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)


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.


Span Tree Legal State Binary String Label Scheme Leader Election 
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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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