Data-Driven Probabilistic Evaluation of Logic Properties with PAC-Confidence on Mealy Machines
This addresses verification and diagnosis tasks for CPS where models are unavailable, offering a practical solution with incremental improvements in confidence estimation.
The paper tackles the problem of evaluating safety probabilities for Cyber-Physical Systems with discrete Mealy machine abstractions, proposing a data-driven approach based on PAC learning and active learning, validated on an automated lane-keeping system with results providing probabilistic confidence.
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.