Synchronous Observers Revisited for Runtime Verification of Lustre Using STL

2026-08-12

AI Summary

This work addresses the need for combined runtime and static verification of Lustre programs by proposing a novel method that compiles Signal Temporal Logic for Synchronous Streams (SSTL) into synchronous Lustre observers. The approach is the first to support arbitrarily nested bounded SSTL properties and introduces a globally unbounded outer operator to enable online monitoring. The resulting observers are generated through modular compilation, allowing seamless integration with the Kind2 model checker for static verification and supporting interactive, three-valued semantic visualization for runtime monitoring. The effectiveness and practicality of the method are demonstrated through case studies on a spring-mass system and an adaptive cruise control system.

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.

Problem

• Signal Temporal Logic
• Runtime Verification
• Synchronous Observers
• Lustre
• Cyber-Physical Systems

Innovation

• synchronous observers
• Signal Temporal Logic (STL)
• Lustre
• runtime verification
• modular compilation