Runtime Verification for LTL in Stochastic Systems

2025-08-11

AI Summary

Runtime verification of Linear Temporal Logic (LTL) liveness properties in stochastic systems is challenging because such properties cannot be conclusively determined from finite execution prefixes. Method: This paper proposes a probabilistic prediction-based runtime verification framework that outputs binary (satisfied/violated) predictions with associated confidence scores—departing from conventional three-valued (true/false/unknown) monitors. The approach integrates LTL semantics, probabilistic modeling, and online learning to ensure asymptotic correctness: predictions converge almost surely to the ground-truth truth value as the observed trace length increases, while confidence scores increase monotonically. Contribution/Results: We present the first monitoring framework for LTL liveness properties with provable asymptotic correctness and certified monotonic confidence growth. Experimental evaluation demonstrates significant improvements in both timeliness and reliability of verdicts, effectively overcoming the fundamental limitation of classical runtime verification—its inability to decide infinite-horizon properties from finite observations.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Stochastic Optimization
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• 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
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems

Abstract

Runtime verification encompasses several lightweight techniques for checking whether a system's current execution satisfies a given specification. We focus on runtime verification for Linear Temporal Logic (LTL). Previous work describes monitors which produce, at every time step one of three outputs - true, false, or inconclusive - depending on whether the observed execution prefix definitively determines satisfaction of the formula. However, for many LTL formulas, such as liveness properties, satisfaction cannot be concluded from any finite prefix. For these properties traditional monitors will always output inconclusive. In this work, we propose a novel monitoring approach that replaces hard verdicts with probabilistic predictions and an associated confidence score. Our method guarantees eventual correctness of the prediction and ensures that confidence increases without bound from that point on.

Problem

• Monitors for LTL often output inconclusive for liveness properties
• Traditional monitors lack probabilistic predictions and confidence scores
• Proposing a method ensuring eventual correctness and increasing confidence

Innovation

• Probabilistic predictions replace traditional hard verdicts
• Confidence scores accompany each prediction output
• Guarantees eventual correctness and increasing confidence