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Probabilistic Bisimulation for Realistic Schedulers

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FM 2015: Formal Methods (FM 2015)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 9109))

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Abstract

Weak distribution bisimilarity is an equivalence notion on probabilistic automata, originally proposed for Markov automata. It has gained some popularity as the coarsest behavioral equivalence enjoying valuable properties like preservation of trace distribution equivalence and compositionality. This holds in the classical context of arbitrary schedulers, but it has been argued that this class of schedulers is unrealistically powerful. This paper studies a strictly coarser notion of bisimilarity, which still enjoys these properties in the context of realistic subclasses of schedulers: Trace distribution equivalence is implied for partial information schedulers, and compositionality is preserved by distributed schedulers. The intersection of the two scheduler classes thus spans a coarser and still reasonable compositional theory of behavioral semantics.

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References

  1. Baier, C., Katoen, J.-P., Hermanns, H., Wolf, V.: Comparative branching-time semantics for Markov chains. Inf. Comput. 200(2), 149–214 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  2. Bernardo, M., De Nicola, R., Loreti, M.: Relating strong behavioral equivalences for processes with nondeterminism and probabilities. Theor. Comput. Sci. 546, 63–92 (2014)

    Article  MATH  MathSciNet  Google Scholar 

  3. Bernstein, D.S., Givan, R., Immerman, N., Zilberstein, S.: The complexity of decentralized control of Markov decision processes. Math. Oper. Res. 27(4), 819–840 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  4. Boudali, H., Crouzen, P., Stoelinga, M.: A rigorous, compositional, and extensible framework for dynamic fault tree analysis. IEEE Trans. Dependable Sec. Comput. 7(2), 128–143 (2010)

    Article  Google Scholar 

  5. Cattani, S., Segala, R.: Decision algorithms for probabilistic bisimulation. In: Brim, L., Jančar, P., Křetínský, M., Kučera, A. (eds.) CONCUR 2002. LNCS, vol. 2421, pp. 371–385. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  6. Chehaibar, G., Garavel, H., Mounier, L., Tawbi, N., Zulian, F.: Specification and Verification of the PowerScale\(^{\scriptsize{\mbox{TM}}}\) bus arbitration protocol: An industrial experiment with lotos. In: FORTE, pp. 435–450 (1996)

    Google Scholar 

  7. De Alfaro, L.: The verification of probabilistic systems under memoryless partial-information policies is hard. Technical report, DTIC Document (1999)

    Google Scholar 

  8. Deng, Y., Hennessy, M.: On the semantics of Markov automata. Information and Computation 222, 139–168 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  9. Deng, Y., van Glabbeek, R., Hennessy, M., Morgan, C.: Testing finitary probabilistic processes. In: Bravetti, M., Zavattaro, G. (eds.) CONCUR 2009. LNCS, vol. 5710, pp. 274–288. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  10. Desharnais, J., Gupta, V., Jagadeesan, R., Panangaden, P.: Weak bisimulation is sound and complete for pCTL*. Inf. Comput. 208(2), 203–219 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  11. Doyen, L., Henzinger, T.A., Raskin, J.: Equivalence of labeled Markov chains. Int. J. Found. Comput. Sci. 19(3), 549–563 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  12. Eisentraut, C., Godskesen, J.C., Hermanns, H., Song, L., Zhang, L.: Late Weak Bisimulation for Markov Automata. CoRR, abs/1202.4116 (2014), http://arxiv.org/abs/1202.4116

  13. Eisentraut, C., Hermanns, H., Katoen, J.-P., Zhang, L.: A semantics for every GSPN. In: Colom, J.-M., Desel, J. (eds.) PETRI NETS 2013. LNCS, vol. 7927, pp. 90–109. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  14. Eisentraut, C., Hermanns, H., Krämer, J., Turrini, A., Zhang, L.: Deciding bisimilarities on distributions. In: Joshi, K., Siegle, M., Stoelinga, M., D’Argenio, P.R. (eds.) QEST 2013. LNCS, vol. 8054, pp. 72–88. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  15. Eisentraut, C., Hermanns, H., Zhang, L.: Concurrency and composition in a stochastic world. In: Gastin, P., Laroussinie, F. (eds.) CONCUR 2010. LNCS, vol. 6269, pp. 21–39. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  16. Eisentraut, C., Hermanns, H., Zhang, L.: On probabilistic automata in continuous time. In: LICS, pp. 342–351 (2010)

