Probability and Nondeterminism in Operational Models of Concurrency

  • Roberto Segala
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4137)


We give a brief overview of operational models for concurrent systems that exhibit probabilistic behavior, focussing on the interplay between probability and nondeterminism. Our survey is carried out from the perspective of probabilistic automata, a model originally developed for the analysis of randomized distributed algorithms.


Transition Relation Process Algebra Fair Coin Logical Characterization 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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Alur, R., Henzinger, T.: Reactive modules. Formal Methods in System Design 15(1), 7–48 (1999)CrossRefMathSciNetGoogle Scholar
  2. 2.
    Andova, S., Willemse, T.: Branching bisimulation for probabilistic systems: characteristics and decidability. Theoretical Computer Science 356(3), 325–355 (2006)CrossRefMathSciNetMATHGoogle Scholar
  3. 3.
    Baier, C., Hermanns, H., Katoen, J.-P., Wolf, V.: Comparative branching-time semantics for markov chains. In: Amadio, R., Lugiez, D. (eds.) CONCUR 2003. LNCS, vol. 2761, pp. 492–507. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  4. 4.
    Baier, C., Stoelinga, M.: Norm Functions for Probabilistic Bisimulations with Delays. In: Tiuryn, J. (ed.) FOSSACS 2000. LNCS, vol. 1784, p. 1. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  5. 5.
    Bartels, F., Sokolova, A., de Vink, E.: A hierarchy of probabilistic system types. Theoretical Computer Science 327(1-2), 3–22 (2004)CrossRefMathSciNetMATHGoogle Scholar
  6. 6.
    Bernardo, M., Gorrieri, R.: Extended markovian process algebra. In: [29]Google Scholar
  7. 7.
    Bravetti, M., D’Argenio, P.R.: Tutte le Algebre Insieme: Concepts, Discussions and Relations of Stochastic Process Algebras with General Distributions. In: Baier, C., Haverkort, B.R., Hermanns, H., Katoen, J.-P., Siegle, M. (eds.) Validation of Stochastic Systems. LNCS, vol. 2925, pp. 44–88. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  8. 8.
    Cattani, S., Segala, R.: Decision algorithms for probabilistic bisimulation. In: Brim, L., Jančar, P., Křetínský, M., Kucera, A. (eds.) CONCUR 2002. LNCS, vol. 2421, pp. 371–385. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  9. 9.
    Cattani, S., Segala, R., Kwiatkowska, M., Norman, G.: Stochastic Transition Systems for Continuous State Spaces and Non-determinism. In: Sassone, V. (ed.) FOSSACS 2005. LNCS, vol. 3441, pp. 125–139. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  10. 10.
    Cheung, L., Lynch, N., Segala, R., Vaandrager, F.: Switched Probabilistic I/O Automata. In: Liu, Z., Araki, K. (eds.) ICTAC 2004. LNCS, vol. 3407, pp. 494–510. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  11. 11.
    Daniele, V., Winskel, G.: Distributing probability over non-determinism. Mathematical Structures in Computer Science 16, 87–113 (2006)CrossRefMATHGoogle Scholar
  12. 12.
    D’Argenio, P., Hermanns, H., Katoen, J.P.: On generative parallel composition. In: Proceedings of PROBMIV 1998. ENTCS, vol. 22 (1999)Google Scholar
  13. 13.
    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, p. 351. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  14. 14.
    Deng, Y.: Axiomatisations and types for probabilistic and mobile processes. PhD thesis, Ecole de Mines (2005)Google Scholar
  15. 15.
    Derman, C.: Finite State Markovian Decision Processes. Academic Press, London (1970)MATHGoogle Scholar
  16. 16.
    Desharnais, J.: Labelled Markov Processes. PhD thesis, McGill University (1999)Google Scholar
  17. 17.
    Desharnais, J., Edalat, A., Panangaden, P.: A logical characterization of bisimulation for labelled Markov processes. In: Proceedings of LICS (1998)Google Scholar
  18. 18.
    Desharnais, J., Edalat, A., Panangaden, P.: Bisimulation for labelled Markov processes. Information and Computation 179(2), 163–193 (2002)CrossRefMathSciNetMATHGoogle Scholar
