Obtaining complete and accurate models for the formal verification of systems is often hard or impossible. We present a data-based verification approach, for properties expressed in a probabilistic logic, that addresses incomplete model knowledge. We obtain experimental data from a system that can be modelled as a parametric Markov chain. We propose a novel verification algorithm to quantify the confidence the underlying system satisfies a given property of interest by using this data. Given a parameterised model of the system, the procedure first generates a feasible set of parameters corresponding to model instances satisfying a given probabilistic property. Simultaneously, we use Bayesian inference to obtain a probability distribution over the model parameter set from data sampled from the underlying system. The results of both steps are combined to compute a confidence the underlying system satisfies the property. The amount data required is minimised by exploiting partial knowledge of the system. Our approach offers a framework to integrate Bayesian inference and formal verification, and in our experiments our new approach requires one order of magnitude less data than standard statistical model checking to achieve the same confidence.

Abstract. We present a new method for statistical verification of quantitative properties over a partially unknown system with actions, utilising a parameterised model (in this work, a parametric Markov decision process) and data collected from experiments performed on the underlying system. We obtain the confidence that the underlying system satisfies a given property, and show that the method uses data efficiently and thus is robust to the amount of data available. These characteristics are achieved by firstly exploiting parameter synthesis to establish a feasible set of parameters for which the underlying system will satisfy the property; secondly, by actively synthesising experiments to increase amount of information in the collected data that is relevant to the property; and finally propagating this information over the model parameters, obtaining a confidence that reflects our belief whether or not the system parameters lie in the feasible set, thereby solving the verification problem.

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