Abstract
Hybrid Automata are a well-known framework used to model hybrid systems, containing both discrete and continuous dynamic behavior. However, reachability analysis of hybrid automata is difficult. Existing work does not scale well to the size of practical problems. This paper gives a review of how we handle the verification of hybrid systems in a path-oriented way. First, we propose a path-oriented bounded reachability analysis method to control the complexity of verification of linear hybrid automata. As we only check the reachability of one path at a time, the resulted state space for each computation is limited and hence can be solved efficiently. Then, we present an infeasible constraint guided path-pruning method to tailor the search space, a shallow synchronization semantics to handle compositional behavior, and a method based on linear temporal logic (LTL) to extend the bounded model checking (BMC) result to an unbounded state space. Such methods and tools are implemented in a tool, BACH, and have been used as the underlying decision procedure of our verification of cyber-physical systems (CPS) and Internet of Things (IoT).
This paper follows the lecture notes presented by the first author at the School on Engineering Trustworthy Software Systems (SETSS) in year 2019.
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Notes
- 1.
\(v_1^2\) denotes the second occurrence of the location \(v_1\) (the 6th location) in the path \(\rho \).
- 2.
Unless otherwise denoted, in this section, \(a_{\bullet }\) and \(b_{\bullet }\) represent real valued constants, and \(c_{\bullet }\) represents real valued constant coefficients, where \(\bullet \) is a subscript for identification purposes.
- 3.
We present two ways of authoring specifications. First, users can author specifications according to given templates. Second, we also present a natural language processing-based method to translate specifications in the form of natural language sentence to LTL formulas. Please refer to [33] for detail.
- 4.
As this paper is used as notes for the tutorial of SETSS 2019, and also due to the space limitation, we do not include experimental data in the paper. Please refer to the series works of BACH for detail.
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Acknowledgement
We are grateful to Dingbao Xie, Yang Yang, Wen Xiong, Xinyue Ren, Shaopeng Xing all from Nanjing University, Qixin Wang from Hong Kong Polytechnic University, Mike Liang, Shi Han, Dongmei Zhang from Microsoft Research Asia, Stefano Tonetta, Alessandro Cimatti from Fondazione Bruno Kessler, Edmund Clarke from Carnegie Mellon University and all the other co-authors for their collaboration in previous works on verification of LHA, CPS, and IoT. This paper is supported in part by the National Natural Science Foundation of China (No. 61632015, No. 61572249, 61561146394).
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Bu, L., Wang, J., Wu, Y., Li, X. (2020). From Bounded Reachability Analysis of Linear Hybrid Automata to Verification of Industrial CPS and IoT. In: Bowen, J., Liu, Z., Zhang, Z. (eds) Engineering Trustworthy Software Systems. SETSS 2019. Lecture Notes in Computer Science(), vol 12154. Springer, Cham. https://doi.org/10.1007/978-3-030-55089-9_2
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