On the Semantics of Markov Automata

  • Yuxin Deng
  • Matthew Hennessy
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6756)


Markov automata describe systems in terms of events which may be nondeterministic, may occur probabilistically, or may be subject to time delays. We define a novel notion of weak bisimulation for such systems and prove that this provides both a sound and complete proof methodology for a natural extensional behavioural equivalence between such systems, a generalisation of reduction barbed congruence, the well-known touchstone equivalence for a large variety of process description languages.


Operational Semantic Label Transition System Full Distribution Behavioural Equivalence Probabilistic Automaton 
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.


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  1. 1.
    Aldini, A., Bernardo, M., Corradini, F.: A Process Algebraic Approach to Software Architecture Design. Springer, Heidelberg (2010)CrossRefzbMATHGoogle Scholar
  2. 2.
    Bernardo, M., Gorrieri, R.: A tutorial on empa: A theory of concurrent processes with nondeterminism, priorities, probabilities and time. Theor. Comput. Sci. 202(1-2), 1–54 (1998)CrossRefzbMATHMathSciNetGoogle Scholar
  3. 3.
    Bravetti, M., Bernardo, M.: Compositional asymmetric cooperations for process algebras with probabilities, priorities, and time. ENTCS 39(3) (2000)Google Scholar
  4. 4.
    Deng, Y., Du, W.: Probabilistic barbed congruence. ENTCS 190(3), 185–203 (2007)zbMATHGoogle Scholar
  5. 5.
    Deng, Y., van Glabbeek, R., Hennessy, M., Morgan, C.: Testing finitary probabilistic processes (extended abstract). In: Bravetti, M., Zavattaro, G. (eds.) CONCUR 2009. LNCS, vol. 5710, pp. 274–288. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  6. 6.
    Desharnais, J., Gupta, V., Jagadeesan, R., Panangaden, P.: Weak bisimulation is sound and complete for pCTL\(^{\mbox{*}}\). Information and Computation 208(2), 203–219 (2010)CrossRefzbMATHMathSciNetGoogle Scholar
  7. 7.
    Eisentraut, C.: Personal communication (2011)Google Scholar
  8. 8.
    Eisentraut, C., Hermanns, H., Zhang, L.: On probabilistic automata in continuous time. In: Proc. LICS 2010, pp. 342–351 (2010)Google Scholar
  9. 9.
    Fournet, C., Gonthier, G.: A hierarchy of equivalences for asynchronous calculi. J. Log. Algebr. Program. 63(1), 131–173 (2005)CrossRefzbMATHMathSciNetGoogle Scholar
  10. 10.
    Hermanns, H.: Interactive Markov Chains: The Quest for Quantified Quality. LNCS, vol. 2428, p. 129. Springer, Heidelberg (2002)zbMATHGoogle Scholar
  11. 11.
    Hermanns, H., Parma, A., Segala, R., Wachter, B., Zhang, L.: Probabilistic logical characterization. Inf. Comput. 209, 154–172 (2011)CrossRefzbMATHMathSciNetGoogle Scholar
  12. 12.
    Hillston, J.: A Compositional Approach to Performance Modelling. Distinguished Dissertations in Computer Science. Cambridge University Press, New York (2005)zbMATHGoogle Scholar
  13. 13.
    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)CrossRefGoogle Scholar
  14. 14.
    Jeffrey, A., Rathke, J.: Contextual equivalence for higher-order pi-calculus revisited. LMCS 1(1:4) (2005)Google Scholar
  15. 15.
    Larsen, K.G., Skou, A.: Bisimulation through probabilistic testing (preliminary report). In: Proc. POPL 1989, pp. 344–352. ACM, New York (1989)Google Scholar
  16. 16.
    Milner, R.: Calculi for synchrony and asynchrony. Theor. Comput. Sci. 25, 267–310 (1983)CrossRefzbMATHMathSciNetGoogle Scholar
  17. 17.
    Milner, R.: Communication and Concurrency. Prentice-Hall, Englewood Cliffs (1989)zbMATHGoogle Scholar
  18. 18.
    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)CrossRefGoogle Scholar
  19. 19.
    Rathke, J., Sobocinski, P.: Deriving structural labelled transitions for mobile ambients. In: van Breugel, F., Chechik, M. (eds.) CONCUR 2008. LNCS, vol. 5201, pp. 462–476. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  20. 20.
    Sangiorgi, D., Kobayashi, N., Sumii, E.: Environmental bisimulations for higher-order languages. In: Proc. LICS 2007, pp. 293–302. IEEE Computer Society, Los Alamitos (2007)Google Scholar
  21. 21.
    Sangiorgi, D., Walker, D.: The π-calculus: a Theory of Mobile Processes. Cambridge University Press, Cambridge (2001)zbMATHGoogle Scholar
  22. 22.
    Segala, R.: Modeling and verification of randomized distributed real-time systems. Technical Report MIT/LCS/TR-676, PhD thesis, MIT, Dept. of EECS (1995)Google Scholar
  23. 23.
    Segala, R.: Testing probabilistic automata. In: Sassone, V., Montanari, U. (eds.) CONCUR 1996. LNCS, vol. 1119, pp. 299–314. Springer, Heidelberg (1996)CrossRefGoogle Scholar
  24. 24.
    Segala, R., Lynch, N.A.: Probabilistic simulations for probabilistic processes. Nord. J. Comput. 2(2), 250–273 (1995)zbMATHMathSciNetGoogle Scholar

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© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Yuxin Deng
    • 1
    • 3
    • 4
  • Matthew Hennessy
    • 2
  1. 1.Shanghai Jiao Tong UniversityChina
  2. 2.Trinity College DublinIreland
  3. 3.Carnegie Mellon UniversityUSA
  4. 4.Chinese Academy of SciencesChina

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