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Behavioural equivalences of a probabilistic pi-calculus

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Abstract

Although different kinds of probabilistic π-calculus have been introduced and found their place in quantitative verification and evaluation, their behavioural equivalences still lack a deep investigation. We propose a simple probabilistic extension of the π-calculus, π p , which is inspired by Herescu and Palamidessi’s probabilistic asynchronous π-calculus. An early semantics of our π p is presented. We generalise several classic behavioural equivalences to probabilistic versions, obtaining the probabilistic (strong) barbed equivalence and probabilistic bisimulation for π p . Then we prove that the coincidence between the barbed equivalence and bisimilarity in the π-calculus is preserved in the probabilistic setting.

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References

  1. Bergstra J A, Ponse A, Smolka S A, et al. Handbook of Process Algebra. Amsterdam-Lausanne-New York-Oxford-Shannon-Tokyo: Elsevier Science, 2001

    MATH  Google Scholar 

  2. Milner R. A Calculus of Communicating Systems. Lect Notes Comput Sci, Vol 92. New York: Springer-Verlag, 1980

    Book  MATH  Google Scholar 

  3. Milner R. Communication and Concurrency. Englewood Cliffs, New Jersey: Prentice-Hall, 1989

    MATH  Google Scholar 

  4. Bergstra J A, Klop J W. Algebra of communicating processes with abstraction. Theor Comput Sci, 1985, 37: 77–121

    Article  MathSciNet  MATH  Google Scholar 

  5. Hoare C A R. Communicating sequential processes. Commun ACM, 1978, 21: 666–677

    Article  MATH  Google Scholar 

  6. Hoare C A R. Communicating Sequential Processes. Englewood Cliffs, New Jersey: Prentice-Hall, 1985

    MATH  Google Scholar 

  7. Milner R, Parrow J, Walker D. A calculus of mobile processes, parts I and II. Inf Comput, 1992, 100: 1–77

    Article  MathSciNet  MATH  Google Scholar 

  8. Milner R. Communicating and Mobile Systems: the π-Calculus. Cambridge: Cambridge University Press, 1999

    Google Scholar 

  9. De Nicola R, Hennessy M C B. Testing equivalences for processes. Theor Comput Sci, 1984, 34: 83–133

    Article  MathSciNet  MATH  Google Scholar 

  10. Padget J, Bradford R. A π-calculus model of a spanish fish market: preliminary report. In: Noriega P, Sierra C, eds. Agent Mediated Electronic Commerce. Berlin/Heidelberg: Springer, 1999. 166–188

    Chapter  Google Scholar 

  11. Boudol G. Asynchrony and the π-calculus (note). Rapport de Recherche 1702, INRIA Sophia-Antipolis, 1992

  12. Honda K, Tokoro M. An object calculus for asynchronous communication. In: America P, ed. Proceedings of European Conference on Object-Oriented Programming, 1991. 133–147

  13. Abadi M, Gordon A D. A calculus for cryptographic protocols: the spi calculus. In: Proceedings of the 4th ACM Conference on Computer and Communications Security. New York: ACM, 1997. 36–47

    Chapter  Google Scholar 

  14. López N, Núñez M. An overview of probabilistic process algebras and their equivalences. In: Baier C, Haverkort B, Hermanns H, et al., eds. Validation of Stochastic Systems. Berlin/Heidelberg: Springer, 2004. 89–123

    Chapter  Google Scholar 

  15. Baeten J, Bergstra J, Smolka S. Axiomatizing probabilistic processes: ACP with generative probabilities. Inf Comput, 1995, 122: 234–255

    Article  MathSciNet  Google Scholar 

  16. Hansson H, Jonsson B. A calculus for communicating systems with time and probabilities. In: Proceedings of the 11th Real-Time Systems Symposium, Lake Buena Vista, 1990. 278–287

  17. Seidel K. Probabilistic communicating processes. Theor Comput Sci, 1995, 152: 219–249

    Article  MathSciNet  MATH  Google Scholar 

  18. Herescu O M, Palamidessi C. Probabilistic asynchronous π-calculus. In: Tiuryn J, ed. Proceedings of the 3rd International Conference on Foundations of Software Science and Computation Structures: Held as Part of the Joint European Conferences on Theory and Practice of Software, ETAPS 2000. 146–160

