Skip to main content

Type-Based Verification of Delegated Control in Hybrid Systems

  • Chapter
  • First Online:
Active Object Languages: Current Research Trends

Abstract

We present a post-region-based verification system for distributed hybrid systems modeled with Hybrid Active Objects. The post-region of a class method is the region of the state space where a physical process must be proven safe to ensure some object invariant. Prior systems computed the post-region locally to a single object and could only verify systems where each object ensures its own safety, or relied on specific, non-modular communication patterns. The system presented here uses a type-and-effect system to structure the interactions between objects and computes post-regions globally, but verifies them locally. Furthermore, we are able to handle systems with delegated control: the object and method that shape the post-region change over time. We exemplify our approach with a model of a cloud-based hybrid system.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 59.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 74.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    All fields, independent of where they are declared, are accessible only from their object.

  2. 2.

    The difference is that the process is scheduled and descheduled immediately at its start.

  3. 3.

    I.e., a process that performs any action instead of descheduling immediately.

  4. 4.

    The post-region is a part of the state space of the object, with time as a dimension.

  5. 5.

    Available at https://formbar.raillab.de/wp-content/uploads/2021/10/nodecloud.zip.

  6. 6.

    As stated in Sect. 3.1, our type system can manage arbitrary loop statements by implicitly and automatically replacing them with dedicated method calls and synchronization. We don’t use this approach in our informal explanation of the type system because even though this automatic approach always works (i.e., it is correct and complete), it adds new methods, calls and synchronization that obfuscate our explanations. Note that we do not require the recursion to be bounded.

References

  1. Ahrendt, W., Beckert, B., Bubel, R., Hähnle, R., Schmitt, P.H., Ulbrich, M. (eds.): Deductive Software Verification - The KeY Book - From Theory to Practice. LNCS, vol. 10001. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-49812-6

    Book  Google Scholar 

  2. Albert, E., Arenas, P., Genaim, S., Gómez-Zamalloa, M., Puebla, G.: COSTABS: a cost and termination analyzer for ABS. In: Kiselyov, O., Thompson, S.J. (eds.) PEPM. ACM (2012)

    Google Scholar 

  3. Albert, E., Correas, J., Johnsen, E.B., Pun, V.K.I., Román-Díez, G.: Parallel cost analysis. ACM Trans. Comput. Log. 19(4) (2018)

    Google Scholar 

  4. Albert, E., et al.: Formal modeling and analysis of resource management for cloud architectures: an industrial case study using real-time ABS. Serv. Oriented Comput. Appl. 8(4) (2014)

    Google Scholar 

  5. Albert, E., Genaim, S., Martin-Martin, E., Merayo, A., Rubio, A.: Lower-bound synthesis using loop specialization and Max-SMT. In: Silva, A., Leino, K.R.M. (eds.) CAV 2021. LNCS, vol. 12760, pp. 863–886. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-81688-9_40

    Chapter  Google Scholar 

  6. 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_30

    Chapter  Google Scholar 

  7. Avanzini, M., Lago, U.D.: Automating sized-type inference for complexity analysis. Proc. ACM Program. Lang. 1(ICFP) (2017)

    Google Scholar 

  8. Baar, T., Staroletov, S.: A control flow graph based approach to make the verification of cyber-physical systems using KeYmaera easier. Model. Anal. Inf. Syst. 25(5) (2019)

    Google Scholar 

  9. Bergstra, J.A., Klop, J.W.: Algebra of communicating processes with abstraction. Theor. Comput. Sci. 37 (1985)

    Google Scholar 

  10. Bergstra, J.A., Middelburg, C.A.: Process algebra for hybrid systems. Theor. Comput. Sci. 335(2–3) (2005)

    Google Scholar 

  11. Bjørk, J., de Boer, F.S., Johnsen, E.B., Schlatte, R., Tapia Tarifa, S.L.: User-defined schedulers for real-time concurrent objects. Innov. Syst. Softw. Eng. 9(1) (2013)

    Google Scholar 

  12. Bocchi, L., Yang, W., Yoshida, N.: Timed multiparty session types. In: Baldan, P., Gorla, D. (eds.) CONCUR 2014. LNCS, vol. 8704, pp. 419–434. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-662-44584-6_29

    Chapter  Google Scholar 

  13. Bohrer, B., Platzer, A.: Structured proofs for adversarial cyber-physical systems. CoRR, abs/2107.08852 (2021)

    Google Scholar 

  14. Bos, V., Kleijn, J.J.T.: Redesign of a systems engineering language: formalisation of X. Formal Aspects Comput. 15(4) (2003)

