Abstract
We study the problem of formalizing and checking probabilistic hyperproperties for models that allow nondeterminism in actions. We extend the temporal logic HyperPCTL, which has been previously introduced for discrete-time Markov chains, to enable the specification of hyperproperties also for Markov decision processes. We generalize HyperPCTL by allowing explicit and simultaneous quantification over schedulers and probabilistic computation trees and show that it can express important quantitative requirements in security and privacy. We show that HyperPCTL model checking over MDPs is in general undecidable for quantification over probabilistic schedulers with memory, but restricting the domain to memoryless non-probabilistic schedulers turns the model checking problem decidable. Subsequently, we propose an SMT-based encoding for model checking this language and evaluate its performance.
This research has been partially supported by the United States NSF SaTC Award 181338, by the Vienna Science and Technology Fund ProbInG Grant ICT19-018 and by the DFG Research and Training Group UnRAVeL. The order of authors is alphabetical and all authors made equal contribution.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
We use the notation \(\hat{\sigma }\) for scheduler variables and \(\sigma \) for schedulers, and analogously \(\hat{s}\) for state variables and \(s\) for states.
References
Clarkson, M.R., Schneider, F.B.: Hyperproperties. J. Comput. Secur. 18(6), 1157–1210 (2010)
Alpern, B., Schneider, F.B.: Defining liveness. Inf. Process. Lett. 21, 181–185 (1985)
Goguen, J.A., Meseguer, J.: Security policies and security models. In: IEEE Symposium on Security and Privacy, pp. 11–20 (1982)
Zdancewic, S., Myers, A.C.: Observational determinism for concurrent program security. In: Proceedings of CSFW 2003, p. 29 (2003)
Wang, Y., Zarei, M., Bonakdarpour, B., Pajic, M.: Statistical verification of hyperproperties for cyber-physical systems. ACM Trans. Embedded Comput. Syst. (TECS) 18(5s), 1–23 (2019)
Bonakdarpour, B., Sanchez, C., Schneider, G.: Monitoring hyperproperties by combining static analysis and runtime verification. In: Margaria, T., Steffen, B. (eds.) ISoLA 2018. LNCS, vol. 11245, pp. 8–27. Springer, Cham (2018). https://doi.org/10.1007/978-3-030-03421-4_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
Ábrahám, E., Bartocci, E., Bonakdarpour, B., Dobe, O.: Parameter synthesis for probabilistic hyperproperties. In: Proceedings of 23rd International Conference on Logic for Programming, Artificial Intelligence and Reasoning, LPAR 23, EPiC Series in Computing. EasyChair, vol. 73, pp. 12–31 (2020)
Wang, Y., Nalluri, S., Bonakdarpour, B., Pajic, M.: Statistical model checking for hyperproperties. In: Proceedings of the IEEE 34th Computer Security Foundations (CSF), (2021, to appear)
Guarnieri, M., Marinovic, S., Basin, D.: Securing databases from probabilistic inference. In: Proceedings of CSF 2017, pp. 343–359 (2017)
Dimitrova, R., Finkbeiner, B., Torfah, H.: Probabilistic hyperproperties of Markov decision processes. In: Proceedings of the 18th Symposium on Automated Technology for Verification and Analysis (ATVA) (2020, to appear)
Ábrahám, E., Bartocci, E., Bonakdarpour, B., Dobe, O.: Probabilistic hyperproperties with nondeterminism. CoRR abs/2005.06115 (2020)
Minh Ngo, T., Stoelinga, M., Huisman, M.: Confidentiality for probabilistic multi-threaded programs and its verification. In: Jürjens, J., Livshits, B., Scandariato, R. (eds.) ESSoS 2013. LNCS, vol. 7781, pp. 107–122. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-36563-8_8
Knuth, D., Yao, A.: The complexity of nonuniform random number generation. In: Algorithms and Complexity: New Directions and Recent Results. Academic Press (1976)
Dehnert, C., Junges, S., Katoen, J.-P., Volk, M.: A storm is coming: a modern probabilistic model checker. In: Majumdar, R., Kunčak, V. (eds.) CAV 2017. LNCS, vol. 10427, pp. 592–600. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-63390-9_31
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
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this paper
Cite this paper
Ábrahám, E., Bartocci, E., Bonakdarpour, B., Dobe, O. (2020). Probabilistic Hyperproperties with Nondeterminism. 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_29
Download citation
DOI: https://doi.org/10.1007/978-3-030-59152-6_29
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)