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

TL;DR

This paper introduces efficient offline algorithms for monitoring STL* formulas with nested freeze variables, significantly improving scalability and enabling long trace analysis in signal temporal logic.

Contribution

It presents the first scalable monitoring algorithms for STL* with nested freeze operators, including an acceleration heuristic for better performance.

Findings

Algorithms can monitor long traces with nested freeze variables.

The acceleration heuristic improves monitoring efficiency.

Experimental results validate the scalability and effectiveness.

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.