Probabilistic Model Checking and Non-standard Multi-objective Reasoning

  • Christel Baier
  • Clemens Dubslaff
  • Sascha Klüppelholz
  • Marcus Daum
  • Joachim Klein
  • Steffen Märcker
  • Sascha Wunderlich
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8411)


Probabilistic model checking is a well-established method for the automated quantitative system analysis. It has been used in various application areas such as coordination algorithms for distributed systems, communication and multimedia protocols, biological systems, resilient systems or security. In this paper, we report on the experiences we made in inter-disciplinary research projects where we contribute with formal methods for the analysis of hardware and software systems. Many performance measures that have been identified as highly relevant by the respective domain experts refer to multiple objectives and require a good balance between two or more cost or reward functions, such as energy and utility. The formalization of these performance measures requires several concepts like quantiles, conditional probabilities and expectations and ratios of cost or reward functions that are not supported by state-ofthe- art probabilistic model checkers. We report on our current work in this direction, including applications in the field of software product line verification.


Conditional Probability Markov Decision Process Reward Function Linear Temporal Logic Software Product Line 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Aggarwal, V., Chandrasekaran, R., Nair, K.: Markov ratio decision processes. Journal of Optimization Theory and Application 21(1) (1977)Google Scholar
  2. 2.
    Andova, S., Hermanns, H., Katoen, J.-P.: Discrete-time rewards model-checked. In: Larsen, K.G., Niebert, P. (eds.) FORMATS 2003. LNCS, vol. 2791, pp. 88–104. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  3. 3.
    Andrés, M., van Rossum, P.: Conditional probabilities over probabilistic and nondeterministic systems. In: Ramakrishnan, C.R., Rehof, J. (eds.) TACAS 2008. LNCS, vol. 4963, pp. 157–172. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  4. 4.
    Baier, C., Daum, M., Dubslaff, C., Klein, J., Klüppelholz, S.: Energy-utility quantiles. In: NFM 2014. LNCS (to appear, 2014)Google Scholar
  5. 5.
    Baier, C., Daum, M., Engel, B., Härtig, H., Klein, J., Klüppelholz, S., Märcker, S., Tews, H., Völp, M.: Locks: Picking key methods for a scalable quantitative analysis. Journal of Computer and System Sciences (to appear, 2014)Google Scholar
  6. 6.
    Baier, C., Engel, B., Klüppelholz, S., Märcker, S., Tews, H., Völp, M.: A probabilistic quantitative analysis of probabilistic-write/copy-select. In: Brat, G., Rungta, N., Venet, A. (eds.) NFM 2013. LNCS, vol. 7871, pp. 307–321. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  7. 7.
    Baier, C., Katoen, J.-P.: Principles of Model Checking. MIT Press (2008)Google Scholar
  8. 8.
    Baier, C., Klein, J., Klüppelholz, S., Märcker, S.: Computing conditional probabilities in Markovian models efficiently. In: TACAS 2014. LNCS (to appear, 2014)Google Scholar
  9. 9.
    Bianco, A., de Alfaro, L.: Model checking of probabilistic and non-deterministic systems. In: Thiagarajan, P.S. (ed.) FSTTCS 1995. LNCS, vol. 1026, pp. 499–513. Springer, Heidelberg (1995)CrossRefGoogle Scholar
  10. 10.
    Boker, U., Chatterjee, K., Henzinger, T.A., Kupferman, O.: Temporal specifications with accumulative values. In: LICS 2011, pp. 43–52. IEEE Computer Society (2011)Google Scholar
  11. 11.
    Brázdil, T., Kučera, A., Stražovský, O.: On the decidability of temporal properties of probabilistic pushdown automata. In: Diekert, V., Durand, B. (eds.) STACS 2005. LNCS, vol. 3404, pp. 145–157. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  12. 12.
    Chatterjee, K., Doyen, L.: Energy and mean-payoff parity Markov decision processes. In: Murlak, F., Sankowski, P. (eds.) MFCS 2011. LNCS, vol. 6907, pp. 206–218. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  13. 13.
    Chatterjee, K., Doyen, L.: Energy parity games. Theoretical Computer Science 458, 49–60 (2012)CrossRefzbMATHMathSciNetGoogle Scholar
  14. 14.
    Chatterjee, K., Majumdar, R., Henzinger, T.: Markov decision processes with multiple objectives. In: Durand, B., Thomas, W. (eds.) STACS 2006. LNCS, vol. 3884, pp. 325–336. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  15. 15.
    Clarke, E., Grumberg, O., Peled, D.: Model Checking. MIT Press (2000)Google Scholar
  16. 16.
