Characterizing Asynchronous Message-Passing Models Through Rounds
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Message-passing models of distributed computing vary along numerous dimensions: degree of synchrony, kind of faults, number of faults... Unfortunately, the sheer number of models and their subtle distinctions hinder our ability to design a general theory of message-passing models. One way out of this conundrum restricts communication to proceed by round. A great variety of message-passing models can then be captured in the Heard-Of model, with predicates on the communication graph at each round. Characterizing a model by such a predicate then depends on how to implement rounds in the model. This is straightforward in synchronous models, thanks to the upper bound on communication delay. On the other hand, asynchronous models allow unbounded message delays, which makes the implementation of rounds dependent on the specific message-passing model. A formalization of rounds for asynchronous message-passing models is built through games: the environment captures the non-determinism of a scheduler while processes decide, in turn, whether to change round or wait for more messages. Strategies of processes for these games, capturing the decision of when to change rounds, are studied through a dominance relation: a dominant strategy for a game implements the communication predicate which characterize the corresponding message-passing model. The results of this study are dominant strategies for classical asynchronous models and the existence, for every waiting game, of a dominating strategy for large classes of strategies. On the whole, those results confirm the power of this formalization and demonstrate the characterization of asynchronous models through rounds as a worthwhile pursuit.
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