Online Monitoring of Spatio-Temporal Properties for Imprecise Signals

TL;DR

This paper introduces an online algorithm for real-time verification of spatio-temporal properties in dynamic systems using STREL logic, accommodating imprecise signals and partial guarantees, demonstrated through environmental monitoring.

Contribution

It extends existing offline STREL monitoring to an online setting, incorporating imprecise signals and partial guarantees for system behavior conformance.

Findings

First online monitoring algorithm for STREL specifications.

Handles imprecise signals and partial guarantees.

Validated in a real-world environmental case study.

Abstract

From biological systems to cyber-physical systems, monitoring the behavior of such dynamical systems often requires to reason about complex spatio-temporal properties of physical and/or computational entities that are dynamically interconnected and arranged in a particular spatial configuration. Spatio-Temporal Reach and Escape Logic (STREL) is a recent logic-based formal language designed to specify and to reason about spatio-temporal properties. STREL considers each system's entity as a node of a dynamic weighted graph representing their spatial arrangement. Each node generates a set of mixed-analog signals describing the evolution over time of computational and physical quantities characterising the node's behavior. While there are offline algorithms available for monitoring STREL specifications over logged simulation traces, here we investigate for the first time an online algorithm enabling the runtime verification during the system's execution or simulation. Our approach extends the original framework by considering imprecise signals and by enhancing the logics' semantics with the possibility to express partial guarantees about the conformance of the system's behavior with its specification. Finally, we demonstrate our approach in a real-world environmental monitoring case study.