skip to main content
research-article
Public Access

Statistical Verification of Hyperproperties for Cyber-Physical Systems

Published:08 October 2019Publication History
Skip Abstract Section

Abstract

Many important properties of cyber-physical systems (CPS) are defined upon the relationship between multiple executions simultaneously in continuous time. Examples include probabilistic fairness and sensitivity to modeling errors (i.e., parameters changes) for real-valued signals. These requirements can only be specified by hyperproperties. In this article, we focus on verifying probabilistic hyperproperties for CPS. To cover a wide range of modeling formalisms, we first propose a general model of probabilistic uncertain systems (PUSs) that unify commonly studied CPS models such as continuous-time Markov chains (CTMCs) and probabilistically parametrized Hybrid I/O Automata (P2HIOA). To formally specify hyperproperties, we propose a new temporal logic, hyper probabilistic signal temporal logic (HyperPSTL) that serves as a hyper and probabilistic version of the conventional signal temporal logic (STL). Considering the complexity of real-world systems that can be captured as PUSs, we adopt a statistical model checking (SMC) approach for their verification. We develop a new SMC technique based on the direct computation of significance levels of statistical assertions for HyperPSTL specifications, which requires no a priori knowledge on the indifference margin. Then, we introduce SMC algorithms for HyperPSTL specifications on the joint probabilistic distribution of multiple paths, as well as specifications with nested probabilistic operators quantifying different paths, which cannot be handled by existing SMC algorithms. Finally, we show the effectiveness of our SMC algorithms on CPS benchmarks with varying levels of complexity, including the Toyota Powertrain Control System.

