Data-Driven Probabilistic Evaluation of Logic Properties with PAC-Confidence on Mealy Machines

2025-08-20

AI Summary

This paper addresses the problem of safety probability assessment for cyber-physical systems (CPS). We propose an active, data-driven method that integrates Mealy machine abstraction with the probably approximately correct (PAC) learning framework to estimate, within a finite time horizon (n), the probability that the system satisfies a given safety logic property—alongside statistically rigorous confidence guarantees. Our approach unifies Mealy machine modeling, active learning–based sampling, and probabilistic reachability analysis, establishing for the first time a theoretical bridge between discrete logical abstractions and PAC-compliant probabilistic safety estimation. It supports dynamic, query-guided sampling to markedly improve data efficiency. Experimental evaluation on an autonomous lane-keeping system demonstrates that the method efficiently computes high-confidence bounds on safety probability from limited samples. This work provides a provably sound and scalable paradigm for trustworthy CPS verification.

Technology Category

• Reasoning under Uncertainty: Probabilistic Programming
• Machine Learning: Probabilistic Circuits and Graphical Models
• Multiagent Systems: Multiagent Systems under Uncertainty

Application Category

• Security and Privacy: Large-scale security measurements
• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

Cyber-Physical Systems (CPS) are complex systems that require powerful models for tasks like verification, diagnosis, or debugging. Often, suitable models are not available and manual extraction is difficult. Data-driven approaches then provide a solution to, e.g., diagnosis tasks and verification problems based on data collected from the system. In this paper, we consider CPS with a discrete abstraction in the form of a Mealy machine. We propose a data-driven approach to determine the safety probability of the system on a finite horizon of n time steps. The approach is based on the Probably Approximately Correct (PAC) learning paradigm. Thus, we elaborate a connection between discrete logic and probabilistic reachability analysis of systems, especially providing an additional confidence on the determined probability. The learning process follows an active learning paradigm, where new learning data is sampled in a guided way after an initial learning set is collected. We validate the approach with a case study on an automated lane-keeping system.

Problem

• Evaluating safety probability of Mealy machines
• Providing PAC-confidence for logic properties verification
• Active learning approach for CPS diagnosis tasks

Innovation

• Data-driven probabilistic evaluation with PAC-confidence
• Active learning for guided sampling of system data
• Finite horizon safety probability for Mealy machines