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A Distributed Algorithm For Unstable Global Predicate Evaluation With Approximately Synchronized Clocks

The ability to evaluate predicates over the global state of a computation is fundamental to distributed application development and control. Algorithms structured on the use of approximately synchronized clocks, for which there is a known bound on the difference of the readings of any two clocks at the same instant of time, are able to detect the occurrence of certain predicates at a point in time during a computation, when this is difficult or impossible otherwise. Existing time-based algorithms for the detection of unstable predicates, for which the truth can vary arbitrarily over time, are centralized. Additionally, these algorithms are able to detect predicates only when they have again become false, or they require a known bound on message delivery delay. We propose an algorithm designed to be more scalable. The algorithm is distributed. Each process only retains a history of its own state that is related to truth of the global predicate. Further, local state information that cannot contribute to the truth of the global predicate is periodically removed. Message delay is assumed to be bounded, but the bound need not be known. When unstable predicates are detected using approximately synchronized clocks, there is some minimum interval for which the predicate must be globally true to ensure its detection using clock values. This arises from the potential difference in process clock values at a single point in time. In this paper, we establish a lower bound on the interval a predicate must be globally true to ensure its detection using approximately synchronized clocks.