On Proof-Labeling Schemes versus Silent Self-stabilizing Algorithms

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 T , then there exists a proof-labeling scheme for 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 T , using ℓ-bit registers, then there exists a silent self-stabilizing algorithm using registers of at most O(ℓ + logn) bits for solving 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 T with k-bits output size in n-node networks, there exists a silent self-stabilizing algorithm solving 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.
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https://hal.inria.fr/hal-01102123
Contributor : Pierre Fraigniaud <>
Submitted on : Monday, January 12, 2015 - 10:31:55 AM
Last modification on : Thursday, March 21, 2019 - 1:00:18 PM

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Lélia Blin, Pierre Fraigniaud, Boaz Patt-Shamir. On Proof-Labeling Schemes versus Silent Self-stabilizing Algorithms. SSS 2014 - 16th International Symposium on Stabilization, Safety, and Security of Distributed Systems, Sep 2014, Paderborn, Germany. pp.18-32, ⟨10.1007/978-3-319-11764-5_2⟩. ⟨hal-01102123⟩

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