Abstract
In distributed computing, multiple processes interact to solve a problem together. The main model of interaction is the message-passing model, where processes communicate by exchanging messages. Nevertheless, there are several models varying along important dimensions: degree of synchrony, kinds of faults, number of faults... This variety is compounded by the lack of a general formalism in which to abstract these models. One way to bring order is to constrain these models to communicate in rounds. This is the setting of the Heard-Of model, which captures many models through predicates on the messages sent in a round and received on time. Yet, it is not easy to define the predicate that captures a given operational model. The question is even harder for the asynchronous case, as unbounded message delay means the implementation of rounds must depend on details of the model. This paper shows that characterising asynchronous models by heard-of predicates is indeed meaningful. This characterization relies on delivered predicates, an intermediate abstraction between the informal operational model and the heard-of predicates. Our approach splits the problem into two steps: first extract the delivered model capturing the informal model, and then characterize the heard-of predicates that are generated by this delivered model. For the first part, we provide examples of delivered predicates, and an approach to derive more. It uses the intuition that complex models are a composition of simpler models. We define operations like union, succession or repetition that make it easier to derive complex delivered predicates from simple ones while retaining expressivity. For the second part, we formalize and study strategies for when to change rounds. Intuitively, the characterizing predicate of a model is the one generated by a strategy that waits for as much messages as possible, without blocking forever.
Highlights
IntroductionThe Heard-Of model provides such an abstraction, but only if we can define and compute a corresponding heard-of predicate for asynchronous message-passing models, which is the hardest case due to lack of an upper bound on communication delay
One way to bring order to these models is to constrain them further, to communicate in rounds. This is the setting of the Heard-Of model, which captures many models through predicates on the messages sent in a round and received on time
We provide a technique to extract a strategy dominating the oblivious strategies of the complex predicate from the strategies of its building blocks; exact computations of the generated heard-of predicates; and a sufficient condition on the building blocks for the result of the operations to be dominated by an oblivious strategy
Summary
The Heard-Of model provides such an abstraction, but only if we can define and compute a corresponding heard-of predicate for asynchronous message-passing models, which is the hardest case due to lack of an upper bound on communication delay. We start with the operational model, derive a “delivered predicate”, and find the heard-of predicates that can be implemented by some rule for changing rounds (called a strategy) for this specific delivered predicate Among such predicates, we propose a criterion to choose the one characterizing the asynchronous message-passing model. For some families of strategies (strategies that only depend on some limited part of the local state of a process, here the messages of the current round or the messages of past and current rounds respectively), the strategy that implements the heard-of predicate corresponding to the full model can be built from the strategies of the building blocks using analogous operations on strategies that we define. As mentioned in Marić [17], the only known works addressing it, one by Hutle and Schiper [15] and the other by Drăgoi et al [9], both limit themselves to specific predicates and partially synchronous system models
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