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On Proof-Labeling Schemes versus Silent Self-stabilizing Algorithms

  • Lélia Blin
  • Pierre Fraigniaud
  • Boaz Patt-Shamir
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8756)

Abstract

It follows from the definition of silent self-stabilization, and from the definition of proof-labeling scheme, that if there exists a silent self-stabilizing algorithm using ℓ-bit registers for solving a task \({\mathcal{T}} \), then there exists a proof-labeling scheme for \({\mathcal{T}} \) using registers of at most ℓ bits. The first result in this paper is the converse to this statement. We show that if there exists a proof-labeling scheme for a task \({\mathcal{T}} \), using ℓ-bit registers, then there exists a silent self-stabilizing algorithm using registers of at most O(ℓ + logn) bits for solving \({\mathcal{T}} \), where n is the number of processes in the system. Therefore, as far as memory space is concerned, the design of silent self-stabilizing algorithms essentially boils down to the design of compact proof-labeling schemes. The second result in this paper addresses time complexity. We show that, for every task \({\mathcal{T}} \) with k-bits output size in n-node networks, there exists a silent self-stabilizing algorithm solving \({\mathcal{T}} \) in O(n) rounds, using registers of O(n 2 + kn) bits. Therefore, as far as running time is concerned, every task has a silent self-stabilizing algorithm converging in a linear number of rounds.

Keywords

Span Tree Legal State Binary String Label Scheme Leader Election 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Lélia Blin
    • 1
  • Pierre Fraigniaud
    • 2
  • Boaz Patt-Shamir
    • 3
  1. 1.LIP6-UPMC, University of Evry-Val d’EssonneFrance
  2. 2.CNRS and University Paris DiderotFrance
  3. 3.Department of Electrical EngineeringTel-Aviv UniversityIsrael

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