We present a novel approach to the offline monitoring of specifications expressed in metric temporal logic (MTL). Our monitoring algorithm exploits multiple one-way reading heads that traverse a trace sequentially. We present both theoretical and practical results that show this substantially improves upon the state-of-the-art. In particular, our algorithm is the first offline monitoring algorithm for MTL with past and bounded-future temporal operators that is almost trace-length independent and outputs a trace of Boolean verdicts denoting the monitored formula's satisfaction at every position in the input trace. In addition, our algorithm's worst-case space complexity is linear in the formula size, while previous algorithms were exponential. Moreover, we compare our implementation of the algorithm with another almost trace-length independent tool that outputs non-standard verdicts to achieve this space complexity. Our tool used less memory and runs significantly faster, for example yielding a 10-fold improvement on average on random formulas, while producing better output.

Runtime monitors analyze system execution traces for policy compliance. Monitors for propositional specification languages, such as metric temporal logic (MTL), produce Boolean verdicts denoting whether the policy is satisfied or violated at a given point in the trace. Given a sufficiently complex policy, it can be difficult for the monitor’s user to understand how the monitor arrived at its verdict. We develop an MTL monitor that outputs verdicts capturing why the policy was satisfied or violated. Our verdicts are proof trees in a sound and complete proof system that we design. We demonstrate that such verdicts can serve as explanations for end users by augmenting our monitor with a graphical interface for the interactive exploration of proof trees. As a second application, our verdicts serve as certificates in a formally verified checker we develop using the Isabelle proof assistant.

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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 at every position in an input trace of timestamped events. Our monitor follows the multi-head paradigm: it reads the input simultaneously at multiple positions and moves its 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 formally prove our algorithm correct in the Isabelle proof assistant, integrate it in the Hydra monitoring tool, and empirically demonstrate its strong performance.

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