  19. 19.
    van Glabbeek, R., Smolka, S., Steffen, B.: Reactive, generative, and stratified models of probabilistic processes. Information and Computation 12(1), 59–80 (1996)Google Scholar
  20. 20.
    Götz, N., Herzog, U., Rettelbach, M.: Multiprocessor and distributed system design: the integration of functional specification and performance analysis using stochastic process algebras. In: Donatiello, L., Nelson, R. (eds.) SIGMETRICS 1993 and Performance 1993. LNCS, vol. 729, pp. 121–146. Springer, Heidelberg (1993)CrossRefGoogle Scholar
  21. 21.
    Hansson, H.: Time and Probability in Formal Design of Distributed Systems. Real-Time Safety Critical Systems, vol. 1. Elsevier, Amsterdam (1994)Google Scholar
  22. 22.
    Hansson, H., Jonsson, B.: A calculus for communicating systems with time and probabilities. In: Proceedings of RTSS (1990)Google Scholar
  23. 23.
    Hermanns, H.: Interactive Markov Chains. LNCS, vol. 2428, p. 2002. Springer, Heidelberg (2002)MATHGoogle Scholar
  24. 24.
    Hillston, J.: A Compositional Approach to Performance Modeling. PhD thesis, Department of Computer Science, University of Edimburgh (UK) (1994)Google Scholar
  25. 25.
    Jonsson, B., Larsen, K.G.: Specification and refinement of probabilistic processes. In: Proceedings of LICS, pp. 266–277 (July 1991)Google Scholar
  26. 26.
    Lynch, N.A., Stark, E.W.: A proof of the Kahn principle for Input/Output automata. Information and Computation 82(1), 81–92 (1989)CrossRefMathSciNetMATHGoogle Scholar
  27. 27.
    Lynch, N.A., Tuttle, M.R.: Hierarchical correctness proofs for distributed algorithms. In: Proceedings of PoDC, pp. 137–151 (1987)Google Scholar
  28. 28.
    McIver, A., Morgan, C.: Abstraction, refinement, and proof for probabilistic systems. Springer, Heidelberg (2005)MATHGoogle Scholar
  29. 29.
    Montanari, U., Sassone, V. (eds.): Proceedings of CONCUR 1996. LNCS, vol. 1119. Springer, Heidelberg (1996)Google Scholar
  30. 30.
    Panangaden, P.: Measure and probability for concurrency theorists. Theoretical Computer Science 253(2), 287–309 (2001)CrossRefMathSciNetMATHGoogle Scholar
  31. 31.
    Parma, A., Segala, R.: Axiomatization of trace semantics for stochastic nondeterministic processes. In: Proceedings of QEST, pp. 294–303 (2004)Google Scholar
  32. 32.
    Philippou, A., Lee, I., Sokolsky, O.: Weak Bisimulation for Probabilistic Systems. In: Palamidessi, C. (ed.) CONCUR 2000. LNCS, vol. 1877, pp. 334–339. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  33. 33.
    Pogosyants, A., Segala, R., Lynch, N.: Verification of the randomized consensus algorithm of Aspnes and Herlihy: a case study. Distrib. Comp. 13, 155–186 (2000)CrossRefGoogle Scholar
  34. 34.
    Rabin, M.O.: Probabilistic automata. Information and Control 6, 230–245 (1963)CrossRefGoogle Scholar
  35. 35.
    Segala, R.: Modeling and Verification of Randomized Distributed Real-Time Systems. PhD thesis. MIT Press (1995)Google Scholar
  36. 36.
    Segala, R., Lynch, N.A.: Probabilistic simulations for probabilistic processes. Nordic Journal of Computing 2(2), 250–273 (1995)MathSciNetMATHGoogle Scholar
  37. 37.
    Segala, R., Turrini, A.: Comparative analysis of bisimulation relations on alternating and non-alternating probabilistic models. In: Proceedings of QEST (2005)Google Scholar
  38. 38.
    Tix, R., Keimel, K., Plotkin, G.: Semantic domains for combining probability and non-determinism. ENTCS 129, 1–104 (2005)MathSciNetMATHGoogle Scholar
  39. 39.
    Vardi, M.Y.: Automatic verification of probabilistic concurrent finite-state programs. In: Proceedings of FoCS, pp. 327–338 (1985)Google Scholar
  40. 40.
    Wu, S.H., Smolka, S., Stark, E.W.: Composition and behaviors of probabilistic I/O automata. Theoretical Computer Science 176(1-2), 1–38 (1999)CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Roberto Segala
    • 1
  1. 1.Dipartimento di InformaticaUniversità di VeronaItaly

Personalised recommendations