Abstract
Linear Hybrid Automata (LHA) is a natural modeling language for real-time embedded systems. However, due to the existences of both discrete and continuous behaviors, formal analysis of LHA is recognized as a very challenging task. Despite decades of active research, the kinds of LHA problems that can be efficiently analyzed is rather limited. On the other hand, Labelled Linear Transition System (LTS) is a widely used modeling language to describe the state changes of the system before and after certain transitions. Lots of research efforts have been devoted into the verification of LTS models. Many off-the-shelf formal techniques and tools are available for analyzing different kinds of problems for LTS systems. In this paper, we propose to express an LHA as an equivalent LTS model explicitly. Then, we can take advantage of all the off-the-shelf formal checkers of LTS to answer different problems of the LHA model. A prototype tool HAT is implemented under this idea. By integrating typical LTS checkers like ARMC and Interproc, we conduct considerably difficult checking problems like reachability verification, termination analysis, and invariant generation of LHA successfully and efficiently. It shows the open possibility of analyzing more kinds of difficult problems of LHA by LTS checkers easily in the future.
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Notes
- 1.
Please refer to [23] for the detail definition of termination for LTS.
- 2.
For any variable z which is not reset in the transition, the corresponding constraint \(z'=z\) is omitted in the picture to keep the figure neat. Meanwhile, the initial conditions in this model are in the format of \(x:=a\), which can be considered as a special case of the general form \(x\in [a,b]\).
- 3.
The editor is integrated from LHA BMC checker BACH [6].
- 4.
In order to make Interproc handle LTS much easier, we modify the input language syntax of Interproc slightly. The modified version of Interproc is available upon request.
- 5.
The comparison between HAT and the PHAVer algorithm \(SpaceEx_{phav}\) is fair as they are addressing the same class of HA. On the other hand, support function algorithm (\(SpaceEx_{supp}\)) is more suitable to handle HA with piecewise affine dynamics which is different from the class of HA considered in this paper. We just list the data here for reference.
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Acknowledgment
The authors want to thank Prof. Edmund Clarke, Dr. Sumit Jha, Dr. Silke Wagner, and Dr. Axel Legay for their constructive discussions on the topic of presenting an LHA as an LTS for fair termination analysis. The authors also want to thank Prof. Andrey Rybalchenko for his help with ARMC. The valuable comments given by all the anonymous reviewers are also appreciated! This paper is supported in part by the National Natural Science Foundation of China (No.61561146394 and No.61572249), in which No.61561146394 is a Joint NSFC-ISF Research Program, jointly funded by the National Natural Science Foundation of China and the Israel Science Foundation.
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Bu, L., Jiang, H., Chen, X., Tang, E., Li, X. (2018). HAT: Analyzing Linear Hybrid Automata as Labelled Transition System. In: Jones, C., Wang, J., Zhan, N. (eds) Symposium on Real-Time and Hybrid Systems. Lecture Notes in Computer Science(), vol 11180. Springer, Cham. https://doi.org/10.1007/978-3-030-01461-2_5
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