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Reachability Analysis and Simulation for Hybridised Event-B Models

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Integrated Formal Methods (IFM 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13274))

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Abstract

The development of cyber-physical systems has become one of the biggest challenges in the field of model-based system engineering. The difficulty stems from the complex nature of cyber-physical systems which have deeply intertwined physical processes, computation and networking system aspects. To provide the highest level of assurance, cyber-physical systems should be modelled and reasoned about at a system-level as their safety depends on a correct interaction between different subsystems. In this paper, we present a development framework of cyber-physical systems which is built upon a refinement and proof based modelling language - Event-B and its extension for modelling hybrid systems. To improve the level of automation in the deductive verification of the resulting hybridised Event-B models, the paper describes a novel approach of integrating reachability analysis in the proof process. Furthermore, to provide a more comprehensive cyber-physical system development and simulation-based validation, we describe mechanism for translating Event-B models of cyber-physical systems to Simulink. The process of applying our framework is evaluated by formally modelling and verifying a cyber-physical railway signalling system.

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Notes

  1. 1.

    Julia programming language website - https://julialang.org/.

References

  1. Abrial, J.R.: Modeling in Event-B: System and Software Engineering. Cambridge University Press, New York (2013)

    MATH  Google Scholar 

  2. Abrial, J.R., Butler, M., Hallerstede, S., Hoang, T.S., Mehta, F., Voisin, L.: Rodin: an open toolset for modelling and reasoning in Event-B. Int. J. Softw. Tools Technol. Transf. 12(6), 447–466 (2010)

    Article  Google Scholar 

  3. Althoff, M., Frehse, G., Girard, A.: Set propagation techniques for reachability analysis. Ann. Rev. Control Robot. Autonom. Syst. 4(1), 369–395 (2021). https://doi.org/10.1146/annurev-control-071420-081941

    Article  Google Scholar 

  4. Alur, R.: Formal verification of hybrid systems. In: Proceedings of the Ninth ACM International Conference on Embedded Software, pp. 273–278. EMSOFT 2011, ACM, New York, NY, USA (2011). https://doi.org/10.1145/2038642.2038685

  5. Babin, G., Aït-Ameur, Y., Nakajima, S., Pantel, M.: Refinement and proof based development of systems characterized by continuous functions. In: Li, X., Liu, Z., Yi, W. (eds.) Dependable Software Engineering: Theories, Tools, and Applications, pp. 55–70. Springer International Publishing, Cham (2015)

    Chapter  Google Scholar 

  6. Banach, R., Butler, M., Qin, S., Verma, N., Zhu, H.: Core hybrid event-b I: single hybrid event-b machines. Sci. Comput. Program. 105, 92–123 (2015)

    Article  Google Scholar 

  7. Barney, D., Haley, D., Nikandros, G.: Calculating train braking distance. In: Proceedings of the Sixth Australian Workshop on Safety Critical Systems and Software - Volume 3, pp. 23–29. SCS 2001, Australian Computer Society Inc., AUS (2001)

    Google Scholar 

  8. Bezanson, J., Edelman, A., Karpinski, S., Shah, V.B.: Julia: a fresh approach to numerical computing. SIAM Rev. 59(1), 65–98 (2017). https://doi.org/10.1137/141000671

    Article  MathSciNet  MATH  Google Scholar 

  9. Bogdiukiewicz, C., et al.: Formal development of policing functions for intelligent systems. In: 2017 IEEE 28th International Symposium on Software Reliability Engineering (ISSRE), pp. 194–204 (2017). https://doi.org/10.1109/ISSRE.2017.40

  10. Bogomolov, S., Forets, M., Frehse, G., Potomkin, K., Schilling, C.: JuliaReach: a toolbox for set-based reachability. In: Proceedings of the 22nd ACM International Conference on Hybrid Systems: Computation and Control, pp. 39–44. HSCC 2019, Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3302504.3311804

  11. Butler, M., Maamria, I.: Practical theory extension in Event-B. In: Liu, Z., Woodcock, J., Zhu, H. (eds.) Theories of Programming and Formal Methods. LNCS, vol. 8051, pp. 67–81. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-39698-4_5