    Google Scholar 

  15. Clarke, D., Wrigstad, T., Östlund, J., Johnsen, E.B.: Minimal ownership for active objects. In: Ramalingam, G. (ed.) APLAS 2008. LNCS, vol. 5356, pp. 139–154. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-89330-1_11

    Chapter  Google Scholar 

  16. Cuijpers, P.J.L., Reniers, M.A.: Hybrid process algebra. J. Log. Algebraic Methods Program. 62(2) (2005)

    Google Scholar 

  17. de Boer, F.S., et al.: A survey of active object languages. ACM Comput. Surv. 50(5) (2017)

    Google Scholar 

  18. Din, C.C., Bubel, R., Hähnle, R.: KeY-ABS: a deductive verification tool for the concurrent modelling language ABS. In: Felty, A.P., Middeldorp, A. (eds.) CADE 2015. LNCS (LNAI), vol. 9195, pp. 517–526. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_35

    Chapter  Google Scholar 

  19. Din, C.C., Owe, O.: Compositional reasoning about active objects with shared futures. Formal Asp. Comput. 27(3) (2015)

    Google Scholar 

  20. Flores-Montoya, A.: Upper and lower amortized cost bounds of programs expressed as cost relations. In: Fitzgerald, J., Heitmeyer, C., Gnesi, S., Philippou, A. (eds.) FM 2016. LNCS, vol. 9995, pp. 254–273. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-48989-6_16

    Chapter  Google Scholar 

  21. 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_36

    Chapter  Google Scholar 

  22. Galpin, V., Bortolussi, L., Hillston, J.: HYPE: hybrid modelling by composition of flows. Formal Aspects Comput. 25(4) (2013)

    Google Scholar 

  23. Giachino, E., Johnsen, E.B., Laneve, C., Pun, K.I.: Time complexity of concurrent programs. In: Braga, C., Ölveczky, P.C. (eds.) FACS 2015. LNCS, vol. 9539, pp. 199–216. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-28934-2_11

    Chapter  Google Scholar 

  24. Goncharov, S., Neves, R., Proença, J.: Implementing hybrid semantics: from functional to imperative. In: Pun, V.K.I., Stolz, V., Simao, A. (eds.) ICTAC 2020. LNCS, vol. 12545, pp. 262–282. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-64276-1_14

    Chapter  Google Scholar 

  25. Hennessy, M., Regan, T.: A process algebra for timed systems. Inf. Comput. 117(2) (1995)

    Google Scholar 

  26. Hoare, C.A.R.: An axiomatic basis for computer programming. Commun. ACM 12(10) (1969)

    Google Scholar 

  27. Jahandideh, I., Ghassemi, F., Sirjani, M.: An actor-based framework for asynchronous event-based cyber-physical systems. Softw. Syst. Model. 20(3) (2021)

    Google Scholar 

  28. Johnsen, E.B., Schlatte, R., Tarifa, S.L.T.: Integrating deployment architectures and resource consumption in timed object-oriented models. J. Log. Algebraic Methods Program. 84(1) (2015)

    Google Scholar 

  29. Kamburjan, E.: Behavioral program logic. In: Cerrito, S., Popescu, A. (eds.) TABLEAUX 2019. LNCS (LNAI), vol. 11714, pp. 391–408. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-29026-9_22

    Chapter  Google Scholar 

  30. Kamburjan, E.: From post-conditions to post-region invariants: deductive verification of hybrid objects. In: HSCC. ACM (2021)

    Google Scholar 

  31. Kamburjan, E.: Modular analysis of distributed hybrid systems using post-regions (full version). CoRR, abs/2309.10470 (2023)

    Google Scholar 

  32. Kamburjan, E., Din, C.C., Hähnle, R., Johnsen, E.B.: Behavioral contracts for cooperative scheduling. In: Ahrendt, W., Beckert, B., Bubel, R., Hähnle, R., Ulbrich, M. (eds.) Deductive Software Verification: Future Perspectives. LNCS, vol. 12345, pp. 85–121. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-64354-6_4

    Chapter  Google Scholar 

  33. Kamburjan, E., Lienhardt, M.: Type-based verification of delegated control in hybrid systems (full version). CoRR, abs/2309.01370 (2023)

    Google Scholar 

  34. Kamburjan, E., Mitsch, S., Hähnle, R.: A hybrid programming language for formal modeling and verification of hybrid systems. Leibniz Trans. Embed. Syst. 8(2), 04:1–04:34 (2022)

    Google Scholar 

  35. Kamburjan, E., Scaletta, M., Rollshausen, N.: Deductive verification of active objects with crowbar. Sci. Comput. Program. 226 (2023)

