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Syntactic Partial Order Compression for Probabilistic Reachability

  • Gereon FoxEmail author
  • Daniel Stan
  • Holger Hermanns
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11388)

Abstract

The state space explosion problem is among the largest impediments to the performance of any model checker. Modelling languages for compositional systems contribute to this problem by placing each instruction of an instruction sequence onto a dedicated transition, giving concurrent processes opportunities to interleave after every instruction. Users wishing to avoid the excessive number of interleavings caused by this default can choose to explicitly declare instruction sequences as atomic, which however requires careful considerations regarding the impact this might have on the model as well as on the properties that are to be checked. We instead propose a preprocessing technique that automatically identifies instruction sequences that can safely be considered atomic. This is done in the context of concurrent variable-decorated Markov Decision Processes. Our approach is compatible with any off-the-shelf probabilistic model checker. We prove that our transformation preserves maximal reachability probabilities and present case studies to illustrate its usefulness.

Keywords

State space explosion Atomicity Partial order reduction Concurrency Interleavings Model checking 

Notes

Acknowledgments

This work is partly supported by the DFG as part of CRC 248 (see perspicuous-computing.science) and by the ERC Advanced Investigators Grant 695614 (POWVER).

References

  1. 1.
    Abdulla, P.A., Aronis, S., Jonsson, B., Sagonas, K.: Source sets: a foundation for optimal dynamic partial order reduction. J. ACM 64(4), 25:1–25:49 (2017).  https://doi.org/10.1145/3073408MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Baier, C., Grosser, M., Ciesinski, F.: Partial order reduction for probabilistic systems. In: 2004 Proceedings First International Conference on the Quantitative Evaluation of Systems, QEST 2004, pp. 230–239, September 2004.  https://doi.org/10.1109/QEST.2004.1348037
  3. 3.
    Baier, C., D’Argenio, P., Groesser, M.: Partial order reduction for probabilistic branching time. Electron. Notes Theor. Comput. Sci. 153(2), 97–116 (2006).  https://doi.org/10.1016/j.entcs.2005.10.034. Proceedings of the Third Workshop on Quantitative Aspects of Programming Languages (QAPL 2005)CrossRefGoogle Scholar
  4. 4.
    Behrmann, G., David, A., Larsen, K.G., Håkansson, J., Pettersson, P., Yi, W., Hendriks, M.: UPPAAL 4.0. In: Third International Conference on the Quantitative Evaluation of Systems (QEST 2006), 11–14 September 2006, Riverside, California, USA. pp. 125–126. IEEE Computer Society (2006).  https://doi.org/10.1109/QEST.2006.59
  5. 5.
    Bohnenkamp, H.C., D’Argenio, P.R., Hermanns, H., Katoen, J.: MODEST: a compositional modeling formalism for hard and softly timed systems. IEEE Trans. Softw. Eng. 32(10), 812–830 (2006).  https://doi.org/10.1109/TSE.2006.104CrossRefGoogle Scholar
  6. 6.
    Brookes, S.D., Hoare, C.A.R., Roscoe, A.W.: A theory of communicating sequential processes. J. ACM 31(3), 560–599 (1984).  https://doi.org/10.1145/828.833MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    D’Argenio, P.R., Niebert, P.: Partial order reduction on concurrent probabilistic programs. In: 1st International Conference on Quantitative Evaluation of Systems (QEST 2004), 27–30 September 2004, Enschede, The Netherlands, pp. 240–249. IEEE Computer Society (2004).  https://doi.org/10.1109/QEST.2004.1348038
  8. 8.