    Chapter  Google Scholar 

  12. Chen, X., Ábrahám, E., Sankaranarayanan, S.: Flow*: an analyzer for non-linear hybrid systems. In: Sharygina, N., Veith, H. (eds.) CAV 2013. LNCS, vol. 8044, pp. 258–263. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-39799-8_18

    Chapter  Google Scholar 

  13. Chutinan, A., Krogh, B.H.: Verification of polyhedral-invariant hybrid automata using polygonal flow pipe approximations. In: Vaandrager, F.W., van Schuppen, J.H. (eds.) HSCC 1999. LNCS, vol. 1569, pp. 76–90. Springer, Heidelberg (1999). https://doi.org/10.1007/3-540-48983-5_10

    Chapter  MATH  Google Scholar 

  14. Déharbe, D., Fontaine, P., Guyot, Y., Voisin, L.: Integrating SMT solvers in Rodin. Sci. Comput. Program. 94(P2), 130–143 (2014)

    Article  Google Scholar 

  15. Dupont, G., Aït-Ameur, Y., Pantel, M., Singh, N.K.: An Event-B based generic framework for hybrid systems formal modelling. In: Dongol, B., Troubitsyna, E. (eds.) IFM 2020. LNCS, vol. 12546, pp. 82–102. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-63461-2_5

    Chapter  Google Scholar 

  16. Dupont, G., Aït-Ameur, Y., Pantel, M., Singh, N.K.: Proof-based approach to hybrid systems development: dynamic logic and Event-B. In: Butler, M., Raschke, A., Hoang, T.S., Reichl, K. (eds.) ABZ 2018. LNCS, vol. 10817, pp. 155–170. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-91271-4_11

    Chapter  Google Scholar 

  17. Dupont, G., Ait-Ameur, Y., Singh, N.K., Pantel, M.: Event-B hybridation: A proof and refinement-based framework for modelling hybrid systems. ACM Trans. Embed. Comput. Syst. 20(4), 1–37 (2021). https://doi.org/10.1145/3448270

  18. Fidge, C.J.: Specification and verification of real-time behaviour using Z and RTL. In: Vytopil, J. (ed.) FTRTFT 1992. LNCS, vol. 571, pp. 393–409. Springer, Heidelberg (1992). https://doi.org/10.1007/3-540-55092-5_22

    Chapter  Google Scholar 

  19. Frehse, G., et al.: SpaceEx: scalable verification of hybrid systems. In: Gopalakrishnan, G., Qadeer, S. (eds.) CAV 2011. LNCS, vol. 6806, pp. 379–395. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-22110-1_30

    Chapter  Google Scholar 

  20. Geretti, L., et al.: ARCH-COMP20 category report: continuous and hybrid systems with nonlinear dynamics. In: Frehse, G., Althoff, M. (eds.) ARCH 2020. 7th International Workshop on Applied Verification of Continuous and Hybrid Systems (ARCH20). EPiC Series in Computing, vol. 74, pp. 49–75. EasyChair (2020). https://doi.org/10.29007/zkf6

  21. Harel, D.: Statecharts: a visual formalism for complex systems. Sci. Comput. Program. 8(3), 231–274 (1987). https://doi.org/10.1016/0167-6423(87)90035-9

    Article  MathSciNet  MATH  Google Scholar 

  22. Iliasov, A., Stankaitis, P., Adjepon-Yamoah, D., Romanovsky, A.: Rodin platform why3 plug-in. In: Butler, M., Schewe, K.-D., Mashkoor, A., Biro, M. (eds.) ABZ 2016. LNCS, vol. 9675, pp. 275–281. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-33600-8_21

    Chapter  Google Scholar 

  23. Immler, F.: Verified reachability analysis of continuous systems. In: Baier, C., Tinelli, C. (eds.) TACAS 2015. LNCS, vol. 9035, pp. 37–51. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-46681-0_3

    Chapter  Google Scholar 

  24. Jifeng, H.: A classical mind. chap. In: From CSP to Hybrid Systems, pp. 171–189. Prentice Hall International (UK) Ltd. (1994)

