Probabilistic self-stabilization
Information Processing Letters
Fast randomized consensus using shared memory
Journal of Algorithms
Token management schemes and random walks yield self-stabilizing mutual exclusion
PODC '90 Proceedings of the ninth annual ACM symposium on Principles of distributed computing
ACM Computing Surveys (CSUR)
Modeling and verification of randomized distributed real-time systems
Modeling and verification of randomized distributed real-time systems
Exact sampling and approximate counting techniques
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
A more rapidly mixing Markov chain for graph colorings
proceedings of the eighth international conference on Random structures and algorithms
Self-stabilizing algorithms for synchronous unidirectional rings
Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
Self-stabilization
Self-stabilizing systems in spite of distributed control
Communications of the ACM
Concrete Math
Two-State Self-Stabilizing Algorithms for Token Rings
IEEE Transactions on Software Engineering
Analyzing Expected Time by Scheduler-Luck Games
IEEE Transactions on Software Engineering
Randomized Finite-State Distributed Algorithms as Markov Chains
DISC '01 Proceedings of the 15th International Conference on Distributed Computing
Markov chain algorithms for planar lattice structures
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Path coupling: A technique for proving rapid mixing in Markov chains
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
1983 Invited address solved problems, unsolved problems and non-problems in concurrency
PODC '84 Proceedings of the third annual ACM symposium on Principles of distributed computing
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
Convergence of the Iterated Prisoner's Dilemma Game
Combinatorics, Probability and Computing
Coupling and self-stabilization
Distributed Computing - Special issue: DISC 04
Coupling and self-stabilization
Distributed Computing - Special issue: DISC 04
All k-bounded policies are equivalent for self-stabilization
SSS'06 Proceedings of the 8th international conference on Stabilization, safety, and security of distributed systems
On stabilization in Herman's algorithm
ICALP'11 Proceedings of the 38th international conference on Automata, languages and programming - Volume Part II
Fault-tolerant and self-stabilizing mobile robots gathering
DISC'06 Proceedings of the 20th international conference on Distributed Computing
Computing with pavlovian populations
OPODIS'11 Proceedings of the 15th international conference on Principles of Distributed Systems
Adversarial scheduling in discrete models of social dynamics
Mathematical Structures in Computer Science
A tighter bound for the self-stabilization time in Herman's algorithm
Information Processing Letters
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A randomized self-stabilizing algorithm A is an algorithm that, whatever the initial configuration is, reaches a set L of legal configurations in finite time with probability 1. The proof of convergence towards L is generally done by exhibiting a potential function ϕ, which measures the "vertical" distance of any configuration to L, such that ϕ decreases with non-null probability at each step of A. We propose here a method, based on the notion of coupling, which makes use of a "horizontal" distance δ between any pair of configurations, such that δ decreases in expectation at each step of A. In contrast with classical methods, our coupling method does not require the knowledge of L. In addition to the proof of convergence, the method allows us to assess the convergence rate according to two different measures. Proofs produced by the method are often simpler or give better upper bounds than their classical counterparts, as examplified here on Herman's mutual exclusion and Iterated Prisoner's Dilemma algorithms in the case of cyclic graphs.