    Google Scholar 

  36. Khadim, U.: A comparative study of process algebras for hybrid systems. Computer science reports. Technische Universiteit Eindhoven (2006)

    Google Scholar 

  37. Laneve, C., Lienhardt, M., Pun, K.I., Román-Díez, G.: Time analysis of actor programs. J. Log. Algebraic Methods Program. 105 (2019)

    Google Scholar 

  38. Lanotte, R., Merro, M.: A calculus of cyber-physical systems. In: Drewes, F., Martín-Vide, C., Truthe, B. (eds.) LATA 2017. LNCS, vol. 10168, pp. 115–127. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-53733-7_8

    Chapter  Google Scholar 

  39. Leavens, G.T., et al.: JML Reference Manual (2013). Draft revision 2344

    Google Scholar 

  40. 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 

  41. Majumdar, R., Yoshida, N., Zufferey, D.: Multiparty motion coordination: from choreographies to robotics programs. Proc. ACM Program. Lang. 4(OOPSLA) (2020)

    Google Scholar 

  42. Milner, R.: A Calculus of Communicating Systems. LNCS, vol. 92. Springer, Cham (1980). https://doi.org/10.1007/3-540-10235-3

    Book  Google Scholar 

  43. Müller, A., Mitsch, S., Retschitzegger, W., Schwinger, W., Platzer, A.: Tactical contract composition for hybrid system component verification. STTT 20(6) (2018)

    Google Scholar 

  44. Platzer, A.: Quantified differential dynamic logic for distributed hybrid systems. In: Dawar, A., Veith, H. (eds.) CSL 2010. LNCS, vol. 6247, pp. 469–483. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-15205-4_36

    Chapter  Google Scholar 

  45. Platzer, A.: A complete axiomatization of quantified differential dynamic logic for distributed hybrid systems. LMCS 8(4) (2012)

    Google Scholar 

  46. Platzer, A.: The complete proof theory of hybrid systems. In: LICS. IEEE (2012)

    Google Scholar 

  47. Platzer, A.: Logical Foundations of Cyber-Physical Systems. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-63588-0

    Book  Google Scholar 

  48. Renshaw, D.W., Loos, S.M., Platzer, A.: Distributed theorem proving for distributed hybrid systems. In: Qin, S., Qiu, Z. (eds.) ICFEM 2011. LNCS, vol. 6991, pp. 356–371. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-24559-6_25

    Chapter  Google Scholar 

  49. Rounds, W.C., Song, H.: The Ö-calculus: a language for distributed control of reconfigurable embedded systems. In: Maler, O., Pnueli, A. (eds.) HSCC 2003. LNCS, vol. 2623, pp. 435–449. Springer, Heidelberg (2003). https://doi.org/10.1007/3-540-36580-X_32

    Chapter  Google Scholar 

  50. Schlatte, R., Johnsen, E.B., Kamburjan, E., Tapia Tarifa, S.L.: Modeling and analyzing resource-sensitive actors: a tutorial introduction. In: Damiani, F., Dardha, O. (eds.) COORDINATION 2021. LNCS, vol. 12717, pp. 3–19. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-78142-2_1

    Chapter  Google Scholar 

  51. Talpin, J.-P., Jouvelot, P.: The type and effect discipline. In: LICS. IEEE (1992)

    Google Scholar 

  52. Wang, S., Zhan, N., Zou, L.: An improved HHL prover: an interactive theorem prover for hybrid systems. In: Butler, M., Conchon, S., Zaïdi, F. (eds.) ICFEM 2015. LNCS, vol. 9407, pp. 382–399. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-25423-4_25

    Chapter  Google Scholar 

Download references

Acknowledgments

This work was partially supported by the Research Council of Norway via the SIRIUS center (Grant Nr. 237898) and the PeTWIN project (Grant Nr. 294600). We thank Reiner Hähnle and Richard Bubel for extensive and constructive feedback on early drafts of this paper.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Eduard Kamburjan .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2024 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Kamburjan, E., Lienhardt, M. (2024). Type-Based Verification of Delegated Control in Hybrid Systems. In: de Boer, F., Damiani, F., Hähnle, R., Broch Johnsen, E., Kamburjan, E. (eds) Active Object Languages: Current Research Trends. Lecture Notes in Computer Science, vol 14360. Springer, Cham. https://doi.org/10.1007/978-3-031-51060-1_12

Download citation

  • DOI: https://doi.org/10.1007/978-3-031-51060-1_12

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-51059-5

  • Online ISBN: 978-3-031-51060-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics