Multi-head Monitoring of Metric Temporal Logic

Abstract

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.

Multi-head Monitoring of Metric Dynamic Logic

“…Our multi-head MTL monitor [20] coincides with our MDL monitor except for the temporal operator cases. For MTL, we use a different data structure that only requires a single reading head per temporal operator.…”

“…Event-rate independence is impossible to achieve for single-head monitors that support past and future temporal operators and output Boolean verdicts for every position in the trace (as we argue in Section 3.3). The multi-head paradigm overcomes this limitation for MTL [20]. Recently, we have used the multi-head model of computation to eliminate non-determinism from functional finite-state transducers [22].…”

“…We have recently proposed third mode of operation for monitors: multi-head monitoring [20,22]. Conceptually, a multi-head monitor has multiple pointers, called reading heads, into a single log file.…”

“…In our previous work [20], we have demonstrated the benefits of multi-head monitoring for metric temporal logic (MTL) [17]. MTL is a widely used propositional specification language capable of expressing qualitative (e.g., happens before) and quantitative (e.g., within the last hour) temporal relationships.…”

“…Our main contribution is a space-efficient multi-head MDL monitor. On a highlevel (Section 3), it resembles our multi-head MTL monitor [20]. In both logics, the main challenge for space-efficiency stems from the presence of both past and future operators, which may require the monitor to buffer the verdicts from the recursive subformula evaluation until a verdict for the overall formula can be produced.…”