Universal dynamic synchronous self–stabilization

Summary.

We prove the existence of a “universal” synchronous self-stabilizing protocol, that is, a protocol that allows a distributed system to stabilize to a desired nonreactive behaviour (as long as a protocol stabilizing to that behaviour exists). Previous proposals required drastic increases in asymmetry and knowledge to work, whereas our protocol does not use any additional knowledge, and does not require more symmetry-breaking conditions than available; thus, it is also stabilizing with respect to dynamic changes in the topology. We prove an optimal quiescence time n+D for a synchronous network of n processors and diameter D; the protocol can be made finite state with a negligible loss in quiescence time. Moreover, an optimal D+1 protocol is given for the case of unique identifiers. As a consequence, we provide an effective proof technique that allows to show whether self-stabilization to a certain behaviour is possible under a wide range of models.