Skip to main content

Alternative Characterizations of Probabilistic Trace Equivalences on Coherent Resolutions of Nondeterminism

  • Conference paper
  • First Online:
Quantitative Evaluation of Systems (QEST 2020)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12289))

Included in the following conference series:

Abstract

For nondeterministic and probabilistic processes, the validity of some desirable properties of probabilistic trace semantics depends both on the class of schedulers used to resolve nondeterminism and on the capability of suitably limiting the power of the considered schedulers. Inclusion of probabilistic bisimilarity, compositionality with respect to typical process operators, and backward compatibility with trace semantics over fully nondeterministic or fully probabilistic processes, can all be achieved by restricting to coherent resolutions of nondeterminism. Here we provide alternative characterizations of probabilistic trace post-equivalence and pre-equivalence in the case of coherent resolutions. The characterization of the former is based on fully coherent trace distributions, whereas the characterization of the latter relies on coherent weighted trace sets.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

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

    Article  MathSciNet  Google Scholar 

  2. Bernardo, M.: Coherent resolutions of nondeterminism. In: Gribaudo, M., Iacono, M., Phung-Duc, T., Razumchik, R. (eds.) EPEW 2019. LNCS, vol. 12039, pp. 16–32. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-44411-2_2

    Chapter  Google Scholar 

  3. Bernardo, M., De Nicola, R., Loreti, M.: Revisiting trace and testing equivalences for nondeterministic and probabilistic processes. Logical Methods Comput. Sci. 10(116), 1–42 (2014)

    MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  5. Bernardo, M., Sangiorgi, D., Vignudelli, V.: On the discriminating power of testing equivalences for reactive probabilistic systems: results and open problems. In: Norman, G., Sanders, W. (eds.) QEST 2014. LNCS, vol. 8657, pp. 281–296. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-10696-0_23

    Chapter  MATH  Google Scholar 

  6. Bianco, A., de Alfaro, L.: Model checking of probabilistic and nondeterministic systems. In: Thiagarajan, P.S. (ed.) FSTTCS 1995. LNCS, vol. 1026, pp. 499–513. Springer, Heidelberg (1995). https://doi.org/10.1007/3-540-60692-0_70

    Chapter  MATH  Google Scholar 

  7. Bonchi, F., Sokolova, A., Vignudelli, V.: The theory of traces for systems with nondeterminism and probability. In: Proceedings of the 34th ACM/IEEE Symposium on Logic in Computer Science (LICS 2019), pp. (19:62)1–14. IEEE-CS Press (2019)

    Google Scholar 

  8. Brookes, S.D., Hoare, C.A.R., Roscoe, A.W.: A theory of communicating sequential processes. J. ACM 31, 560–599 (1984)

    Article  MathSciNet  Google Scholar 

  9. Cheung, L., Lynch, N.A., Segala, R., Vaandrager, F.: Switched PIOA: parallel composition via distributed scheduling. Theoret. Comput. Sci. 365, 83–108 (2006)

    Article  MathSciNet  Google Scholar 

  10. de Alfaro, L., Henzinger, T.A., Jhala, R.: Compositional methods for probabilistic systems. In: Larsen, K.G., Nielsen, M. (eds.) CONCUR 2001. LNCS, vol. 2154, pp. 351–365. Springer, Heidelberg (2001). https://doi.org/10.1007/3-540-44685-0_24

    Chapter  Google Scholar 

  11. Deng, Y., van Glabbeek, R.J., Hennessy, M., Morgan, C.: Characterising testing preorders for finite probabilistic processes. Logical Methods Comput. Sci. 4(4:4), 1–33 (2008)

    MathSciNet  MATH  Google Scholar 

  12. Deng, Y., van Glabbeek, R., Morgan, C., Zhang, C.: Scalar outcomes suffice for finitary probabilistic testing. In: De Nicola, R. (ed.) ESOP 2007. LNCS, vol. 4421, pp. 363–378. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-71316-6_25

    Chapter  Google Scholar 

  13. Derman, C.: Finite State Markovian Decision Processes. Academic Press, Cambridge (1970)

    MATH  Google Scholar 

  14. Georgievska, S., Andova, S.: Probabilistic may/must testing: retaining probabilities by restricted schedulers. Formal Aspects Comput. 24, 727–748 (2012). https://doi.org/10.1007/s00165-012-0236-5

    Article  MathSciNet  MATH  Google Scholar 

  15. Giro, S., D’Argenio, P.R.: On the expressive power of schedulers in distributed probabilistic systems. In: Proceedings of the 7th International Workshop on Quantitative Aspects of Programming Languages (QAPL 2009), ENTCS, vol. 253(3), pp. 45–71. Elsevier (2009)

