Formalization of an Optimized Monitoring Algorithm for Metric First-Order Dynamic Logic with Aggregations

A monitor is a runtime verification tool that solves the following problem: Given a stream of time-stamped events and a policy formulated in a specification language, decide whether the policy is satisfied at every point in the stream. We verify the correctness of an executable monitor for specifications given as formulas in metric first-order dynamic logic (MFODL), which combines the features of metric first-order temporal logic (MFOTL) and metric dynamic logic. Thus, MFODL supports real-time constraints, first-order parameters, and regular expressions. Additionally, the monitor supports aggregation operations such as count and sum. This formalization, which is described in a forthcoming paper at IJCAR 2020, significantly extends previous work on a verified monitor for MFOTL. Apart from the addition of regular expressions and aggregations, we implemented multi-way joins and a specialized sliding window algorithm to further optimize the monitor.