    Díaz, Á.F., Baier, C., Earle, C.B., Fredlund, L.: Static partial order reduction for probabilistic concurrent systems. In: Ninth International Conference on Quantitative Evaluation of Systems. QEST 2012, London, United Kingdom, 17–20 September 2012, pp. 104–113. IEEE Computer Society (2012).  https://doi.org/10.1109/QEST.2012.22
  9. 9.
    Flanagan, C., Godefroid, P.: Dynamic partial-order reduction for model checking software. In: Palsberg, J., Abadi, M. (eds.) Proceedings of the 32nd ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, POPL 2005, 12–14 January 2005, Long Beach, California, USA, pp. 110–121. ACM (2005).  https://doi.org/10.1145/1040305.1040315
  10. 10.
    Garavel, H., Lang, F., Serwe, W.: From LOTOS to LNT. In: Katoen, J.-P., Langerak, R., Rensink, A. (eds.) ModelEd, TestEd, TrustEd. LNCS, vol. 10500, pp. 3–26. Springer, Cham (2017).  https://doi.org/10.1007/978-3-319-68270-9_1CrossRefGoogle Scholar
  11. 11.
    Giro, S., D’Argenio, P.R., Ferrer Fioriti, L.M.: Partial order reduction for probabilistic systems: a revision for distributed schedulers. In: Bravetti, M., Zavattaro, G. (eds.) CONCUR 2009. LNCS, vol. 5710, pp. 338–353. Springer, Heidelberg (2009).  https://doi.org/10.1007/978-3-642-04081-8_23CrossRefGoogle Scholar
  12. 12.
    Godefroid, P. (ed.): Partial-Order Methods for the Verification of Concurrent Systems - An Approach to the State-Explosion Problem. LNCS, vol. 1032. Springer, Heidelberg (1996).  https://doi.org/10.1007/3-540-60761-7CrossRefzbMATHGoogle Scholar
  13. 13.
    Hahn, E.M., Hartmanns, A., Hermanns, H., Katoen, J.: A compositional modelling and analysis framework for stochastic hybrid systems. Formal Methods Syst. Des. 43(2), 191–232 (2013).  https://doi.org/10.1007/s10703-012-0167-zCrossRefzbMATHGoogle Scholar
  14. 14.
    Hartmanns, A.: On the analysis of stochastic timed systems. Ph.D. thesis, Saarland University (2015).  https://doi.org/10.22028/D291-26597
  15. 15.
    Hermanns, H., Kwiatkowska, M.Z., Norman, G., Parker, D., Siegle, M.: On the use of mtbdds for performability analysis and verification of stochastic systems. J. Log. Algebr. Program. 56(1–2), 23–67 (2003).  https://doi.org/10.1016/S1567-8326(02)00066-8MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Holzmann, G.J.: Design and Validation of Computer Protocols. Prentice-Hall, Englewood Cliffs (1991)Google Scholar
  17. 17.
    Katz, S., Peled, D.A.: Defining conditional independence using collapses. Theor. Comput. Sci. 101(2), 337–359 (1992).  https://doi.org/10.1016/0304-3975(92)90054-JMathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Peled, D.: All from one, one for all: on model checking using representatives. In: Courcoubetis, C. (ed.) CAV 1993. LNCS, vol. 697, pp. 409–423. Springer, Heidelberg (1993).  https://doi.org/10.1007/3-540-56922-7_34CrossRefGoogle Scholar
  19. 19.
    Puterman, M.L.: Markov Decision Processes: Discrete Stochastic Dynamic Programming, 1st edn. Wiley, New York (1994).  https://doi.org/10.1002/9780470316887CrossRefzbMATHGoogle Scholar
  20. 20.
    Teige, T.: Stochastic satisfiability modulo theories: a symbolic technique for the analysis of probabilistic hybrid systems. Ph.D. thesis, Carl von Ossietzky University of Oldenburg (2012). https://oops.uni-oldenburg.de/id/eprint/1389
  21. 21.
    Valmari, A.: Stubborn sets for reduced state space generation. In: Rozenberg, G. (ed.) ICATPN 1989. LNCS, vol. 483, pp. 491–515. Springer, Heidelberg (1991).  https://doi.org/10.1007/3-540-53863-1_36CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Saarland UniversitySaarbrückenGermany
  2. 2.Saarbrücken Graduate School of Computer ScienceSaarbrückenGermany

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