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Model Repair for Probabilistic Systems

  • Ezio Bartocci
  • Radu Grosu
  • Panagiotis Katsaros
  • C. R. Ramakrishnan
  • Scott A. Smolka
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6605)

Abstract

We introduce the problem of Model Repair for Probabilistic Systems as follows. Given a probabilistic system M and a probabilistic temporal logic formula φ such that M fails to satisfy φ, the Model Repair problem is to find an M′ that satisfies φ and differs from M only in the transition flows of those states in M that are deemed controllable. Moreover, the cost associated with modifying M’s transition flows to obtain M′ should be minimized. Using a new version of parametric probabilistic model checking, we show how the Model Repair problem can be reduced to a nonlinear optimization problem with a minimal-cost objective function, thereby yielding a solution technique. We demonstrate the practical utility of our approach by applying it to a number of significant case studies, including a DTMC reward model of the Zeroconf protocol for assigning IP addresses, and a CTMC model of the highly publicized Kaminsky DNS cache-poisoning attack.

Keywords

Model Repair Probabilistic Model Checking Nonlinear Programming 

References

  1. 1.
    Alexiou, N., Deshpande, T., Basagiannis, S., Smolka, S.A., Katsaros, P.: Formal analysis of the kaminsky DNS cache-poisoning attack using probabilistic model checking. In: Proceedings of the 12th IEEE International High Assurance Systems Engineering Symposium, pp. 94–103. IEEE Computer Society, Los Alamitos (2010)Google Scholar
  2. 2.
    Biegler, L.T., Zavala, V.M.: Large-scale nonlinear programming using IPOPT: An integrating framework for enterprise-wide dynamic optimization. Computers & Chemical Engineering 33(3), 575–582 (2009)CrossRefGoogle Scholar
  3. 3.
    Bonakdarpour, B., Ebnenasir, A., Kulkarni, S.S.: Complexity results in revising UNITY programs. ACM Trans. Auton. Adapt. Syst. 4(1), 1–28 (2009)CrossRefGoogle Scholar
  4. 4.
    Boyd, S., Vandenberghe, L.: Convex Optimization. Camb. Univ. Press, Cambridge (2004)CrossRefzbMATHGoogle Scholar
  5. 5.
    Buccafurri, F., Eiter, T., Gottlob, G., Leone, N.: Enhancing model checking in verification by AI techniques. Artif. Intell. 112(1-2), 57–104 (1999)CrossRefzbMATHGoogle Scholar
  6. 6.
    Clarke, E.M., Emerson, E.A., Sifakis, J.: Model checking: Algorithmic verification and debugging. Communications of the ACM 52(11), 74–84 (2009)CrossRefGoogle Scholar
  7. 7.
    Daws, C.: Symbolic and parametric model checking of discrete-time Markov chains. In: Liu, Z., Araki, K. (eds.) ICTAC 2004. LNCS, vol. 3407, pp. 280–294. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  8. 8.
    Donaldson, R., Gilbert, D.: A model checking approach to the parameter estimation of biochemical pathways. In: Heiner, M., Uhrmacher, A.M. (eds.) CMSB 2008. LNCS (LNBI), vol. 5307, pp. 269–287. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  9. 9.
    Dong, Y., Sarna-Starosta, B., Ramakrishnan, C.R., Smolka, S.A.: Vacuity checking in the modal mu-calculus. In: Kirchner, H., Ringeissen, C. (eds.) AMAST 2002. LNCS, vol. 2422, pp. 147–162. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  10. 10.
    Epifani, I., Ghezzi, C., Mirandola, R., Tamburrelli, G.: Model evolution by run-time parameter adaptation. In: ICSE 2009: Proceedings of the 31st International Conference on Software Engineering, pp. 111–121. IEEE Computer Society Press, Washington, DC, USA (2009)CrossRefGoogle Scholar
  11. 11.
    Giacalone, A., Chang Jou, C., Smolka, S.A.: Algebraic reasoning for probabilistic concurrent systems. In: Proc. of the IFIP TC2 Working Conference on Programming Concepts and Methods, pp. 443–458. North-Holland, Amsterdam (1990)Google Scholar
  12. 12.
    Granvilliers, L., Benhamou, F.: RealPaver: an interval solver using constraint satisfaction techniques. ACM Trans. Math. Softw. 32, 138–156 (2006)CrossRefzbMATHGoogle Scholar
  13. 13.
    Hahn, E., Hermanns, H., Zhang, L.: Probabilistic reachability for parametric Markov models. International Journal on Software Tools for Technology Transfer, 1–17 (April 2010)Google Scholar
  14. 14.
    Hahn, E.M.: Parametric Markov model analysis. Master’s thesis, Saarland University (2008)Google Scholar
  15. 15.
    Hahn, E.M., Hermanns, H., Wachter, B., Zhang, L.: PARAM: A Model Checker for Parametric Markov Models. In: Touili, T., Cook, B., Jackson, P. (eds.) CAV 2010. LNCS, vol. 6174, pp. 660–664. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  16. 16.
    Han, T., Katoen, J.-P., Mereacre, A.: Approximate parameter synthesis for probabilistic time-bounded reachability. In: IEEE International Real-Time Systems Symposium, pp. 173–182 (2008)Google Scholar
  17. 17.
    Hansson, H., Jonsson, B.: A logic for reasoning about time and reliability. Formal Aspects of Computing 6, 102–111 (1994)CrossRefzbMATHGoogle Scholar
  18. 18.
    Jobstmann, B., Griesmayer, A., Bloem, R.: Program repair as a game. In: Etessami, K., Rajamani, S.K. (eds.) CAV 2005. LNCS, vol. 3576, pp. 226–238. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  19. 19.
    Knuth, D., Yao, A.: The complexity of nonuniform random number generation. In: Algorithms and Complexity: New Directions and Recent Results. Academic Press, London (1976)Google Scholar
  20. 20.
    Kwiatkowska, M.Z., Norman, G., Parker, D.: Stochastic model checking. In: Bernardo, M., Hillston, J. (eds.) SFM 2007. LNCS, vol. 4486, pp. 220–270. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  21. 21.
    Lanotte, R., Maggiolo-Schettini, A., Troina, A.: Parametric probabilistic transition systems for system sesign and analysis. Formal Aspects of Computing 19(1), 93–109 (2007)CrossRefzbMATHGoogle Scholar
  22. 22.
    Sinha, S.M.: Duality in nonlinear programming. In: Mathematical Programming, pp. 423–430. Elsevier Science, Burlington (2006)CrossRefGoogle Scholar
  23. 23.
    Zhang, D., Cleaveland, R.: Fast on-the-fly parametric real-time model checking. In: Proceedings of the 26th IEEE International Real-Time Systems Symposium, pp. 157–166. IEEE Computer Society, Los Alamitos (2005)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Ezio Bartocci
    • 1
  • Radu Grosu
    • 2
  • Panagiotis Katsaros
    • 3
  • C. R. Ramakrishnan
    • 2
  • Scott A. Smolka
    • 2
  1. 1.Department of Applied Math and StatisticsStony Brook UniversityStony BrookUSA
  2. 2.Department of Computer ScienceStony Brook UniversityStony BrookUSA
  3. 3.Department of InformaticsAristotle University of ThessalonikiThessalonikiGreece

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