An Algebraic Framework for Runtime Verification

Runtime verification (RV) is a pragmatic and scalable, yet rigorous technique, to assess the correctness of complex systems, including cyber-physical systems (CPSs). Modern RV tools also allow to measure the distance of a CPS behavior from a given formal requirement, thus, to quantify the robustness of a CPS with respect to perturbations caused by the physical environment. In this paper, we propose algebraic RV (ARV), a general, semantic framework for correctness and robustness monitoring. ARV implements an abstract monitoring procedure, in which the specification language (STL) can be instantiated with various qualitative and quantitative semantics. This allows us to expose the core aspects of RV, by separating the monitoring algorithm from the concrete choice of the STL and its semantics. We demonstrate the effectiveness of our framework on two examples from the automotive domain.