Multi-Head Monitoring of Metric Dynamic Logic

Martin Raszyk, David Basin, Dmitriy Traytel

Abstract

We develop a monitoring algorithm for metric dynamic logic, an extension of metric temporal logic with regular expressions. The monitor computes whether a given formula is satisfied or violated at every position in an input trace of time-stamped events. Our monitor follows the multi-head paradigm: it reads the input simultaneously at multiple positions and moves these reading heads asynchronously. This mode of operation results in unprecedented space complexity guarantees for metric dynamic logic: The monitor's memory consumption neither depends on the event-rate, i.e., the number of events within a fixed time-unit, nor on the numeric constants occurring in the quantitative temporal constraints in the given formula. We implement our algorithm in the Hydra monitoring tool and empirically demonstrate its strong performance.

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