A 1-Strong Self-stabilizing Transformer

In this paper we study k-strong self-stabilizing systems, which satisfy the properties of strong confinement and of k-linear time adaptivity. Strong confinement means that a non faulty processor has the same behavior with or without the presence of faults elsewhere in the system (in other words faults are confined). k-linear time adaptivity means that after k or less faults hitting the system in a correct state, the recovery takes a number of rounds linear in k. We show, under some conditions, how an asynchronous self-stabilizing system can be automatically transformed into an equivalent synchronous 1-strong self-stabilizing system where the recovery takes at most 3 rounds. We present in detail the transformer as well as a 1-strong synchronous unison algorithm. We also discuss how the construction can be extended to the k-strong case, for an arbitrary k.

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