    Google Scholar 

  25. Jones, C.B.: Systematic Software Development Using VDM, 2nd edn. Prentice-Hall Inc., USA (1990)

    MATH  Google Scholar 

  26. Kim, K.D., Kumar, P.R.: Cyber-physical systems: a perspective at the centennial. In: Proceedings of the IEEE 100 (Special Centennial Issue), pp. 1287–1308, May 2012. https://doi.org/10.1109/JPROC.2012.2189792

  27. Lamport, L.: Hybrid systems in TLA+. In: Grossman, R.L., Nerode, A., Ravn, A.P., Rischel, H. (eds.) HS 1991-1992. LNCS, vol. 736, pp. 77–102. Springer, Heidelberg (1993). https://doi.org/10.1007/3-540-57318-6_25

    Chapter  Google Scholar 

  28. Larsen, P.G., et al.: Integrated tool chain for model-based design of cyber-physical systems: the INTO-CPS project. In: 2016 2nd International Workshop on Modelling, Analysis, and Control of Complex CPS (CPS Data), pp. 1–6 (2016). https://doi.org/10.1109/CPSData.2016.7496424

  29. Lee, E.A.: Cyber physical systems: design challenges. In: 2008 11th IEEE International Symposium on Object Oriented Real-Time Distributed Computing (ISORC), pp. 363–369. IEEE (2008)

    Google Scholar 

  30. Lee, E.A., Zheng, H.: Operational semantics of hybrid systems. In: Hybrid Systems: Computation and Control, 8th International Workshop, HSCC 2005, Zurich, Switzerland, March 9–11, 2005, Proceedings, pp. 25–53 (2005). https://doi.org/10.1007/978-3-540-31954-2_2

  31. Lee, E.A., Zheng, H.: HyVisual: a hybrid system modeling framework based on Ptolemy II. IFAC Proc. Vol. 39(5), 270–271 (2006). https://doi.org/10.3182/20060607-3-IT-3902.00050

  32. Leuschel, M., Butler, M.: ProB: a model checker for B. In: Araki, K., Gnesi, S., Mandrioli, D. (eds.) FME 2003. LNCS, vol. 2805, pp. 855–874. Springer, Heidelberg (2003). https://doi.org/10.1007/978-3-540-45236-2_46

    Chapter  Google Scholar 

  33. Liebrenz, T., Herber, P., Glesner, S.: Deductive Verification of Hybrid Control Systems Modeled in Simulink with KeYmaera X. In: Sun, J., Sun, M. (eds.) ICFEM 2018. LNCS, vol. 11232, pp. 89–105. Springer, Cham (2018). https://doi.org/10.1007/978-3-030-02450-5_6

    Chapter  Google Scholar 

  34. Liu, J., et al.: A calculus for hybrid CSP. In: Ueda, K. (ed.) APLAS 2010. LNCS, vol. 6461, pp. 1–15. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-17164-2_1

    Chapter  Google Scholar 

  35. MathWorks, T.: Simulink user’s guide (2021)

    Google Scholar 

  36. MathWorks, T.: Stateflow user’s guide (2021)

    Google Scholar 

  37. Platzer, A., Quesel, J.-D.: KeYmaera: a hybrid theorem prover for hybrid systems (system description). In: Armando, A., Baumgartner, P., Dowek, G. (eds.) IJCAR 2008. LNCS (LNAI), vol. 5195, pp. 171–178. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-71070-7_15

    Chapter  Google Scholar 

  38. Rochard, B.P., Schmid, F.: A review of methods to measure and calculate train resistances. Proc. Inst. Mech. Eng. Part F J. Rail Rapid Transit. 214(4), 185–199 (2000). https://doi.org/10.1243/0954409001531306

    Article  Google Scholar 

  39. Sanwal, M.U., Hasan, O.: Formally analyzing continuous aspects of cyber-physical systems modeled by homogeneous linear differential equations. In: Berger, C., Mousavi, M.R. (eds.) CyPhy 2015. LNCS, vol. 9361, pp. 132–146. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-25141-7_10

