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Refinement and Difference for Probabilistic Automata

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Book cover Quantitative Evaluation of Systems (QEST 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8054))

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Abstract

This paper studies a difference operator for stochastic systems whose specifications are represented by Abstract Probabilistic Automata (APAs). In the case refinement fails between two specifications, the target of this operator is to produce a specification APA that represents all witness PAs of this failure. Our contribution is an algorithm that allows to approximate the difference of two deterministic APAs with arbitrary precision. Our technique relies on new quantitative notions of distances between APAs used to assess convergence of the approximations as well as on an in-depth inspection of the refinement relation for APAs. The procedure is effective and not more complex than refinement checking.

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References

  1. Aliprantis, C.D., Border, K.C.: Infinite Dimensional Analysis: A Hitchhiker’s Guide, 3rd edn. Springer (2007)

    Google Scholar 

  2. Aljazzar, H., Leue, S.: Directed explicit state-space search in the generation of counterexamples for stochastic model checking. IEEE Trans. Software Eng. (2010)

    Google Scholar 

  3. Alur, R., Feder, T., Henzinger, T.A.: The benefits of relaxing punctuality. J. ACM 43(1), 116–146 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  4. Andrés, M.E., D’Argenio, P., van Rossum, P.: Significant diagnostic counterexamples in probabilistic model checking. In: Chockler, H., Hu, A.J. (eds.) HVC 2008. LNCS, vol. 5394, pp. 129–148. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  5. Baier, C., Katoen, J.-P.: Principles of Model Checking. MIT Press (2008)

    Google Scholar 

  6. Bauer, S.S., Fahrenberg, U., Legay, A., Thrane, C.: General quantitative specification theories with modalities. In: Hirsch, E.A., Karhumäki, J., Lepistö, A., Prilutskii, M. (eds.) CSR 2012. LNCS, vol. 7353, pp. 18–30. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  7. Caillaud, B., Delahaye, B., Larsen, K.G., Legay, A., Pedersen, M.L., Wasowski, A.: Constraint Markov chains. TCS 412(34), 4373–4404 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  8. Chadha, R., Viswanathan, M.: A counterexample-guided abstraction-refinement framework for Markov decision processes. ACM Trans. Comput. Log. 12(1), 1 (2010)

    Article  MathSciNet  Google Scholar 

  9. Cobleigh, J.M., Avrunin, G.S., Clarke, L.A.: Breaking up is hard to do: An evaluation of automated assume-guarantee reasoning. ACM Trans. Softw. Eng. Methodol. 17(2) (2008)

    Google Scholar 

  10. Cobleigh, J.M., Giannakopoulou, D., Păsăreanu, C.S.: Learning assumptions for compositional verification. In: Garavel, H., Hatcliff, J. (eds.) TACAS 2003. LNCS, vol. 2619, pp. 331–346. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  11. de Alfaro, L., Henzinger, T.A.: Interface automata. In: FSE, pp. 109–120. ACM (2001)

    Google Scholar 

  12. de Alfaro, L., Majumdar, R., Raman, V., Stoelinga, M.: Game relations and metrics. In: LICS, pp. 99–108. IEEE Computer Society (2007)

    Google Scholar 

  13. Delahaye, B., Fahrenberg, U., Larsen, K.G., Legay, A.: Refinement and difference for probabilistic automata - long version (2013), http://delahaye.benoit.free.fr/rapports/QEST13-long.pdf

  14. Delahaye, B., Katoen, J.-P., Larsen, K.G., Legay, A., Pedersen, M.L., Sher, F., Wąsowski, A.: Abstract probabilistic automata. In: Jhala, R., Schmidt, D. (eds.) VMCAI 2011. LNCS, vol. 6538, pp. 324–339. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  15. Delahaye, B., Katoen, J.-P., Larsen, K.G., Legay, A., Pedersen, M.L., Sher, F., Wąsowski, A.: New results on abstract probabilistic automata. In: ACSD, pp. 118–127. IEEE (2011)

    Google Scholar 

  16. Delahaye, B., Larsen, K.G., Legay, A., Pedersen, M.L., Wąsowski, A.: APAC: A tool for reasoning about abstract probabilistic automata. In: QEST, pp. 151–152. IEEE (2011)

    Google Scholar 

  17. Desharnais, J., Gupta, V., Jagadeesan, R., Panangaden, P.: Metrics for labelled Markov processes. TCS 318(3), 323–354 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  18. 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)

    Chapter  Google Scholar 

  19. Han, T., Katoen, J.-P., Damman, B.: Counterexample generation in probabilistic model checking. IEEE Trans. Software Eng. 35(2), 241–257 (2009)

    Article  Google Scholar 

  20. Hansson, H., Jonsson, B.: A logic for reasoning about time and reliability. Formal Asp. Comput. 6(5), 512–535 (1994)

    Article  MATH  Google Scholar 

  21. Hermanns, H., Herzog, U., Katoen, J.: Process algebra for performance evaluation. TCS 274(1-2), 43–87 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  22. Hermanns, H., Wachter, B., Zhang, L.: Probabilistic CEGAR. In: Gupta, A., Malik, S. (eds.) CAV 2008. LNCS, vol. 5123, pp. 162–175. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  23. 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)

    Chapter  Google Scholar 

  24. Jansen, N., Ábrahám, E., Katelaan, J., Wimmer, R., Katoen, J.-P., Becker, B.: Hierarchical counterexamples for discrete-time Markov chains. In: Bultan, T., Hsiung, P.-A. (eds.) ATVA 2011. LNCS, vol. 6996, pp. 443–452. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  25. Jonsson, B., Larsen, K.G.: Specification and refinement of probabilistic processes. In: LICS, pp. 266–277. IEEE (1991)

