Logical Methods in Computer Science (Nov 2017)

A Framework for Certified Self-Stabilization

  • Karine Altisen,
  • Pierre Corbineau,
  • Stephane Devismes

DOI
https://doi.org/10.23638/LMCS-13(4:14)2017
Journal volume & issue
Vol. Volume 13, Issue 4

Abstract

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We propose a general framework to build certified proofs of distributed self-stabilizing algorithms with the proof assistant Coq. We first define in Coq the locally shared memory model with composite atomicity, the most commonly used model in the self-stabilizing area. We then validate our framework by certifying a non trivial part of an existing silent self-stabilizing algorithm which builds a $k$-clustering of the network. We also certify a quantitative property related to the output of this algorithm. Precisely, we show that the computed $k$-clustering contains at most $\lfloor \frac{n-1}{k+1} \rfloor + 1$ clusterheads, where $n$ is the number of nodes in the network. To obtain these results, we also developed a library which contains general tools related to potential functions and cardinality of sets.

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