    Google Scholar 

  16. Huynh, D.T., Tian, L.: On some equivalence relations for probabilistic processes. Fundamenta Informaticae 17, 211–234 (1992)

    MathSciNet  MATH  Google Scholar 

  17. Jonsson, B., Ho-Stuart, C., Yi, W.: Testing and refinement for nondeterministic and probabilistic processes. In: Langmaack, H., de Roever, W.-P., Vytopil, J. (eds.) FTRTFT 1994. LNCS, vol. 863, pp. 418–430. Springer, Heidelberg (1994). https://doi.org/10.1007/3-540-58468-4_176

    Chapter  Google Scholar 

  18. Jonsson, B., Yi, W.: Compositional testing preorders for probabilistic processes. In: Proceedings of the 10th IEEE Symposium on Logic in Computer Science (LICS 1995), pp. 431–441. IEEE-CS Press (1995)

    Google Scholar 

  19. Jonsson, B., Yi, W.: Testing preorders for probabilistic processes can be characterized by simulations. Theoret. Comput. Sci. 282, 33–51 (2002)

    Article  MathSciNet  Google Scholar 

  20. Jou, C.-C., Smolka, S.A.: Equivalences, congruences, and complete axiomatizations for probabilistic processes. In: Baeten, J.C.M., Klop, J.W. (eds.) CONCUR 1990. LNCS, vol. 458, pp. 367–383. Springer, Heidelberg (1990). https://doi.org/10.1007/BFb0039071

    Chapter  Google Scholar 

  21. Keller, R.M.: Formal verification of parallel programs. Commun. ACM 19, 371–384 (1976)

    Article  MathSciNet  Google Scholar 

  22. Kemeny, J.G., Snell, J.L.: Finite Markov Chains. Van Nostrand, London (1960)

    MATH  Google Scholar 

  23. Lynch, N., Segala, R., Vaandrager, F.: Compositionality for probabilistic automata. In: Amadio, R., Lugiez, D. (eds.) CONCUR 2003. LNCS, vol. 2761, pp. 208–221. Springer, Heidelberg (2003). https://doi.org/10.1007/978-3-540-45187-7_14

    Chapter  Google Scholar 

  24. Segala, R.: Modeling and Verification of Randomized Distributed Real-Time Systems. Ph.D. thesis (1995)

    Google Scholar 

  25. 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). https://doi.org/10.1007/3-540-60218-6_17

    Chapter  Google Scholar 

  26. Segala, R.: Testing probabilistic automata. In: Montanari, U., Sassone, V. (eds.) CONCUR 1996. LNCS, vol. 1119, pp. 299–314. Springer, Heidelberg (1996). https://doi.org/10.1007/3-540-61604-7_62

    Chapter  Google Scholar 

  27. Segala, R., Lynch, N.: Probabilistic simulations for probabilistic processes. In: Jonsson, B., Parrow, J. (eds.) CONCUR 1994. LNCS, vol. 836, pp. 481–496. Springer, Heidelberg (1994). https://doi.org/10.1007/978-3-540-48654-1_35

    Chapter  Google Scholar 

  28. van Glabbeek, R.J.: The linear time - branching time spectrum I. In: Handbook of Process Algebra, pp. 3–99. Elsevier (2001)

    Google Scholar 

  29. van Glabbeek, R.J., Smolka, S.A., Steffen, B.: Reactive, generative and stratified models of probabilistic processes. Inf. Comput. 121, 59–80 (1995)

    Article  MathSciNet  Google Scholar 

  30. Vardi, M.Y.: Automatic verification of probabilistic concurrent finite-state programs. In: Proceedings of the 26th IEEE Symposium on Foundations of Computer Science (FOCS 1985), pp. 327–338. IEEE-CS Press (1985)

    Google Scholar 

  31. Yi, W., Larsen, K.G.: Testing probabilistic and nondeterministic processes. In: Proceedings of the 12th International Symposium on Protocol Specification, Testing and Verification (PSTV 1992), pp. 47–61. North-Holland (1992)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Marco Bernardo .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Bernardo, M. (2020). Alternative Characterizations of Probabilistic Trace Equivalences on Coherent Resolutions of Nondeterminism. In: Gribaudo, M., Jansen, D.N., Remke, A. (eds) Quantitative Evaluation of Systems. QEST 2020. Lecture Notes in Computer Science(), vol 12289. Springer, Cham. https://doi.org/10.1007/978-3-030-59854-9_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-59854-9_5

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-59853-2

  • Online ISBN: 978-3-030-59854-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics