Skip to main content

Probabilistic Hyperproperties of Markov Decision Processes

  • Conference paper
  • First Online:
Automated Technology for Verification and Analysis (ATVA 2020)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 12302))

Abstract

Hyperproperties are properties that describe the correctness of a system as a relation between multiple executions. Hyperproperties generalize trace properties and include information-flow security requirements, like noninterference, as well as requirements like symmetry, partial observation, robustness, and fault tolerance. We initiate the study of the specification and verification of hyperproperties of Markov decision processes (MDPs). We introduce the temporal logic PHL (Probabilistic Hyper Logic), which extends classic probabilistic logics with quantification over schedulers and traces. PHL can express a wide range of hyperproperties for probabilistic systems, including both classical applications, such as probabilistic noninterference, and novel applications in areas such as robotics and planning. While the model checking problem for PHL is in general undecidable, we provide methods both for proving and for refuting formulas from a fragment of the logic. The fragment includes many probabilistic hyperproperties of interest.

This work was partially supported by the Collaborative Research Center “Foundations of Perspicuous Software Systems” (TRR 248, 389792660), the European Research Council (ERC) Grant OSARES (No. 683300), the DARPA Assured Autonomy program, the iCyPhy center, and by Berkeley Deep Drive.

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

Access this chapter

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
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

Similar content being viewed by others

Notes

  1. 1.

    In the literature, schedulers are also known as strategies or policies.

References

  1. Abraham, E., Bartocci, E., Bonakdarpour, B., Dobe, O.: Probabilistic hyperproperties with nondeterminism. In: Proceedings of Automated Technology for Verification and Analysis, ATVA 2020 (2020)

    Google Scholar 

  2. Ábrahám, E., Bonakdarpour, B.: HyperPCTL: a temporal logic for probabilistic hyperproperties. In: McIver, A., Horvath, A. (eds.) QEST 2018. LNCS, vol. 11024, pp. 20–35. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-99154-2_2

    Chapter  Google Scholar 

  3. Aminof, B., Kwiatkowska, M., Maubert, B., Murano, A., Rubin, S.: Probabilistic strategy logic. In: Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence, IJCAI 2019, pp. 32–38 (2019)

    Google Scholar 

  4. Baier, C.: On model checking techniques for randomized distributed systems. In: Méry, D., Merz, S. (eds.) IFM 2010. LNCS, vol. 6396, pp. 1–11. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-16265-7_1

    Chapter  Google Scholar 

  5. Baier, C., Bertrand, N., Größer, M.: On decision problems for probabilistic Büchi automata. In: Amadio, R. (ed.) FoSSaCS 2008. LNCS, vol. 4962, pp. 287–301. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-78499-9_21

    Chapter  Google Scholar 

  6. Baier, C., Brázdil, T., Größer, M., Kucera, A.: Stochastic game logic. Acta Inform. 49(4), 203–224 (2012). https://doi.org/10.1007/s00236-012-0156-0

    Article  MathSciNet  MATH  Google Scholar 

  7. Baier, C., Katoen, J.: Principles of Model Checking. MIT Press, Cambridge (2008)

    MATH  Google Scholar 

  8. Brázdil, T., Brozek, V., Forejt, V., Kucera, A.: Stochastic games with branching-time winning objectives. In: Proceedings of 21th IEEE Symposium on Logic in Computer Science (LICS 2006), pp. 349–358. IEEE Computer Society (2006)

    Google Scholar 

  9. Clarkson, M.R., Finkbeiner, B., Koleini, M., Micinski, K.K., Rabe, M.N., Sánchez, C.: Temporal logics for hyperproperties. In: Abadi, M., Kremer, S. (eds.) POST 2014. LNCS, vol. 8414, pp. 265–284. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-642-54792-8_15

    Chapter  Google Scholar 

  10. Clarkson, M.R., Schneider, F.B.: Hyperproperties. J. Comput. Secur. 18(6), 1157–1210 (2010)

    Article  Google Scholar 

  11. Coenen, N., Finkbeiner, B., Sánchez, C., Tentrup, L.: Verifying hyperliveness. In: Dillig, I., Tasiran, S. (eds.) CAV 2019. LNCS, vol. 11561, pp. 121–139. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-25540-4_7

