Skip to main content
SpringerLink
Log in

Formally Verifying Decompositions of Stochastic Specifications

  • Conference paper
  • First Online:
Formal Methods for Industrial Critical Systems (FMICS 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13487))

Abstract

According to the principles of compositional verification, verifying that lower-level components satisfy their specification will ensure that the whole system satisfies its top-level specification. The key step is to ensure that the lower-level specifications constitute a correct decomposition of the top-level specification. In a non-stochastic context, such decomposition can be analyzed using techniques of theorem proving. In industrial applications, especially for safety-critical systems, specifications are often of stochastic nature, for example giving a bound on the probability that system failure will occur before a given time. A decomposition of such a specification requires techniques beyond traditional theorem proving. The first contribution of the paper is a theoretical framework that allows the representation of, and reasoning about, stochastic and timed behavior of systems as well as specifications for such behaviors. The framework is based on traces that describe the continuous-time evolution of a system, and specifications are formulated using timed automata combined with probabilistic acceptance conditions. The second contribution is a novel approach to verifying decomposition of such specifications by reducing the problem to checking emptiness of the solution space for a system of linear inequalities.

Supported by Vinnova FFI through the SafeDim project.

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

Access this chapter

Log in via an institution
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 79.99
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

References

  1. Linear optimization. https://online-optimizer.appspot.com. Accessed 27 May 2022

  2. Alur, R., Dill, D.: Automata for modeling real-time systems. In: Paterson, M.S. (ed.) ICALP 1990. LNCS, vol. 443, pp. 322–335. Springer, Heidelberg (1990). https://doi.org/10.1007/BFb0032042

    Chapter  MATH  Google Scholar 

  3. Alur, R., Dill, D.L.: A theory of timed automata. Theoret. Comput. Sci. 126(2), 183–235 (1994)

    Article  MathSciNet  Google Scholar 

  4. Aziz, A., Sanwal, K., Singhal, V., Brayton, R.: Verifying continuous time Markov chains. In: Alur, R., Henzinger, T.A. (eds.) CAV 1996. LNCS, vol. 1102, pp. 269–276. Springer, Heidelberg (1996). https://doi.org/10.1007/3-540-61474-5_75

    Chapter  Google Scholar 

  5. Aziz, A., Sanwal, K., Singhal, V., Brayton, R.: Model-checking continuous-time Markov chains. ACM Trans. Comput. Logic (TOCL) 1(1), 162–170 (2000)

    Article  MathSciNet  Google Scholar 

  6. Baier, C., Katoen, J.P., Hermanns, H., Wolf, V.: Comparative branching-time semantics for Markov chains. Inf. Comput. 200(2), 149–214 (2005)

    Article  MathSciNet  Google Scholar 

  7. Benveniste, A., Caillaud, B., Ferrari, A., Mangeruca, L., Passerone, R., Sofronis, C.: Multiple viewpoint contract-based specification and design. In: de Boer, F.S., Bonsangue, M.M., Graf, S., de Roever, W.-P. (eds.) FMCO 2007. LNCS, vol. 5382, pp. 200–225. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-92188-2_9

    Chapter  MATH  Google Scholar 

  8. Caillaud, B., Delahaye, B., Larsen, K.G., Legay, A., Pedersen, M.L., Wasowski, A.: Compositional design methodology with constraint Markov chains. In: 2010 Seventh International Conference on the Quantitative Evaluation of Systems, pp. 123–132. IEEE (2010)

    Google Scholar 

  9. Clarke, E.M., Grumberg, O., Kurshan, R.P.: A synthesis of two approaches for verifying finite state concurrent systems. In: Meyer, A.R., Taitslin, M.A. (eds.) Logic at Botik 1989. LNCS, vol. 363, pp. 81–90. Springer, Heidelberg (1989). https://doi.org/10.1007/3-540-51237-3_7

    Chapter  Google Scholar 

  10. Cuoq, P., Kirchner, F., Kosmatov, N., Prevosto, V., Signoles, J., Yakobowski, B.: Frama-C. In: Eleftherakis, G., Hinchey, M., Holcombe, M. (eds.) SEFM 2012. LNCS, vol. 7504, pp. 233–247. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-33826-7_16

    Chapter  Google Scholar 

  11. Dantzig, G.B.: Origins of the simplex method. In: A History of Scientific Computing, pp. 141–151 (1990)

    Google Scholar 

  12. David, A., Larsen, K.G., Legay, A., Nyman, U., Wasowski, A.: Timed I/O automata: a complete specification theory for real-time systems. In: Proceedings of the 13th ACM International Conference on Hybrid Systems: Computation and Control, pp. 91–100 (2010)

    Google Scholar 

  13. Delahaye, B., Caillaud, B., Legay, A.: Probabilistic contracts: a compositional reasoning methodology for the design of systems with stochastic and/or non-deterministic aspects. Form. Methods Syst. Des. 38(1), 1–32 (2011)

    Article  Google Scholar 

  14. Delahaye, B., et al.: Abstract probabilistic automata. In: Jhala, R., Schmidt, D. (eds.) VMCAI 2011. LNCS, vol. 6538, pp. 324–339. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-18275-4_23

    Chapter  Google Scholar 

  15. Donatelli, S., Haddad, S., Sproston, J.: Model checking timed and stochastic properties with CSL\(^\wedge \)\(\{\rm TA\}\). IEEE Trans. Softw. Eng. 35(2), 224–240 (2008)

    Google Scholar 

  16. Gössler, G., Xu, D.N., Girault, A.: Probabilistic contracts for component-based design. Form. Methods Syst. Des. 41(2), 211–231 (2012)

