Fast Robust Monitoring for Signal Temporal Logic with Value Freezing Operators (STL*)

Abstract: Researchers have previously proposed augmenting Signal Temporal Logic (STL) with the value freezing operator in order to express engineering properties that cannot be expressed in STL. This augmented logic is known as STL*. The previous algorithms for STL* monitoring were intractable, and did not scale formulae with nested freeze variables. We present offline discrete-time monitoring algorithms with an acceleration heuristic, both for Boolean monitoring as well as for quantitative robustness monitoring. The acceleration heuristic operates over time intervals where subformulae hold true, rather than over the original trace sample-points. We present experimental validation of our algorithms, the results show that our algorithms can monitor over long traces for formulae with two or three nested freeze variables. Our work is the first work with monitoring algorithm implementations for STL* formulae with nested freeze variables.