Uniform self-stabilizing rings
A self-stabilizing system has the property that it eventually reaches a legitimate configuration when started in any arbitrary configuration. Dijkstra originally introduced the self-stabilization problem and gave several solutions for a ring of processors [Dij74]. His solutions, and others that have appeared, use a distinguished processor in the ring, which can help to drive the system toward stability. Dijkstra observed that a distinguished processor is essential if the number of processors in the ring is composite [Dij82]. We show that there is a self-stabilizing system with no distinguished processor if the size of the ring is prime. Our basic protocol use Θ(n2) states in each processor, where n is the size of the ring. We also give a refined protocol which uses only Θ(n2/ln n) states.
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