    Classen, A., Cordy, M., Schobbens, P.-Y., Heymans, P., Legay, A., Raskin, J.-F.: Featured transition systems: Foundations for verifying variability-intensive systems and their application to ltl model checking. In: IEEE TSE (2012)Google Scholar
  17. 17.
    Clements, P., Northrop, L.: Software Product Lines: Practices and Patterns. Addison-Wesley Professional (2001)Google Scholar
  18. 18.
    Courcoubetis, C., Yannakakis, M.: The complexity of probabilistic verification. Journal of the ACM 42(4), 857–907 (1995)CrossRefzbMATHMathSciNetGoogle Scholar
  19. 19.
    de Alfaro, L.: Formal Verification of Probabilistic Systems. PhD thesis, Stanford University, Department of Computer Science (1997)Google Scholar
  20. 20.
    de Alfaro, L.: How to specify and verify the long-run average behavior of probabilistic systems. In: LICS 1998, pp. 454–465. IEEE Computer Society (1998)Google Scholar
  21. 21.
    de Alfaro, L.: Computing minimum and maximum reachability times in probabilistic systems. In: Baeten, J.C.M., Mauw, S. (eds.) CONCUR 1999. LNCS, vol. 1664, pp. 66–81. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  22. 22.
    Dubslaff, C., Klüppelholz, S., Baier, C.: Probabilistic model checking for energy analysis in software product lines. In: MODULARITY 2014 (to appear, 2014)Google Scholar
  23. 23.
    Etessami, K., Kwiatkowska, M., Vardi, M., Yannakakis, M.: Multi-objective model checking of Markov decision processes. Logical Methods in Computer Science 4(4) (2008)Google Scholar
  24. 24.
    Gao, Y., Xu, M., Zhan, N., Zhang, L.: Model checking conditional CSL for continuous-time Markov chains. IPL 113(1-2), 44–50 (2013)CrossRefzbMATHMathSciNetGoogle Scholar
  25. 25.
    Grädel, E., Thomas, W., Wilke, T. (eds.): Automata, Logics, and Infinite Games. LNCS, vol. 2500. Springer, Heidelberg (2002)Google Scholar
  26. 26.
    Hähnel, M., Döbel, B., Völp, M., Härtig, H.: ebond: Energy saving in heterogeneous R.A.I.N. In: Proc. of the Fourth International Conference on Future Energy Systems, e-Energy 2013, pp. 193–202. ACM (2013)Google Scholar
  27. 27.
    Hansson, H., Jonsson, B.: A logic for reasoning about time and reliability. Formal Aspects of Computing 6, 512–535 (1994)CrossRefzbMATHGoogle Scholar
  28. 28.
    Haverkort, B.: Performance of Computer Communication Systems: A Model-Based Approach. Wiley (1998)Google Scholar
  29. 29.
    Hinton, A., Kwiatkowska, M., Norman, G., Parker, D.: PRISM: A tool for automatic verification of probabilistic systems. In: Hermanns, H., Palsberg, J. (eds.) TACAS 2006. LNCS, vol. 3920, pp. 441–444. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  30. 30.
    Ji, M., Wu, D., Chen, Z.: Verification method of conditional probability based on automaton. Journal of Networks 8(6), 1329–1335 (2013)CrossRefGoogle Scholar
  31. 31.
    Katoen, J.-P., Zapreev, I., Hahn, E., Hermanns, H., Jansen, D.: The ins and outs of the probabilistic model checker MRMC. Performance Evaluation 68(2) (2011)Google Scholar
  32. 32.
    Kulkarni, V.: Modeling and Analysis of Stochastic Systems. Chapman & Hall (1995)Google Scholar
  33. 33.
    Puterman, M.: Markov Decision Processes: Discrete Stochastic Dynamic Programming. Wiley (1994)Google Scholar
  34. 34.
    Serfling, R.J.: Approximation Theorems of Mathematical Statistics. Wiley (1980)Google Scholar
  35. 35.
    Tomita, T., Hiura, S., Hagihara, S., Yonezaki, N.: A temporal logic with mean-payoff constraints. In: Aoki, T., Taguchi, K. (eds.) ICFEM 2012. LNCS, vol. 7635, pp. 249–265. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  36. 36.
    Ummels, M., Baier, C.: Computing quantiles in Markov reward models. In: Pfenning, F. (ed.) FOSSACS 2013. LNCS, vol. 7794, pp. 353–368. Springer, Heidelberg (2013)Google Scholar
  37. 37.
    Vardi, M.: Automatic verification of probabilistic concurrent finite-state programs. In: FOCS 1985, pp. 327–338. IEEE Computer Society (1985)Google Scholar
  38. 38.
    von Essen, C., Jobstmann, B.: Synthesizing systems with optimal average-case behavior for ratio objectives. In: iWIGP 2011. EPTCS, vol. 50, pp. 17–32 (2011)Google Scholar
  39. 39.
    von Rhein, A., Apel, S., Kästner, C., Thüm, T., Schaefer, I.: The PLA model: On the combination of product-line analyses. In: Proc. of VaMoS 2013. ACM (2013)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Christel Baier
    • 1
  • Clemens Dubslaff
    • 1
  • Sascha Klüppelholz
    • 1
  • Marcus Daum
    • 1
  • Joachim Klein
    • 1
  • Steffen Märcker
    • 1
  • Sascha Wunderlich
    • 1
  1. 1.Institute for Theoretical Computer ScienceTechnische Universität DresdenGermany

Personalised recommendations