Resource bounds for self stabilizing message driven protocols

Self-stabilizing message driven protocols are defined and discussed. The class weakexclusion that contains many natural tasks such as `-exclusion and token-passing is defined, and it is shown that in any execution of any self-stabilizing protocol for a task in this class, the configuration size must grow at least in a logarithmic rate. This last lower bound is valid even if the system is supported by a time-out mechanism that prevents communication deadlocks. Then we present three self-stabilizing message driven protocols for token-passing. The rate of growth of configuration size for all three protocols matches the aforementioned lower bound. Our protocols are presented for two processor systems but can be easily adapted to rings of arbitrary size. Our results have an interesting interpretation in terms of automata theory.

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