Bayesian statistical parameter synthesis for linear temporal properties of stochastic models

Abstract

Parameterized verification of temporal properties is an active research area, being extremely relevant for model-based design of complex systems. In this paper, we focus on parameter synthesis for stochastic models, looking for regions of the parameter space where the model satisfies a linear time specification with probability greater (or less) than a given threshold. We propose a statistical approach relying on simulation and leveraging a machine learning method based on Gaussian Processes for statistical parametric verification, namely Smoothed Model Checking. By injecting active learning ideas, we obtain an efficient synthesis routine which is able to identify the target regions with statistical guarantees. Our approach, which is implemented in Python, scales better than existing ones with respect to state space of the model and number of parameters. It is applicable to linear time specifications with time constraints and to more complex stochastic models than Markov Chains.