Cutting Corners on Uncertainty: Zonotope Abstractions for Stream-based Runtime Monitoring

2026-01-16

AI Summary

This work addresses the challenge of measurement error propagation in streaming runtime monitoring, where sensor inaccuracies can distort verdicts, and traditional approaches fail to satisfy bounded-memory constraints due to unbounded growth of slack variables. The paper introduces, for the first time, the zonotope abstract domain into online monitoring of RLola specifications. By leveraging affine arithmetic, the monitor’s state is precisely represented, and a suite of over-approximation strategies is designed to uniformly handle symbolic slack variables. This approach ensures soundness while maintaining memory usage within strict bounds. Experimental results demonstrate that the proposed method effectively balances monitoring performance and false alarm rates under controlled memory overhead, confirming its feasibility and practical utility.

Technology Category

• Knowledge Representation and Reasoning: Nonmonotonic Reasoning
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Machine Learning: Calibration & Uncertainty Quantification

Application Category

• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization

Abstract

Stream-based monitoring assesses the health of safety-critical systems by transforming input streams of sensor measurements into output streams that determine a verdict. These inputs are often treated as accurate representations of the physical state, although real sensors introduce calibration and measurement errors. Such errors propagate through the monitor's computations and can distort the final verdict. Affine arithmetic with symbolic slack variables can track these errors precisely, but independent measurement noise introduces a fresh slack variable upon each measurement event, causing the monitor's state representation to grow without bound over time. Therefore, any bounded-memory monitoring algorithm must unify slack variables at runtime in a way that generates a sound approximation. This paper introduces zonotopes as an abstract domain for online monitoring of RLola specifications. We demonstrate that zonotopes precisely capture the affine state of the monitor and that their over-approximation produces a sound bounded-memory monitor. We present a comparison of different zonotope over-approximation strategies in the context of runtime monitoring, evaluating their performance and false-positive rates.

Problem

• runtime monitoring
• sensor uncertainty
• bounded-memory
• error propagation
• stream-based monitoring

Innovation

• zonotope
• runtime monitoring
• affine arithmetic
• bounded-memory
• uncertainty propagation