    Chapter  Google Scholar 

  12. Dimitrova, R., Finkbeiner, B., Torfah, H.: Probabilistic hyperproperties of Markov decision processes. CoRR arxiv:2005.03362 (2020)

  13. Dwork, C.: Differential privacy. In: van Tilborg, H.C.A., Jajodia, S. (eds.) Encyclopedia of Cryptography and Security, 2nd edn., pp. 338–340. Springer, Boston (2011). https://doi.org/10.1007/978-1-4419-5906-5_752

    Chapter  Google Scholar 

  14. Finkbeiner, B., Hahn, C., Lukert, P., Stenger, M., Tentrup, L.: Synthesizing reactive systems from hyperproperties. In: Chockler, H., Weissenbacher, G. (eds.) CAV 2018. LNCS, vol. 10981, pp. 289–306. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-96145-3_16

    Chapter  Google Scholar 

  15. Finkbeiner, B., Hahn, C., Stenger, M.: EAHyper: satisfiability, implication, and equivalence checking of hyperproperties. In: Majumdar, R., Kunčak, V. (eds.) CAV 2017. LNCS, vol. 10427, pp. 564–570. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-63390-9_29

    Chapter  Google Scholar 

  16. Finkbeiner, B., Rabe, M.N., Sánchez, C.: Algorithms for model checking HyperLTL and HyperCTL\(^*\). In: Kroening, D., Păsăreanu, C.S. (eds.) CAV 2015. LNCS, vol. 9206, pp. 30–48. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21690-4_3

    Chapter  Google Scholar 

  17. Goguen, J.A., Meseguer, J.: Security policies and security models. In: 1982 IEEE Symposium on Security and Privacy. IEEE Computer Society (1982)

    Google Scholar 

  18. Gray, J.W.: Toward a mathematical foundation for information flow security. J. Comput. Secur. 1(3–4), 255–294 (1992)

    Article  MathSciNet  Google Scholar 

  19. Kwiatkowska, M., Norman, G., Parker, D.: Probabilistic model checking: advances and applications. In: Drechsler, R. (ed.) Formal System Verification, pp. 73–121. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-57685-5_3

    Chapter  Google Scholar 

  20. Kwiatkowska, M., Norman, G., Parker, D.: PRISM 4.0: verification of probabilistic real-time systems. In: Gopalakrishnan, G., Qadeer, S. (eds.) CAV 2011. LNCS, vol. 6806, pp. 585–591. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-22110-1_47

    Chapter  Google Scholar 

  21. O’Neill, K.R., Clarkson, M.R., Chong, S.: Information-flow security for interactive programs. In: 19th IEEE Computer Security Foundations Workshop, (CSFW-19 2006), pp. 190–201. IEEE Computer Society (2006)

    Google Scholar 

  22. Pnueli, A.: The temporal logic of programs. In: 18th Annual Symposium on Foundations of Computer Science, pp. 46–57. IEEE Computer Society (1977)

    Google Scholar 

  23. Sabelfeld, A., Sands, D.: Probabilistic noninterference for multi-threaded programs. In: Proceedings of the 13th IEEE Computer Security Foundations Workshop, CSFW 2000, pp. 200–214. IEEE Computer Society (2000)

    Google Scholar 

  24. Volpano, D.M., Smith, G.: Probabilistic noninterference in a concurrent language. J. Comput. Secur. 7(1), 231–253 (1999)

    Article  Google Scholar 

  25. Wang, Y., Zarei, M., Bonakdarpour, B., Pajic, M.: Statistical verification of hyperproperties for cyber-physical systems. ACM Trans. Embed. Comput. Syst. 18(5s), 1–23 (2019)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Rayna Dimitrova .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Dimitrova, R., Finkbeiner, B., Torfah, H. (2020). Probabilistic Hyperproperties of Markov Decision Processes. In: Hung, D.V., Sokolsky, O. (eds) Automated Technology for Verification and Analysis. ATVA 2020. Lecture Notes in Computer Science(), vol 12302. Springer, Cham. https://doi.org/10.1007/978-3-030-59152-6_27

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-59152-6_27

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-59151-9

  • Online ISBN: 978-3-030-59152-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics