Skip to main content
SpringerLink
Log in

Complete Proof Systems for Amortised Probabilistic Bisimulations

  • Regular Paper
  • Published:
Journal of Computer Science and Technology Aims and scope Submit manuscript

Abstract

The notion of amortisation has been integrated in quantitative bisimulations to make long-term behavioral comparisons between nondeterministic systems. In this paper, we present sound and complete proof systems for amortised strong probabilistic bisimulation and its observational congruence on a process algebra with probability and nondeterminism, and prove their soundness and completeness. Our results make it possible to reason about long-term (observable) probabilistic behaviors by syntactic manipulations.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Milner R. Communication and Concurrency. Upper Saddle River, NJ, USA: Prentice Hall, 1989.

  2. Lin H. PAM: A process algebra manipulator. Formal Methods in System Design, 1995, 7(3): 243–259.

    Article  Google Scholar 

  3. Larsen K G, Skou A. Bisimulation through probabilistic testing. Information and Computation, 1991, 94(1): 1–28.

    Article  MathSciNet  MATH  Google Scholar 

  4. Kiehn A, Arun-Kumar S. Amortised bisimulations. In Proc. the 25th FORTE, Oct. 2005, pp.320-334.

  5. de Frutos-Escrig D, Rosa-Velardo F, Gregorio-Rodr´ıguez C. New bisimulation semantics for distributed systems. In Proc. the 27th FORTE, June 2007, pp.143-159.

  6. Xu L, Chatzikokolakis K, Lin H. Metrics for differential privacy in concurrent systems. In Proc. the 34th FORTE, June 2014, pp.199-215.

  7. Dwork C. Differential privacy. In Proc. the 33rd ICALP, July 2006, pp.1-12.

  8. Chatzikokolakis K, Andr´es M E, Bordenabe N E, Palamidessi C. Broadening the scope of differential privacy using metrics. In Proc. the 13th Int. Symp. Privacy Enhancing Technologies, July 2013, pp.82-102.

  9. Bandini E, Segala R. Axiomatizations for probabilistic bisimulation. In Proc. the 28th ICALP, July 2001, pp.370-381.

  10. Hennessy M. A calculus for costed computations. Logical Methods in Computer Science, 2011, 7(1): 7:1–7:35.

  11. Deng Y, Hennessy M. Compositional reasoning for weighted Markov decision processes. Science of Computer Programming, 2013, 78(12): 2537–2579.

    Article  Google Scholar 

  12. Desharnais J, Laviolette F, Tracol M. Approximate analysis of probabilistic processes: Logic, simulation and games. In Proc. the 5th International Conference on Quantitative Evaluation of Systems, Sept. 2008, pp.264-273.

  13. Tracol M, Desharnais J, Zhioua A. Computing distances between probabilistic automata. In Proc. the 9th QAPL, April 2011, pp.148-162.

  14. Deng Y, Palamidessi C, Pang J. Compositional reasoning for probabilistic finite-state behaviors. In Lecture Notes in Computer Science 3838, Middeldorp A, van Oostrom V, van Raamsdonk F, de Vrijer (eds.), Spring-Verlag, 2005, pp.309–337.

  15. Deng Y, Palamidessi C. Axiomatizations for probabilistic finite-state behaviors. In Proc. the 8th FoSSaCS, April 2005, pp.110–124.

  16. Segala R. Modeling and verification of randomized distributed real-time systems [Ph.D. Thesis]. Massachusetts Institute of Technology, 1995.

  17. Segala R, Lynch N. Probabilistic simulations for probabilistic processes. Nordic Journal of Computing, 1995, 2(2): 250–273.

    MathSciNet  MATH  Google Scholar 

  18. Hennessy M, Lin H. Proof systems for message-passing process algebras. In Proc. the 4th CONCUR, August 1993, pp.202-216.

  19. Desharnais J, Jagadeesan R, Gupta V, Panangaden P. The metric analogue of weak bisimulation for probabilistic processes. In Proc. the 17th LICS, July 2002, pp.413-422.

  20. D’Argenio P R, Gebler D, Lee M D. Axiomatizing bisimulation equivalences and metrics from probabilistic SOS rules. In Proc. the 17th FoSSaCS, April 2014, pp.289-303.

  21. Chatzikokolakis K, Gebler D, Palamidessi C, Xu L. Generalized bisimulation metrics. In Proc. the 25th CONCUR, Sept. 2014, pp.32-46.

Download references

Author information

Authors and Affiliations

  1. State Key Laboratory of Computer Science, Institute of Software, Chinese Academy of Sciences, Beijing, 100190, China

    Li-Li Xu & Hui-Min Lin

  2. University of Chinese Academy of Sciences, Beijing, 100049, China

    Li-Li Xu

  3. École Polytechnique, Palaiseau, 91120, France

    Li-Li Xu

Authors
  1. Li-Li Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hui-Min Lin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Li-Li Xu.

Additional information

This work was supported by the National Natural Science Foundation of China under Grant No. 60833001.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Xu, LL., Lin, HM. Complete Proof Systems for Amortised Probabilistic Bisimulations. J. Comput. Sci. Technol. 31, 300–316 (2016). https://doi.org/10.1007/s11390-016-1628-4

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11390-016-1628-4

Keywords

Search

Navigation