Continuous simulation abstraction refinement for Markov decision processes

Combating state space explosion problem is the main challenge of the application of probabilistic model checking. This paper presents an abstraction refinement technique which can analyze the probabilistic reach-ability property of Markov Decision Process in case of very large state space. This method which is called continuous simulation abstraction refinement (CSAR) divides the state space of the concrete model into regions and computes minimum and maximum values for reach-ability properties of the regions rather than that of concrete states in the model. In order to compute these valuations, the method iterates over all regions and considers the concrete states in each region in turn. The algorithm dynamically refines the regions and converges when the difference between the valuations meets the specified accuracy requirements. Otherwise, the region will be refined into smaller regions. Furthermore, based on two case studies, experimental results illustrate that this method can calculate precise measures while reducing memory requirements.