    Chapter  Google Scholar 

  40. Singh, N.K., Lawford, M., Maibaum, T.S.E., Wassyng, A.: Stateflow to tabular expressions. In: Proceedings of the Sixth International Symposium on Information and Communication Technology, pp. 312–319. SoICT 2015, Association for Computing Machinery, New York, NY, USA (2015). https://doi.org/10.1145/2833258.2833285

  41. Stankaitis, P., Dupont, G., Singh, N.K., Ait-Ameur, Y., Iliasov, A., Romanovsky, A.: Modelling hybrid train speed controller using proof and refinement. In: 2019 24th International Conference on Engineering of Complex Computer Systems (ICECCS), pp. 107–113 (2019). https://doi.org/10.1109/ICECCS.2019.00019

  42. Stankaitis, P., Iliasov, A., Ameur, Y.A., Kobayashi, T., Ishikawa, F., Romanovsky, A.: A refinement based method for developing distributed protocols. In: IEEE 19th International Symposium on High Assurance Systems Engineering (HASE), pp. 90–97 (2019)

    Google Scholar 

  43. Su, W., Abrial, J.-R.: Aircraft landing gear system: approaches with event-b to the modeling of an industrial system. In: Boniol, F., Wiels, V., Ait Ameur, Y., Schewe, K.-D. (eds.) ABZ 2014. CCIS, vol. 433, pp. 19–35. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-07512-9_2

    Chapter  Google Scholar 

  44. Verhoef, M., Larsen, P.G., Hooman, J.: Modeling and validating distributed embedded real-time systems with VDM++. In: Misra, J., Nipkow, T., Sekerinski, E. (eds.) FM 2006. LNCS, vol. 4085, pp. 147–162. Springer, Heidelberg (2006). https://doi.org/10.1007/11813040_11

    Chapter  Google Scholar 

  45. Chaochen, Z., Ji, W., Ravn, A.P.: A formal description of hybrid systems. In: Alur, R., Henzinger, T.A., Sontag, E.D. (eds.) HS 1995. LNCS, vol. 1066, pp. 511–530. Springer, Heidelberg (1996). https://doi.org/10.1007/BFb0020972

    Chapter  Google Scholar 

  46. Zou, L., Zhan, N., Wang, S., Fränzle, M.: Formal verification of Simulink/Stateflow diagrams. In: Automated Technology for Verification and Analysis - 13th International Symposium, ATVA 2015, Shanghai, China, 12–15 October 2015, Proceedings, pp. 464–481 (2015). https://doi.org/10.1007/978-3-319-24953-7_33

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Acknowledgements

This work was partially supported by the Air Force Office of Scientific Research under award no. FA2386-17-1-4065. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the United States Air Force. This work is also supported by the DISCONT project of the French National Research Agency (ANR-17-CE25-0005, The DISCONT Project, https://discont.loria.fr).

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Authors and Affiliations

  1. INPT–ENSEEIHT, 2 Rue Charles Camichel, Toulouse, France

    Yamine Aït-Ameur, Guillaume Dupont & Neeraj Kumar Singh

  2. School of Computing, Newcastle University, Newcastle upon Tyne, UK

    Sergiy Bogomolov & Paulius Stankaitis

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  1. Yamine Aït-Ameur
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  2. Sergiy Bogomolov
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  3. Guillaume Dupont
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  4. Neeraj Kumar Singh
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  5. Paulius Stankaitis
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Correspondence to Paulius Stankaitis .

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Editors and Affiliations

  1. ISTI-CNR, Pisa, Italy

    Maurice H. ter Beek

  2. Maynooth University, Maynooth, Ireland

    Rosemary Monahan

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Aït-Ameur, Y., Bogomolov, S., Dupont, G., Singh, N.K., Stankaitis, P. (2022). Reachability Analysis and Simulation for Hybridised Event-B Models. In: ter Beek, M.H., Monahan, R. (eds) Integrated Formal Methods. IFM 2022. Lecture Notes in Computer Science, vol 13274. Springer, Cham. https://doi.org/10.1007/978-3-031-07727-2_7

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