Abstract
Model checking techniques have often been applied to the verification of railway interlocking systems. However, these techniques may fail to scale to interlockings controlling large railway networks, composed by hundreds of controlled entities, due to the state space explosion problem. We have previously proposed a compositional method to reduce the size of networks to be model checked: the idea is to divide the network of the system to be verified into two sub-networks and then model check the model instances for these sub-networks instead of that for the full network. If given well-formedness conditions are satisfied by the network and the kind of division performed, it is proved that model checking safety properties of all such sub-networks guarantees safety properties of the full network. In this paper we observe that such a network division can be repeated, so that in the end, the full network has been divided into a number of sub-networks of minimal size, each being an instance of one of a limited set of “elementary networks”, for which safety proofs have easily been given by model checking once for all. The paper defines a division algorithm, and shows how, applying it to some examples of different complexity, a network can be automatically decomposed into a set of elementary networks, hence proving its safety. The execution time for such a verification turns out to be a very small fraction of the time needed for a model checker to verify safety of the full network.
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Notes
- 1.
- 2.
- 3.
We are considering modern ERTMS level 2 based interlocking systems for which there are no physical signals. They are replaced by markerboards, and in the control system there are virtual signals associated with the markerboards. Throughout the paper we use the term signal as a synonym for markerboard.
- 4.
A network is loop-free, if there are no physically possible path through the network containing the same section more than once.
- 5.
Throughout this paper, as generic model and safety properties, we are using those from [20]. The properties are the no collision and no derailment properties, shared by the vast literature on interlocking verification.
- 6.
The notion of flank protection is explained in the end of Sect. 4.2.
- 7.
By connected we mean that by navigating the graph of the not yet visited part of the network starting from the two sides we eventually reach a common point.
- 8.
Note that when coming from the stem, we do not have such a problem, as a route cannot pass through a point via its two branches.
- 9.
The decompose function was repeatedly invoked with each of the network’s borders as the border parameter b of decompose, and then the average execution time was computed. Note that the invocations with different b on the same network sometimes produce slightly different sets of networks: the cardinalities of the sets of networks returned by two different invocations are the same and networks are usually the same, except that sometimes a linear section may be included in a different sub-network.
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Acknowledgements
The authors would like to thank (1) Jan Peleska and Linh H. Vu together with whom Anne Haxthausen developed the RobustRailS verification method and tools, (2) Hugo D. Macedo, who contributed to the initial work on the applied compositional method, and to (3) Anna Nam Anh Nguyen and Ole Eilgaard for their network cutter tool which we have integrated in our decomposer tool. The contribution by the second and third author was carried out within the MOST – Sustainable Mobility National Research Center and received funding from the European Union Next-GenerationEU (Piano Nazionale di Ripresa e Resilienza (PNRR) – Missione 4 Componente 2, Investimento 1.4 – D.D. 1033 17/06/2022, CN00000023). This manuscript reflects only the authors’ views and opinions, neither the European Union nor the European Commission can be considered responsible for them.
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Haxthausen, A.E., Fantechi, A., Gori, G., Mikkelsen, Ó.K., Petersen, SA. (2023). Automated Compositional Verification of Interlocking Systems. In: Milius, B., Collart-Dutilleul, S., Lecomte, T. (eds) Reliability, Safety, and Security of Railway Systems. Modelling, Analysis, Verification, and Certification. RSSRail 2023. Lecture Notes in Computer Science, vol 14198. Springer, Cham. https://doi.org/10.1007/978-3-031-43366-5_9
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