Robust Online Monitoring of Signal Temporal Logic

Requirements of cyberphysical systems (CPS) can be rigorously specified using Signal Temporal Logic (STL). STL comes equipped with semantics that are able to quantify how robustly a given signal satisfies an STL property. In a setting where signal values over the entire time horizon of interest are available, efficient algorithms for offline computation of the robust satisfaction value have been proposed. Only a few methods exist for the online setting, i.e., where only a partial signal trace is available and rest of the signal becomes available in increments (such as in a real system or during numerical simulations). In this paper, we formalize the semantics for robust online monitoring of partial signals using the notion of robust satisfaction intervals (\(\mathtt {RoSI}\)s). We propose an efficient algorithm to compute the \(\mathtt {RoSI}\) and demonstrate its usage on two real-world case studies from the automotive domain and massively-online CPS education. As online algorithms permit early termination when the satisfaction or violation of a property is found, we show that savings in computationally expensive simulations far outweigh any overheads incurred by the online approach.