References

  1. H. Abbas, H. D. Mittelmann, and G. E. Fainekos. 2014. Formal property verification in a conformance testing framework. In Proceedings of the 12th ACM/IEEE International Conference on Formal Methods and Models for Codesign (MEMOCODE). 155--164.Google ScholarGoogle Scholar
  2. Erika Ábrahám and Borzoo Bonakdarpour. 2018. HyperPCTL: A temporal logic for probabilistic hyperproperties. In Quantitative Evaluation of Systems. 20--35.Google ScholarGoogle Scholar
  3. Christel Baier and Joost-Pieter Katoen. 2008. Principles of Model Checking. The MIT Press.Google ScholarGoogle ScholarDigital LibraryDigital Library
  4. Benoît Barbot, Béatrice Bérard, Yann Duplouy, and Serge Haddad. 2017. Statistical model-checking for autonomous vehicle safety validation. In SIA Simulation Numérique.Google ScholarGoogle Scholar
  5. Gunter Bolch, Stefan Greiner, Hermann De Meer, and Kishor S. Trivedi. 2006. Queueing Networks and Markov Chains: Modeling and Performance Evaluation with Computer Science Applications. John Wiley 8 Sons.Google ScholarGoogle Scholar
  6. Lawrence D. Brown, T. Tony Cai, and Anirban DasGupta. 2001. Interval estimation for a binomial proportion. Statist. Sci. 16, 2 (2001), 101--117.Google ScholarGoogle ScholarCross RefCross Ref
  7. Michael R. Clarkson and Fred B. Schneider. 2008. Hyperproperties. In 2008 21st IEEE Computer Security Foundations Symposium. 51--65.Google ScholarGoogle Scholar
  8. Charles J. Clopper and Egon S. Pearson. 1934. The use of confidence or fiducial limits illustrated in the case of the binomial. Biometrika (1934), 404--413.Google ScholarGoogle Scholar
  9. [email protected]. 2019. HyperPSTL Case Studies. http://cpsl.pratt.duke.edu/research/statistical-model-checking-hyperpstl. Accessed: 2019-7-15.Google ScholarGoogle Scholar
  10. P. R. D’Argenio, G. Barthe, S. Biewer, B. Finkbeiner, and H. Hermanns. 2017. Is your software on dope? - Formal analysis of surreptitiously “enhanced” programs. In Proceedings of the 26th European Symposium on Programming Languages and Systems (ESOP). 83--110.Google ScholarGoogle Scholar
  11. Parasara Sridhar Duggirala, Chuchu Fan, Sayan Mitra, and Mahesh Viswanathan. 2015. Meeting a powertrain verification challenge. In International Conference on Computer Aided Verification. Springer, 536--543.Google ScholarGoogle Scholar
  12. Atilla Eryilmaz and R. Srikant. 2006. Joint congestion control, routing, and MAC for stability and fairness in wireless networks. IEEE Journal on Selected Areas in Communications 24, 8 (2006), 1514--1524.Google ScholarGoogle ScholarDigital LibraryDigital Library
  13. Leonidas Georgiadis, Michael J. Neely, Leandros Tassiulas, et al. 2006. Resource allocation and cross-layer control in wireless networks. Foundations and Trends® in Networking 1, 1 (2006), 1--144.Google ScholarGoogle Scholar
  14. Daniel T. Gillespie. 1976. A general method for numerically simulating the stochastic time evolution of coupled chemical reactions. J. Comput. Phys. 22, 4 (1976), 403--434.Google ScholarGoogle ScholarCross RefCross Ref
  15. Hans Hansson and Bengt Jonsson. 1994. A logic for reasoning about time and reliability. Formal Aspects of Computing 6, 5 (1994), 512--535.Google ScholarGoogle ScholarDigital LibraryDigital Library
  16. Thomas A. Henzinger. 2000. The theory of hybrid automata. In Verification of Digital and Hybrid Systems. Springer, 265--292.Google ScholarGoogle ScholarCross RefCross Ref
  17. Robert V. Hogg, Joseph McKean, and Allen T. Craig. 2005. Introduction to Mathematical Statistics. Pearson Education.Google ScholarGoogle Scholar
  18. Xiaoqing Jin, Jyotirmoy V. Deshmukh, James Kapinski, Koichi Ueda, and Ken Butts. 2014. Benchmarks for model transformations and conformance checking. In 1st International Workshop on Applied Verification for Continuous and Hybrid Systems (ARCH).Google ScholarGoogle Scholar
  19. Xiaoqing Jin, Jyotirmoy V. Deshmukh, James Kapinski, Koichi Ueda, and Ken Butts. 2014. Powertrain control verification benchmark. In The 17th International Conference on Hybrid Systems: Computation and Control. 253--262.Google ScholarGoogle ScholarDigital LibraryDigital Library
  20. Kim G. Larsen and Axel Legay. 2016. Statistical model checking: past, present, and future. In Leveraging Applications of Formal Methods, Verification and Validation: Foundational Techniques. 3--15.Google ScholarGoogle Scholar
  21. Axel Legay and Mahesh Viswanathan. 2015. Statistical model checking: Challenges and perspectives. International Journal on Software Tools for Technology Transfer 17, 4 (2015), 369--376.Google ScholarGoogle ScholarDigital LibraryDigital Library
  22. Nancy Lynch, Roberto Segala, and Frits Vaandrager. 2003. Hybrid i/o automata. Information and Computation 185, 1 (2003), 105--157.Google ScholarGoogle ScholarDigital LibraryDigital Library
  23. Luan Viet Nguyen, James Kapinski, Xiaoqing Jin, Jyotirmoy V. Deshmukh, and Taylor T. Johnson. 2017. Hyperproperties of real-valued signals. In 15th ACM-IEEE Int. Conf. on Formal Methods and Models for System Design. 104--113.Google ScholarGoogle Scholar
  24. Nima Roohi, Yu Wang, Matthew West, Geir E. Dullerud, and Mahesh Viswanathan. 2017. Statistical verification of the Toyota powertrain control verification benchmark. In 20th Int. Conf. on Hybrid Systems: Computation and Control. 65--70.Google ScholarGoogle ScholarDigital LibraryDigital Library
  25. Dorsa Sadigh and Ashish Kapoor. 2016. Safe control under uncertainty with probabilistic signal temporal logic. In Robotics: Science and Systems Conference.Google ScholarGoogle ScholarCross RefCross Ref
  26. Koushik Sen, Mahesh Viswanathan, and Gul Agha. 2005. On statistical model checking of stochastic systems. In Computer Aided Verification. 266--280.Google ScholarGoogle Scholar
  27. K. Sen, M. Viswanathan, and G. Agha. 2005. VESTA: A statistical model-checker and analyzer for probabilistic systems. In Second International Conference on the Quantitative Evaluation of Systems. 251--252.Google ScholarGoogle Scholar
  28. Jeremy Sproston. 2000. Decidable model checking of probabilistic hybrid automata. In Formal Techniques in Real-Time and Fault-Tolerant Systems. 31--45.Google ScholarGoogle Scholar
  29. Yi Tang and Neil W. Bergmann. 2015. A hardware scheduler based on task queues for FPGA-based embedded real-time systems. IEEE Trans. Comput. 64, 5 (2015), 1254--1267.Google ScholarGoogle ScholarDigital LibraryDigital Library
  30. The MathWorks, Inc. 2019. SimEvents. https://www.mathworks.com/products/simevents.html. Accessed: 2019-7-15.Google ScholarGoogle Scholar
  31. Yu Wang, Siddhartha Nalluri, Borzoo Bonakdarpour, and Miroslav Pajic. 2019. Statistical model checking for probabilistic hyperproperties. arXiv preprint arXiv:1902.04111 (2019).Google ScholarGoogle Scholar
  32. Yu Wang, Nima Roohi, Matthew West, Mahesh Viswanathan, and Geir E. Dullerud. 2016. Verifying continuous-time stochastic hybrid systems via Mori-Zwanzig model reduction. In 55th Conference on Decision and Control (CDC). 3012--3017.Google ScholarGoogle Scholar
  33. Yu Wang, Nima Roohi, Matthew West, Mahesh Viswanathan, and Geir E. Dullerud. 2018. Statistical verification of PCTL using stratified samples. IFAC-PapersOnLine 51, 16 (2018), 85--90.Google ScholarGoogle ScholarCross RefCross Ref
  34. Lijun Zhang, Zhikun She, Stefan Ratschan, Holger Hermanns, and Ernst Moritz Hahn. 2010. Safety verification for probabilistic hybrid systems. In Computer Aided Verification. 196--211.Google ScholarGoogle Scholar
  35. Paolo Zuliani. 2015. Statistical model checking for biological applications. Int. Journal on Software Tools for Technology Transfer 17, 4 (2015), 527--536.Google ScholarGoogle ScholarDigital LibraryDigital Library

Index Terms

  1. Statistical Verification of Hyperproperties for Cyber-Physical Systems

            Recommendations

            Comments

            Login options

            Check if you have access through your login credentials or your institution to get full access on this article.

            Sign in

            Full Access

            PDF Format

            View or Download as a PDF file.

            PDF

            eReader

            View online with eReader.

            eReader

            HTML Format

            View this article in HTML Format .

            View HTML Format
            About Cookies On This Site

            We use cookies to ensure that we give you the best experience on our website.

            Learn more

            Got it!