Probabilistic Transition System Specification: Congruence and Full Abstraction of Bisimulation

  • Pedro Rubén D’Argenio
  • Matias David Lee
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7213)


We present a format for the specification of probabilistic transition systems that guarantees that bisimulation equivalence is a congruence for any operator defined in this format. In this sense, the format is somehow comparable to the ntyft/ntyxt format in a non-probabilistic setting. We also study the modular construction of probabilistic transition systems specifications and prove that some standard conservative extension theorems also hold in our setting. Finally, we show that the trace congruence for image-finite processes induced by our format is precisely bisimulation on probabilistic systems.


Transition System Transition Relation Operational Semantic Process Algebra Conservative Extension 
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.
    Aceto, L., Fokkink, W., Verhoef, C.: Conservative extension in structural operational semantics. In: Current Trends in Theor. Comput. Sci., pp. 504–524. World Scientific (2001)Google Scholar
  2. 2.
    Aceto, L., Fokkink, W., Verhoef, C.: Structural operational semantics. In: Handbook of Process Algebra, pp. 197–292. Elsevier (2001)Google Scholar
  3. 3.
    Baeten, J.C.M., Bergstra, J.A.: Process Algebra with a Zero Object. In: Baeten, J.C.M., Klop, J.W. (eds.) CONCUR 1990. LNCS, vol. 458, pp. 83–98. Springer, Heidelberg (1990)Google Scholar
  4. 4.
    Baeten, J.C.M., Bergstra, J.A., Smolka, S.A.: Axiomatizing probabilistic processes: ACP with generative probabilities. Inf. Comput. 121(2), 234–255 (1995)MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    Baier, C.: On Algorithmics Verification Methods for Probabilistic Systems. Habilitation thesis, University of Mannheim (1999)Google Scholar
  6. 6.
    Bartels, F.: GSOS for probabilistic transition systems. Electr. Notes Theor. Comput. Sci. 65(1) (2002)Google Scholar
  7. 7.
    Bartels, F.: On Generalised Coinduction and Probabilistic Specification Formats. PhD thesis, Vrije Universiteit (2004)Google Scholar
  8. 8.
    Bloom, B., Istrail, S., Meyer, A.R.: Bisimulation can’t be traced. J. ACM 42(1), 232–268 (1995)MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    Bol, R., Groote, J.F.: The meaning of negative premises in transition system specifications. J. ACM 43(5), 863–914 (1996)MathSciNetzbMATHCrossRefGoogle Scholar
  10. 10.
    D’Argenio, P.R., Verhoef, C.: A general conservative extension theorem in process algebras with inequalities. Theor. Comput. Sci. 177(2), 351–380 (1997)MathSciNetzbMATHCrossRefGoogle Scholar
  11. 11.
    Fokkink, W., van Glabbeek, R.J.: Ntyft/ntyxt rules reduce to ntree rules. Inf. Comput. 126(1) (1996)Google Scholar
  12. 12.
    Groote, J.F.: Transition system specifications with negative premises. Theor. Comput. Sci. 118(2), 263–299 (1993)MathSciNetzbMATHCrossRefGoogle Scholar
  13. 13.
    Groote, J.F., Vaandrager, F.: Structured operational semantics and bisimulation as a congruence. Inf. Comput. 100(2), 202–260 (1992)MathSciNetzbMATHCrossRefGoogle Scholar
  14. 14.
    Jonsson, B., Larsen, K.G., Yi, W.: Probabilistic extensions of process algebras. In: Handbook of Process Algebra, pp. 685–710. Elsevier (2001)Google Scholar
  15. 15.
    Klin, B.: Bialgebras for structural operational semantics: An introduction. Theor. Comput. Sci. 412(38), 5043–5069 (2011)MathSciNetzbMATHCrossRefGoogle Scholar
  16. 16.
    Lanotte, R., Tini, S.: Probabilistic Congruence for Semistochastic Generative Processes. In: Sassone, V. (ed.) FOSSACS 2005. LNCS, vol. 3441, pp. 63–78. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  17. 17.
    Lanotte, R., Tini, S.: Probabilistic bisimulation as a congruence. ACM Trans. Comput. Log. 10(2) (2009)Google Scholar
  18. 18.
    Larsen, K.G., Skou, A.: Bisimulation through probabilistic testing. Inf. Comput. 94(1), 1–28 (1991)MathSciNetzbMATHCrossRefGoogle Scholar
  19. 19.
    Milner, R.: Communication and Concurrency. Prentice-Hall, Inc. (1989)Google Scholar
  20. 20.
    Mousavi, M.R., Reniers, M.A., Groote, J.F.: SOS formats and meta-theory: 20 years after. Theor. Comput. Sci. 373(3), 238–272 (2007)MathSciNetzbMATHCrossRefGoogle Scholar
  21. 21.
    Plotkin, G.: A structural approach to operational semantics. Report DAIMI FN-19, Aarhus University (1981); reprinted in J. Log. Algebr. Program. 60-61, 17–139 (2004)Google Scholar
  22. 22.
    Segala, R.: Modeling and Verification of Randomized Distributed Real-Time Systems. PhD thesis. MIT (1995)Google Scholar
  23. 23.
    Turi, D., Plotkin, G.D.: Towards a mathematical operational semantics. In: LICS, pp. 280–291 (1997)Google Scholar
  24. 24.
    van Glabbeek, R.J.: The meaning of negative premises in transition system specifications II. J. Log. Algebr. Program. 60-61, 229–258 (2004)CrossRefGoogle Scholar
  25. 25.
    van Glabbeek, R.J., Smolka, S.A., Steffen, B.: Reactive, generative and stratified models of probabilistic processes. Inf. Comput. 121(1), 59–80 (1995)zbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Pedro Rubén D’Argenio
    • 1
  • Matias David Lee
    • 1
  1. 1.FaMAFUniversidad Nacional de Córdoba – CONICETArgentina

Personalised recommendations