  19. Hermanns H, Herzog U, Katoen J-P. Process algebra for performance evaluation. Theor Comput Sci, 2002, 274: 43–87

    Article  MathSciNet  MATH  Google Scholar 

  20. Priami C. Stochastic π-calculus. Comput J, 1995, 38: 578–589

    Article  Google Scholar 

  21. Ying M. pi-calculus with noisy channels. Acta Inform, 2005, 41: 525–593

    Article  MathSciNet  MATH  Google Scholar 

  22. Cao Y. Reliability of mobile processes with noisy channels. IEEE Trans Comput, 2011, doi: 10.1109/TC.2011.147, in press

  23. Huang S, Cao Y, Wang H, et al. Value-passing CCS with noisy channels. Theor Comput Sci, 2012, 433: 43–59

    Article  MATH  Google Scholar 

  24. Cao Y. A hierarchy of behavioral equivalences in the π-calculus with noisy channels. Comput J, 2010, 53: 3–20

    Article  Google Scholar 

  25. Segala R, Lynch N. Probabilistic simulations for probabilistic processes. Nord J Comput, 1995, 2: 250–273

    MathSciNet  MATH  Google Scholar 

  26. Sokolova A, De Vink E P. Probabilistic automata: system types, parallel composition and comparison. In: Baier C, Haverkort B R, Hermanns H, et al., eds. Validation of Stochastic Systems. Berlin/Heidelberg: Springer, 2004. 1–44

    Chapter  Google Scholar 

  27. van Glabbeek R J, Smolka S A, Steffen B, et al. Reactive, generative, and stratified models of probabilistic processes. In: Mitchell J C, ed. Proceedings of the 5th Annual IEEE Symposium on Logic in Computer Science, 1990. 130–141

  28. Giacalone A, Jou C-C, Smolka S A. Algebraic reasoning for probabilistic concurrent systems. In: Broy M, Jones C B, eds. Proceedings of Working Conference on Programming Concepts and Methods IFIP TC2, 1990. 443–458

  29. Milner R. Calculi for synchrony and asynchrony. Theor Comput Sci, 1983, 25: 267–310

    Article  MathSciNet  MATH  Google Scholar 

  30. Bhargava M, Palamidessi C. Probabilistic anonymity. In: Abadi M, De Alfaro L, eds. Proceedings of the 16th International Conference on Concurrency Theory, 2005. 171–185

  31. Pradalier S, Palamidessi C. Expressiveness of probabilistic π-calculus. Electr Notes Theor Comput Sci, 2006, 164: 119–136

    Article  Google Scholar 

  32. Chatzikokolakis K, Palamidessi C. A framework for analyzing probabilistic protocols and its application to the partial secrets exchange. In: De Nicola R, Sangiorgi D, eds. Trustworthy Global Computing. Berlin/Heidelberg: Springer, 2005. 146–162

    Chapter  Google Scholar 

  33. Varacca D, Yoshida N. Probabilistic π-calculus and event structures. Electr Notes Theor Comput Sci, 2007, 190: 147–166

    Article  Google Scholar 

  34. Varacca D, Völzer H, Winskel G. Probabilistic event structures and domains. Theor Comput Sci, 2006, 358: 173–199

    Article  MATH  Google Scholar 

  35. Sangiorgi D, Walker D. The π-calculus: A Theory of Mobile Processes. Cambridge: Cambridge University Press, 2001

    Google Scholar 

  36. Larsen K G, Skou A. Bisimulation through probabilistic testing. Inf Comput, 1991, 94: 1–28

    Article  MathSciNet  MATH  Google Scholar 

  37. Wu P, Palamidessi C, Lin H. Symbolic bisimulations for probabilistic systems. In: the 4th International Conference on the Quantitative Evaluation of Systems, Edinburgh, 2007. 179–188

  38. Parrow J. An introduction to the π-calculus. In: Bergstra J, Ponse A, Smolka S A, eds. Handbook of Process Algebra. Amsterdam-Lausanne-New York-Oxford-Shannon-Tokyo: Elsevier Science, 2001. 479–543

    Chapter  Google Scholar 

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Authors and Affiliations

  1. Key Laboratory of High Confidence Software Technologies, Ministry of Education of China, Institute of Software, School of Electronics Engineering and Computer Science, Peking University, Beijing, 100871, China

    WeiEn Chen, YongZhi Cao & HanPin Wang

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  1. WeiEn Chen
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  2. YongZhi Cao
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  3. HanPin Wang
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Correspondence to YongZhi Cao.

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Chen, W., Cao, Y. & Wang, H. Behavioural equivalences of a probabilistic pi-calculus. Sci. China Inf. Sci. 55, 2031–2043 (2012). https://doi.org/10.1007/s11432-012-4660-1

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