismes
  • Université de Picardie Jules Verne, MIS, 80039 Amiens, France

Funding

This work has been partially funded by the ANR project SkyData (ANR-22-CE25-0008-01).

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Karine Altisen, Pierre Corbineau, and Stéphane Devismes. Certified Round Complexity of Self-Stabilizing Algorithms. In 37th International Symposium on Distributed Computing (DISC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 281, pp. 2:1-2:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023) https://doi.org/10.4230/LIPIcs.DISC.2023.2

Abstract

A proof assistant is an appropriate tool to write sound proofs. The need of such tools in distributed computing grows over the years due to the scientific progress that leads algorithmic designers to consider always more difficult problems. In that spirit, the PADEC Coq library has been developed to certify self-stabilizing algorithms. Efficiency of self-stabilizing algorithms is mainly evaluated by comparing their stabilization times in rounds, the time unit that is primarily used in the self-stabilizing area. In this paper, we introduce the notion of rounds in the PADEC library together with several formal tools to help the certification of the complexity analysis of self-stabilizing algorithms. We validate our approach by certifying the stabilization time in rounds of the classical Dolev et al’s self-stabilizing Breadth-first Search spanning tree construction.

Subject Classification

ACM Subject Classification
  • Theory of computation → Distributed algorithms
  • Theory of computation → Logic and verification
Keywords
  • Certification
  • proof assistant
  • Coq
  • self-stabilization
  • round complexity

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