Synchronous Observers Revisited for Runtime Verification of Lustre Using STL

Abstract

Signal Temporal Logic (STL) is a popular formalism for the temporal safety properties of cyber-physical systems, most often used for runtime verification. In the synchronous family of languages, safety properties are instead expressed as synchronous observers, modules composed with a program for static verification, which are also runnable specifications suitable for runtime verification, though this use is rarely explored. We present a technique for compiling the synchronous fragment of STL (SSTL) into synchronous observers in the dataflow language Lustre. Unlike previous work, we allow arbitrary nesting of bounded SSTL properties via modular compilation, and admit a globally unbounded outer operator for online monitoring; the resulting observers serve both runtime verification and, as a by-product, static verification with the Kind2 model checker. We further contribute an interactive visualiser that renders a property's three-valued verdict over an editable trace, and evaluate on two case studies from the literature: a spring-mass system and a car-following cruise controller.