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A three-valued model abstraction framework for PCTL* stochastic model checking

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Abstract

Stochastic model checking can automatically verify and analyse the software-driven autonomous systems with stochastic behaviors, which is a formal verification technique based on system models. When coping with large-scale systems, it suffers from state space explosion problem very seriously. Model abstraction is a potential technique for mitigating this problem. At present, only a few properties specified by PCTL (Probabilistic Computation Tree Logic), such as probabilistic safety and probabilistic reachability, can be preserved in the practical model abstraction of stochastic model checking, which are the proper subset of PCTL* (Probabilistic Computation Tree Logic*) properties. For dealing with this, an effective and efficient three-valued model abstraction framework for full PCTL* stochastic model checking is proposed in this paper. We propose a new abstract model to preserve full PCTL* properties for nondeterministic and probabilistic system, which orthogonally integrates interval probability of transition and game for nondeterminism. A game-based three-valued PCTL* stochastic model checking algorithm is developed to verify abstract model, and a BPSO (binary particle swarm optimization) algorithm integrated with sample learning is designed to refine the indefinite result of three-valued PCTL* stochastic model checking abstract model. It is proved that full PCTL* properties are preserved when the result of three-valued stochastic model checking is definite, and the efficiency of this framework is demonstrated by some large cases.

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Acknowledgements

The work was supported by Singapore-UK Cyber Security of EPSRC under Grant Nos. EP/N020170/1, MOE Humanities and Social Sciences Foundation of China under Grant Nos. 20YJCZH102. We would like to extend our deepest respects to Professor Edmund M. Clarke at Carnegie Mellon University, USA, who received ACM Turing Award for his pioneering work of model checking and passed away on December 22, 2020. He inspired us a lot through his books and papers, especially the direct discussion about abstraction for stochastic model checking. Thanks to Professor Marta Kwiatkowska at University of Oxford, UK, for discussion with her about the game semantics for three-valued stochastic model checking.

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  1. Institute of Logistics Science and Engineering, Shanghai Maritime University, Shanghai, 201306, China

    Yang Liu & Yongsheng Yang

  2. School of Accounting, Nanjing University of Finance and Economics, Nanjing, 210023, China

    Yan Ma

  3. School of Computing, National University of Singapore, Singapore, 117417, Singapore

    Yang Liu & Yan Ma

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Liu, Y., Ma, Y. & Yang, Y. A three-valued model abstraction framework for PCTL* stochastic model checking. Autom Softw Eng 29, 29 (2022). https://doi.org/10.1007/s10515-022-00327-z

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