    Google Scholar 

  26. Katoen, J.-P., Klink, D., Leucker, M., Wolf, V.: Three-valued abstraction for continuous-time Markov chains. In: Damm, W., Hermanns, H. (eds.) CAV 2007. LNCS, vol. 4590, pp. 311–324. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  27. Komuravelli, A., Păsăreanu, C.S., Clarke, E.M.: Assume-guarantee abstraction refinement for probabilistic systems. In: Madhusudan, P., Seshia, S.A. (eds.) CAV 2012. LNCS, vol. 7358, pp. 310–326. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  28. Kwiatkowska, M.Z., Norman, G., Parker, D., Qu, H.: Assume-guarantee verification for probabilistic systems. In: Esparza, J., Majumdar, R. (eds.) TACAS 2010. LNCS, vol. 6015, pp. 23–37. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  29. Larsen, K.G.: Modal specifications. In: Sifakis, J. (ed.) CAV 1989. LNCS, vol. 407, pp. 232–246. Springer, Heidelberg (1990)

    Chapter  Google Scholar 

  30. Larsen, K.G., Fahrenberg, U., Thrane, C.: Metrics for weighted transition systems: Axiomatization and complexity. TCS 412(28), 3358–3369 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  31. Lynch, N., Tuttle, M.R.: An introduction to Input/Output automata. CWI 2(3) (1989)

    Google Scholar 

  32. Lynch, N.A.: Distributed Algorithms. Morgan Kaufmann (1996)

    Google Scholar 

  33. Manna, Z., Pnueli, A.: The Temporal Logic of Reactive and Concurrent Systems. Springer (1992)

    Google Scholar 

  34. Raclet, J.-B.: Quotient de spécifications pour la réutilisation de composants. PhD thesis, Université de Rennes I (December 2007) (in French)

    Google Scholar 

  35. Sassolas, M., Chechik, M., Uchitel, S.: Exploring inconsistencies between modal transition systems. Software and System Modeling 10(1), 117–142 (2011)

    Article  Google Scholar 

  36. Schmalz, M., Varacca, D., Völzer, H.: Counterexamples in probabilistic LTL model checking for Markov chains. In: Bravetti, M., Zavattaro, G. (eds.) CONCUR 2009. LNCS, vol. 5710, pp. 587–602. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  37. Segala, R., Lynch, N.A.: Probabilistic simulations for probabilistic processes. In: Jonsson, B., Parrow, J. (eds.) CONCUR 1994. LNCS, vol. 836, pp. 481–496. Springer, Heidelberg (1994)

    Chapter  Google Scholar 

  38. Sher, F., Katoen, J.-P.: Compositional abstraction techniques for probabilistic automata. In: Baeten, J.C.M., Ball, T., de Boer, F.S. (eds.) TCS 2012. LNCS, vol. 7604, pp. 325–341. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  39. Thrane, C., Fahrenberg, U., Larsen, K.G.: Quantitative analysis of weighted transition systems. JLAP 79(7), 689–703 (2010)

    MathSciNet  MATH  Google Scholar 

  40. van Breugel, F., Mislove, M.W., Ouaknine, J., Worrell, J.: An intrinsic characterization of approximate probabilistic bisimilarity. In: Gordon, A.D. (ed.) FOSSACS 2003. LNCS, vol. 2620, pp. 200–215. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  41. Vardi, M.Y.: Automatic verification of probabilistic concurrent finite-state programs. In: FOCS, pp. 327–338. IEEE (1985)

    Google Scholar 

  42. Wimmer, R., Braitling, B., Becker, B.: Counterexample generation for discrete-time Markov chains using bounded model checking. In: Jones, N.D., Müller-Olm, M. (eds.) VMCAI 2009. LNCS, vol. 5403, pp. 366–380. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  43. Wimmer, R., Jansen, N., Ábrahám, E., Becker, B., Katoen, J.-P.: Minimal critical subsystems for discrete-time Markov models. In: Flanagan, C., König, B. (eds.) TACAS 2012. LNCS, vol. 7214, pp. 299–314. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

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Author information

Authors and Affiliations

  1. INRIA/IRISA, France

    Benoît Delahaye, Uli Fahrenberg & Axel Legay

  2. Aalborg University, Denmark

    Kim Guldstrand Larsen

Authors
  1. Benoît Delahaye
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  2. Uli Fahrenberg
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  3. Kim Guldstrand Larsen
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  4. Axel Legay
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Editor information

Editors and Affiliations

  1. AT&T Labs Research, 180 Park Avenue, Building 103, 07932, Florham Park, NJ, USA

    Kaustubh Joshi

  2. Institut für Technische Informatik, Universität der Bundeswehr München, Werner-Heisenberg Weg 39, 85577, Neubiberg, Germany

    Markus Siegle

  3. Faculty of Electrical Engineering, Mathematics and Computer Science, University of Twente, Drienerlolaan 5, Zilverling Building, 7522 NB, Enschede, The Netherlands

    Mariëlle Stoelinga

  4. Facultad de Matemáticas, Astronomía y Física, Universidad Nacional de Córdoba – CONICET, Medina Allende s/n, X5000HUA, Córdoba, Argentina

    Pedro R. D’Argenio

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Delahaye, B., Fahrenberg, U., Guldstrand Larsen, K., Legay, A. (2013). Refinement and Difference for Probabilistic Automata. In: Joshi, K., Siegle, M., Stoelinga, M., D’Argenio, P.R. (eds) Quantitative Evaluation of Systems. QEST 2013. Lecture Notes in Computer Science, vol 8054. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40196-1_3

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  • DOI: https://doi.org/10.1007/978-3-642-40196-1_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-40195-4

  • Online ISBN: 978-3-642-40196-1

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