    Google Scholar 

  17. Feng, Y., Zhang, L.: When equivalence and bisimulation join forces in probabilistic automata. In: Jones, C., Pihlajasaari, P., Sun, J. (eds.) FM 2014. LNCS, vol. 8442, pp. 247–262. Springer, Heidelberg (2014)

    Chapter  Google Scholar 

  18. Giro, S., D’Argenio, P.R.: Quantitative model checking revisited: neither decidable nor approximable. In: Raskin, J.-F., Thiagarajan, P.S. (eds.) FORMATS 2007. LNCS, vol. 4763, pp. 179–194. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  19. Guck, D., Timmer, M., Hatefi, H., Ruijters, E., Stoelinga, M.: Modelling and analysis of markov reward automata. In: Cassez, F., Raskin, J.-F. (eds.) ATVA 2014. LNCS, vol. 8837, pp. 168–184. Springer, Heidelberg (2014)

    Chapter  Google Scholar 

  20. Halmos, P.R.: Measure theory, vol. 1950. Springer (1974)

    Google Scholar 

  21. He, F., Gao, X., Wang, B., Zhang, L.: Leveraging weighted automata in compositional reasoning about concurrent probabilistic systems. In: POPL, pp. 503–514. ACM (2015)

    Google Scholar 

  22. Hennessy, M.: Exploring probabilistic bisimulations, part I. Formal Asp. Comput. 24(4-6), 749–768 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  23. Hermanns, H.: Interactive Markov chains: and the quest for quantified quality. Springer, Heidelberg (2002)

    Book  Google Scholar 

  24. Hermanns, H., Krčál, J., Křetínský, J.: Probabilistic bisimulation: Naturally on distributions. In: Baldan, P., Gorla, D. (eds.) CONCUR 2014. LNCS, vol. 8704, pp. 249–265. Springer, Heidelberg (2014)

    Chapter  Google Scholar 

  25. Honda, K., Tokoro, M.: On asynchronous communication semantics. In: Zatarain-Cabada, R., Wang, J. (eds.) ECOOP-WS 1991. LNCS, vol. 612, pp. 21–51. Springer, Heidelberg (1992)

    Chapter  Google Scholar 

  26. Kwiatkowska, M., 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 

  27. Philippou, A., Lee, I., Sokolsky, O.: Weak bisimulation for probabilistic systems. In: Palamidessi, C. (ed.) CONCUR 2000. LNCS, vol. 1877, pp. 334–349. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  28. Rudin, W.: Real and complex analysis. Tata McGraw-Hill Education (2006)

    Google Scholar 

  29. Schuster, J., Siegle, M.: Markov automata: Deciding weak bisimulation by means of non-navely vanishing states. Information and Computation 237, 151–173 (2014)

    Article  MATH  MathSciNet  Google Scholar 

  30. Segala, R.: A compositional trace-based semantics for probabilistic automata. In: Lee, I., Smolka, S.A. (eds.) CONCUR 1995. LNCS, vol. 962, pp. 234–248. Springer, Heidelberg (1995)

    Chapter  Google Scholar 

  31. Segala, R.: Modeling and Verification of Randomized Distributed Realtime Systems. PhD thesis. MIT (1995)

    Google Scholar 

  32. Song, L., Feng, Y., Zhang, L.: Decentralized bisimulation for multiagent systems. In: AAMAS, pp. 209–217. IFAAMAS (2015)

    Google Scholar 

  33. Timmer, M., van de Pol, J., Stoelinga, M.I.A.: Confluence reduction for markov automata. In: Braberman, V., Fribourg, L. (eds.) FORMATS 2013. LNCS, vol. 8053, pp. 243–257. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

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Eisentraut, C., Godskesen, J.C., Hermanns, H., Song, L., Zhang, L. (2015). Probabilistic Bisimulation for Realistic Schedulers. In: Bjørner, N., de Boer, F. (eds) FM 2015: Formal Methods. FM 2015. Lecture Notes in Computer Science(), vol 9109. Springer, Cham. https://doi.org/10.1007/978-3-319-19249-9_16

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  • DOI: https://doi.org/10.1007/978-3-319-19249-9_16

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-19248-2

  • Online ISBN: 978-3-319-19249-9

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