    Article  Google Scholar 

  17. Grunske, L.: Specification patterns for probabilistic quality properties. In: 2008 ACM/IEEE 30th International Conference on Software Engineering, pp. 31–40. IEEE (2008)

    Google Scholar 

  18. Hampus, A., Nyberg, M.: Formally verifying decompositions of stochastic specifications (with proofs). Technical report (2022). http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-315290. oai:DiVA.org:kth-315290

  19. ISO 21434: Road vehicles - Cybersecurity engineering (2021)

    Google Scholar 

  20. ISO 26262: Road vehicles - Functional safety (2018)

    Google Scholar 

  21. Jonsson, B., Larsen, K.G.: Specification and refinement of probabilistic processes. In: Proceedings 1991 Sixth Annual IEEE Symposium on Logic in Computer Science, pp. 266–267. IEEE Computer Society (1991)

    Google Scholar 

  22. Jonsson, B., Yi, W.: Testing preorders for probabilistic processes can be characterized by simulations. Theoret. Comput. Sci. 282(1), 33–51 (2002)

    Article  MathSciNet  Google Scholar 

  23. Kern, C., Greenstreet, M.R.: Formal verification in hardware design: a survey. ACM Trans. Des. Autom. Electron. Syst. (TODAES) 4(2), 123–193 (1999)

    Article  Google Scholar 

  24. Lanotte, R., Maggiolo-Schettini, A., Troina, A.: Parametric probabilistic transition systems for system design and analysis. Formal Aspects Comput. 19(1), 93–109 (2007)

    Article  Google Scholar 

  25. Mereacre, A., Katoen, J.P., Han, T., Chen, T.: Model checking of continuous-time Markov chains against timed automata specifications. Log. Methods Comput. Sci. 7 (2011)

    Google Scholar 

  26. Meyer, B.: Applying ‘design by contract’. Computer 25(10), 40–51 (1992)

    Article  Google Scholar 

  27. de Moura, L., Bjørner, N.: Z3: an efficient SMT solver. In: Ramakrishnan, C.R., Rehof, J. (eds.) TACAS 2008. LNCS, vol. 4963, pp. 337–340. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-78800-3_24

    Chapter  Google Scholar 

  28. Nash, J.C.: The (Dantzig) simplex method for linear programming. Comput. Sci. Eng. 2(1), 29–31 (2000)

    Article  MathSciNet  Google Scholar 

  29. Nuzzo, P., Li, J., Sangiovanni-Vincentelli, A.L., Xi, Y., Li, D.: Stochastic assume-guarantee contracts for cyber-physical system design. ACM Trans. Embed. Comput. Syst. (TECS) 18(1), 1–26 (2019)

    Article  Google Scholar 

  30. Nyberg, M., Westman, J., Gurov, D.: Formally proving compositionality in industrial systems with informal specifications. In: Margaria, T., Steffen, B. (eds.) ISoLA 2020. LNCS, vol. 12478, pp. 348–365. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-61467-6_22

    Chapter  Google Scholar 

  31. Paolieri, M., Horváth, A., Vicario, E.: Probabilistic model checking of regenerative concurrent systems. IEEE Trans. Software Eng. 42(2), 153–169 (2015)

    Article  Google Scholar 

  32. Resnick, S.: A Probability Path. Birkhäuser Boston (2019)

    Google Scholar 

  33. Roever, W.-P.: The need for compositional proof systems: a survey. In: de Roever, W.-P., Langmaack, H., Pnueli, A. (eds.) COMPOS 1997. LNCS, vol. 1536, pp. 1–22. Springer, Heidelberg (1998). https://doi.org/10.1007/3-540-49213-5_1

    Chapter  Google Scholar 

  34. Segala, R., Lynch, N.: Probabilistic simulations for probabilistic processes. In: Jonsson, B., Parrow, J. (eds.) CONCUR 1994. LNCS, vol. 836, pp. 481–496. Springer, Heidelberg (1994). https://doi.org/10.1007/978-3-540-48654-1_35

    Chapter  Google Scholar 

  35. Slind, K., Norrish, M.: A brief overview of HOL4. In: Mohamed, O.A., Muñoz, C., Tahar, S. (eds.) TPHOLs 2008. LNCS, vol. 5170, pp. 28–32. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-71067-7_6

    Chapter  Google Scholar 

  36. Vardi, M.Y., Wolper, P.: Reasoning about infinite computations. Inf. Comput. 115(1), 1–37 (1994)

    Article  MathSciNet  Google Scholar 

  37. Westman, J., Nyberg, M.: Conditions of contracts for separating responsibilities in heterogeneous systems. Form. Methods Syst. Des. 52(2), 147–192 (2017). https://doi.org/10.1007/s10703-017-0294-7

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. KTH Royal Institute of Technology, Stockholm, Sweden

    Anton Hampus & Mattias Nyberg

  2. Scania, Södertälje, Sweden

    Mattias Nyberg

Authors
  1. Anton Hampus
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mattias Nyberg
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Anton Hampus or Mattias Nyberg .

Editor information

Editors and Affiliations

  1. Eindhoven University of Technology, Eindhoven, The Netherlands

    Jan Friso Groote

  2. University of Twente, Enschede, The Netherlands

    Marieke Huisman

Rights and permissions

Reprints and permissions

Copyright information

© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Hampus, A., Nyberg, M. (2022). Formally Verifying Decompositions of Stochastic Specifications. In: Groote, J.F., Huisman, M. (eds) Formal Methods for Industrial Critical Systems. FMICS 2022. Lecture Notes in Computer Science, vol 13487. Springer, Cham. https://doi.org/10.1007/978-3-031-15008-1_13

Download citation

  • DOI: https://doi.org/10.1007/978-3-031-15008-1_13

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-15007-4

  • Online ISBN: 978-3-031-15008-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation