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Parallel Composition and Modular Verification of Computer Controlled Systems in Differential Dynamic Logic

  • Simon Lunel
  • Stefan Mitsch
  • Benoit Boyer
  • Jean-Pierre TalpinEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11800)

Abstract

Computer-Controlled Systems (CCS) are a subclass of hybrid systems where the periodic relation of control components to time is paramount. Since they additionally are at the heart of many safety-critical devices, it is of primary importance to correctly model such systems and to ensure they function correctly according to safety requirements. Differential dynamic logic \(d\mathcal {L}\) is a powerful logic to model hybrid systems and to prove their correctness. We contribute a component-based modeling and reasoning framework to \(d\mathcal {L}\) that separates models into components with timing guarantees, such as reactivity of controllers and controllability of continuous dynamics. Components operate in parallel, with coarse-grained interleaving, periodic execution and communication. We present techniques to automate system safety proofs from isolated, modular, and possibly mechanized proofs of component properties parameterized with timing characteristics.

References

  1. 1.
    Alur, R., Courcoubetis, C., Henzinger, T.A., Ho, P.-H.: Hybrid automata: an algorithmic approach to the specification and verification of hybrid systems. In: Grossman, R.L., Nerode, A., Ravn, A.P., Rischel, H. (eds.) HS 1991-1992. LNCS, vol. 736, pp. 209–229. Springer, Heidelberg (1993).  https://doi.org/10.1007/3-540-57318-6_30CrossRefGoogle Scholar
  2. 2.
    Benveniste, A., et al.: Contracts for system design. Technical report (2012)Google Scholar
  3. 3.
    Fulton, N., Mitsch, S., Quesel, J.-D., Völp, M., Platzer, A.: KeYmaera X: an axiomatic tactical theorem prover for hybrid systems. In: Felty, A.P., Middeldorp, A. (eds.) CADE 2015. LNCS (LNAI), vol. 9195, pp. 527–538. Springer, Cham (2015).  https://doi.org/10.1007/978-3-319-21401-6_36CrossRefGoogle Scholar
  4. 4.
    Henzinger, T.A., Minea, M., Prabhu, V.: Assume-guarantee reasoning for hierarchical hybrid systems. In: Di Benedetto, M.D., Sangiovanni-Vincentelli, A. (eds.) HSCC 2001. LNCS, vol. 2034, pp. 275–290. Springer, Heidelberg (2001).  https://doi.org/10.1007/3-540-45351-2_24CrossRefzbMATHGoogle Scholar
  5. 5.
    Jifeng, H.: From CSP to hybrid systems. In: A Classical Mind, pp. 171–189. Prentice Hall International (UK) Ltd. (1994)Google Scholar
  6. 6.
    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_1CrossRefGoogle Scholar
  7. 7.
    Lunel, S., Boyer, B., Talpin, J.-P.: Compositional proofs in differential dynamic logic. In: Legay, A., Schneider, K. (eds.) ACSD (2017)Google Scholar
  8. 8.
    Lunel, S., Mitsch, S., Boyer, B., Talpin, J.-P.: Parallel composition and modular verification of computer controlled systems in differential dynamic logic. CoRR, abs/1907.02881, July 2019Google Scholar
  9. 9.
    Lynch, N.A., Segala, R., Vaandrager, F.W.: Hybrid I/O automata. Inf. Comput. 185(1), 105–157 (2003)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Müller, A., Mitsch, S., Retschitzegger, W., Schwinger, W., Platzer, A.: A component-based approach to hybrid systems safety verification. In: Ábrahám, E., Huisman, M. (eds.) IFM 2016. LNCS, vol. 9681, pp. 441–456. Springer, Cham (2016).  https://doi.org/10.1007/978-3-319-33693-0_28CrossRefGoogle Scholar
  11. 11.
    Müller, A., Mitsch, S., Retschitzegger, W., Schwinger, W., Platzer, A.: Tactical contract composition for hybrid system component verification. STTT 20(6), 615–643 (2018). Special issue for selected papers from FASE 2017CrossRefGoogle Scholar
  12. 12.
    Platzer, A.: The complete proof theory of hybrid systems. In: LICS, pp. 541–550. IEEE (2012)Google Scholar
  13. 13.
    Platzer, A.: A complete uniform substitution calculus for differential dynamic logic. J. Autom. Reas. 59(2), 219–265 (2017)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Platzer, A.: Logical Foundations of Cyber-Physical Systems. Springer, Cham (2018).  https://doi.org/10.1007/978-3-319-63588-0CrossRefzbMATHGoogle Scholar
  15. 15.
    Platzer, A., Tan, Y.K.: Differential equation axiomatization: the impressive power of differential ghosts. In: Dawar, A., Grädel, E. (eds.) LICS, pp. 819–828. ACM, New York (2018)Google Scholar
  16. 16.
    Signoles, J., Cuoq, P., Kirchner, F., Kosmatov, N., Prevosto, V., Yakobowski, B.: Frama-C: a software analysis perspective. Form. Asp. Comput. 27, 573–609 (2012)MathSciNetGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Simon Lunel
    • 1
    • 2
  • Stefan Mitsch
    • 3
  • Benoit Boyer
    • 1
  • Jean-Pierre Talpin
    • 2
    Email author
  1. 1.Mitsubishi Electric R&D Centre EuropeRennes CEDEX 7France
  2. 2.Inria, Centre de recherche Rennes - Bretagne - Atlantique, Campus universitaire de BeaulieuRennes CedexFrance
  3. 3.Computer Science DepartmentCarnegie Mellon UniversityPittsburghUSA

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