Probabilistic Model Checking of Incomplete Models

  • Shiraj Arora
  • M. V. Panduranga RaoEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9952)


It is crucial for accurate model checking that the model be a complete and faithful representation of the system. Unfortunately, this is not always possible, mainly because of two reasons: (i) the model is still under development and (ii) the correctness of implementation of some modules is not established. In such circumstances, is it still possible to get correct answers for some model checking queries?

This paper is a step towards answering this question. We formulate the problem for the Discrete Time Markov Chains (DTMC) modeling formalism and the Probabilistic Computation Tree Logic (PCTL) query language. We then propose a simple solution by modifying DTMC and PCTL to accommodate three valued logic. The technique builds on existing model checking algorithms and tools, obviating the need for new ones to account for three valued logic. Finally, we provide an experimental demonstration of our approach.


Probabilistic models Probabilistic model checking three-valued logic Discrete time markov chain Probabilistic computation tree logic 


  1. 1.
    AlTurki, M., Meseguer, J.: PVeStA: a parallel statistical model checking and quantitative analysis tool. In: Corradini, A., Klin, B., Cîrstea, C. (eds.) CALCO 2011. LNCS, vol. 6859, pp. 386–392. Springer, Heidelberg (2011). doi: 10.1007/978-3-642-22944-2_28 CrossRefGoogle Scholar
  2. 2.
    Baier, C., Haverkort, B., Hermanns, H., Katoen, J.P.: Model-checking algorithms for continuous-time markov chains. IEEE Trans. Software Eng. 29(6), 524–541 (2003)CrossRefzbMATHGoogle Scholar
  3. 3.
    Baier, C., Katoen, J.P.: Principles of Model Checking (Representation and Mind Series). The MIT Press, Cambridge (2008)zbMATHGoogle Scholar
  4. 4.
    Bruns, G., Godefroid, P.: Model checking partial state spaces with 3-valued temporal logics. In: Halbwachs, N., Peled, D. (eds.) CAV 1999. LNCS, vol. 1633, pp. 274–287. Springer, Heidelberg (1999). doi: 10.1007/3-540-48683-6_25 CrossRefGoogle Scholar
  5. 5.
    Bruns, G., Godefroid, P.: Generalized model checking: reasoning about partial state spaces. In: Palamidessi, C. (ed.) CONCUR 2000. LNCS, vol. 1877, pp. 168–182. Springer, Heidelberg (2000). doi: 10.1007/3-540-44618-4_14 CrossRefGoogle Scholar
  6. 6.
    Caillaud, B., Delahaye, B., Larsen, K.G., Legay, A., Pedersen, M.L., Wsowski, A.: Constraint markov chains. Theoret. Comput. Sci. 412(34), 4373–4404 (2011). MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Chechik, M.: On interpreting results of model-checking with abstraction. University of Toronto, Technical report (2000)Google Scholar
  8. 8.
    Chechik, M., Easterbrook, S., Petrovykh, V.: Model-checking over multi-valued logics. In: Oliveira, J.N., Zave, P. (eds.) FME 2001. LNCS, vol. 2021, pp. 72–98. Springer, Heidelberg (2001). doi: 10.1007/3-540-45251-6_5 CrossRefGoogle Scholar
  9. 9.
    Courcoubetis, C., Yannakakis, M.: Verifying temporal properties of finite-state probabilistic programs. In: 1988, 29th Annual Symposium on Foundations of Computer Science, pp. 338–345. IEEE (1988)Google Scholar
  10. 10.
    Delahaye, B., Katoen, J.P., Larsen, K.G., Legay, A., Pedersen, M.L., Sher, F., Wsowski, A.: Abstract probabilistic automata. Inf. Comput. 232, 66–116 (2013). MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Fecher, H., Leucker, M., Wolf, V.: Don’t Know in probabilistic systems. In: Valmari, A. (ed.) SPIN 2006. LNCS, vol. 3925, pp. 71–88. Springer, Heidelberg (2006). doi: 10.1007/11691617_5 CrossRefGoogle Scholar
  12. 12.
    Godefroid, P., Piterman, N.: LTL generalized model checking revisited. Int. J. Softw. Tools Technol. Transfer 13(6), 571–584 (2011)CrossRefzbMATHGoogle Scholar
  13. 13.
    Hansson, H., Jonsson, B.: A logic for reasoning about time and reliability. Formal Asp. Comput. 6(5), 512–535 (1994). CrossRefzbMATHGoogle Scholar
  14. 14.
    Huth, M., Piterman, N., Wagner, D.: Three-valued abstractions of markov chains: completeness for a sizeable fragment of PCTL. In: Kutyłowski, M., Charatonik, W., Gębala, M. (eds.) FCT 2009. LNCS, vol. 5699, pp. 205–216. Springer, Heidelberg (2009). doi: 10.1007/978-3-642-03409-1_19 CrossRefGoogle Scholar
  15. 15.
    Klink, D.: Three-Valued Abstraction for Stochastic Systems. Verlag Dr. Hut, Munich (2010)Google Scholar
  16. 16.
    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). doi: 10.1007/978-3-642-22110-1_47 CrossRefGoogle Scholar
  17. 17.
    Legay, A., Delahaye, B., Bensalem, S.: Statistical model checking: an overview. In: Barringer, H., Falcone, Y., Finkbeiner, B., Havelund, K., Lee, I., Pace, G., Roşu, G., Sokolsky, O., Tillmann, N. (eds.) RV 2010. LNCS, vol. 6418, pp. 122–135. Springer, Heidelberg (2010). doi: 10.1007/978-3-642-16612-9_11 CrossRefGoogle Scholar
  18. 18.
    Malinowski, G.: Many-Valued Logics. Clarendon Press, Oxford (1993)zbMATHGoogle Scholar
  19. 19.
    Putnam, H.: Three-valued logic. Philos. Stud. 8(5), 73–80 (1957)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Rescher, N.: Many-Valued Logic. Springer, Netherlands (1968)CrossRefzbMATHGoogle Scholar
  21. 21.
    Sebastio, S., Vandin, A.: Multivesta: statistical model checking for discrete event simulators. In: 7th International Conference on Performance Evaluation Methodologies and Tools, ValueTools 2013, Torino, Italy, December 10–12, 2013, pp. 310–315 (2013)Google Scholar
  22. 22.
    Sen, K., Viswanathan, M., Agha, G.A.: VESTA: a statistical model-checker and analyzer for probabilistic systems. In: Second International Conference on the Quantitative Evaluation of Systems (QEST 2005), 19–22, September 2005, Torino, Italy, pp. 251–252 (2005)Google Scholar
  23. 23.
    Younes, H.L.S., Kwiatkowska, M.Z., Norman, G., Parker, D.: Numerical vs. statistical probabilistic model checking: an empirical study. In: Tools and Algorithms for the Construction and Analysis of Systems, 10th International Conference on TACAS 2004, Held as Part of the Joint European Conference on Theory and Practice of Software, ETAPS 2004, Barcelona, Spain, 29 March–2 April, 2004, Proceedings, pp. 46–60 (2004)Google Scholar
  24. 24.
    Younes, H.L.S., Simmons, R.G.: Probabilistic verification of discrete event systems using acceptance sampling. In: Brinksma, E., Larsen, K.G. (eds.) CAV 2002. LNCS, vol. 2404, pp. 223–235. Springer, Heidelberg (2002). doi: 10.1007/3-540-45657-0_17 CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  1. 1.Indian Institute of Technology HyderabadHyderabadIndia

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