Robust online monitoring of signal temporal logic

Signal temporal logic (STL) is a formalism used to rigorously specify requirements of cyberphysical systems (CPS), i.e., systems mixing digital or discrete components in interaction with a continuous environment or analog components. STL is naturally equipped with a quantitative semantics which can be used for various purposes: from assessing the robustness of a specification to guiding searches over the input and parameter space with the goal of falsifying the given property over system behaviors. Algorithms have been proposed and implemented for offline computation of such quantitative semantics, but only few methods exist for an online setting, where one would want to monitor the satisfaction of a formula during simulation. In this paper, we formalize a semantics for robust online monitoring of partial traces, i.e., traces for which there might not be enough data to decide the Boolean satisfaction (and to compute its quantitative counterpart). We propose an efficient algorithm to compute it and demonstrate its usage on two large scale real-world case studies coming from the automotive domain and from CPS education in a Massively Open Online Course setting. We show that savings in computationally expensive simulations far outweigh any overheads incurred by an online approach.