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A Compositional Modelling and Verification Framework for Stochastic Hybrid Systems

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Formal Aspects of Computing

Abstract

In this paper, we propose a general compositional approach for modelling and verification of stochastic hybrid systems (SHSs). We extend Hybrid CSP (HCSP), a very expressive process algebra-like formal modeling language for hybrid systems, by introducing probability and stochasticity to model SHSs, which we call stochastic HCSP (SHCSP). Especially, non-deterministic choice is replaced by probabilistic choice, ordinary differential equations are replaced by stochastic differential equations (SDEs), and communication interrupts are generalized by communication interrupts with weights. We extend Hybrid Hoare Logic to specify and reason about SHCSP processes: On the one hand, we introduce the probabilistic formulas for describing probabilistic states, and on the other hand, we propose the notions of local stochastic differential invariants for characterizing SDEs and global loop invariants for repetition. Throughout the paper, we demonstrate our approach by an aircraft running example.

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Authors and Affiliations

  1. State Key Laboratory of Computer Science, Institute of Software, Chinese Academy of Sciences, Building 5, Software Park, No. 4, South 4th Street, Zhongguancun, Haidian District, Beijing, China

    Shuling Wang, Naijun Zhan & Lijun Zhang

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  1. Shuling Wang
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  2. Naijun Zhan
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  3. Lijun Zhang
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Correspondence to Shuling Wang.

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Cliff Jones, Xuandong Li, and Zhiming Liu

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Wang, S., Zhan, N. & Zhang, L. A Compositional Modelling and Verification Framework for Stochastic Hybrid Systems. Form Asp Comp 29, 751–775 (2017). https://doi.org/10.1007/s00165-017-0421-7

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  • DOI: https://doi.org/10.1007/s00165-017-0421-7

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