Weak vs. Self vs. Probabilistic Stabilization

Stéphane Devismes 1 Sébastien Tixeuil 2, 3 Masafumi Yamashita 4
2 GRAND-LARGE - Global parallel and distributed computing
CNRS - Centre National de la Recherche Scientifique : UMR8623, Inria Saclay - Ile de France, UP11 - Université Paris-Sud - Paris 11, LIFL - Laboratoire d'Informatique Fondamentale de Lille, LRI - Laboratoire de Recherche en Informatique
Abstract : Self-stabilization is a strong property that guarantees that a network always resume correct behavior starting from an arbitrary initial state. Weaker guarantees have later been introduced to cope with impossibility results: probabilistic stabilization only gives probabilistic convergence to a correct behavior. Also, weak stabilization only gives the possibility of convergence. In this paper, we investigate the relative power of weak, self, and probabilistic stabilization, with respect to the set of problems that can be solved. We formally prove that in that sense, weak stabilization is strictly stronger that self-stabilization. Also, we refine previous results on weak stabilization to prove that, for practical schedule instances, a deterministic weak-stabilizing protocol can be turned into a probabilistic self-stabilizing one. This latter result hints at more practical use of weak-stabilization, as such algorthms are easier to design and prove than their (probabilistic) self-stabilizing counterparts.
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Contributor : Rapport de Recherche Inria <>
Submitted on : Monday, November 26, 2007 - 10:58:32 AM
Last modification on : Thursday, March 21, 2019 - 1:07:50 PM
Long-term archiving on : Tuesday, September 21, 2010 - 2:48:15 PM


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  • HAL Id : inria-00189952, version 2
  • ARXIV : 0711.3672


Stéphane Devismes, Sébastien Tixeuil, Masafumi Yamashita. Weak vs. Self vs. Probabilistic Stabilization. [Research Report] RR-6366, INRIA. 2007. ⟨inria-00189952v2⟩



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