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Probabilistic Operational Correspondence

Authors Anna Schmitt , Kirstin Peters

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Author Details

Anna Schmitt
  • TU Darmstadt, Germany
Kirstin Peters
  • Augsburg University, Germany

Acknowledgements

We thank the anonymous reviewers of a preliminary version of this paper for their comments and hints.

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Anna Schmitt and Kirstin Peters. Probabilistic Operational Correspondence. In 34th International Conference on Concurrency Theory (CONCUR 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 279, pp. 15:1-15:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
https://doi.org/10.4230/LIPIcs.CONCUR.2023.15

Abstract

Encodings are the main way to compare process calculi. By applying quality criteria to encodings we analyse their quality and rule out trivial or meaningless encodings. Thereby, operational correspondence is one of the most common and most important quality criteria. It ensures that processes and their translations have the same abstract behaviour. We analyse probabilistic versions of operational correspondence to enable such a verification for probabilistic systems. Concretely, we present three versions of probabilistic operational correspondence: weak, middle, and strong. We show the relevance of the weaker version using an encoding from a sublanguage of probabilistic CCS into the probabilistic π-calculus. Moreover, we map this version of probabilistic operational correspondence onto a probabilistic behavioural relation that directly relates source and target terms. Then we can analyse the quality of the criterion by analysing the relation it induces between a source term and its translation. For the second version of probabilistic operational correspondence we proceed in the opposite direction. We start with a standard simulation relation for probabilistic systems and map it onto a probabilistic operational correspondence criterion.

Subject Classification

ACM Subject Classification
  • Theory of computation → Process calculi
Keywords
  • Probabilistic Process Calculi
  • Encodings
  • Operational Correspondence

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References

  1. C. Baier and H. Hermanns. Weak Bisimulation for Fully Probabilistic Processes. In Computer Aided Verification, pages 119-130. Springer, 1997. URL: https://doi.org/10.1007/3-540-63166-6_14.
  2. C. Baier, H. Hermanns, J.-P. Katoen, and V. Wolf. Bisimulation and Simulation Relationsfor Markov Chains. Electronic Notes in Theoretical Computer Science, 162:73-78, 2006. URL: https://doi.org/10.1016/j.entcs.2005.12.078.
  3. B. Bisping, U. Nestmann, and K. Peters. Coupled Similarity: the first 32 years. Acta Informatica, 57:439-463, 2019. URL: https://doi.org/10.1007/s00236-019-00356-4.
  4. G. Boudol. Asynchrony and the π-calculus (note). Note, INRIA, 1992. Google Scholar
  5. L. Cardelli and A.D. Gordon. Mobile Ambients. Theoretical Computer Science, 240(1):177-213, 2000. URL: https://doi.org/10.1016/S0304-3975(99)00231-5.
  6. Y. Deng. Bisimulations for Probabilistic and Quantum Processes. In Proc. of CONCUR, volume 118, pages 2:1-2:14, 2018. URL: https://doi.org/10.4230/LIPIcs.CONCUR.2018.2.
  7. Y. Deng and W. Du. Probabilistic Barbed Congruence. Electronic Notes in Theoretical Computer Science, 190(3):185-203, 2007. URL: https://doi.org/10.1016/j.entcs.2007.07.011.
  8. Y. Deng and Y. Feng. Open Bisimulation for Quantum Processes. In Proc. of TCS, volume 7604, pages 119-133. Springer, 2012. URL: https://doi.org/10.1007/978-3-642-33475-7_9.
  9. Y Feng, Y. Deng, and M. Ying. Symbolic Bisimulation for Quantum Processes. CoRR, 2012. URL: https://doi.org/10.48550/arXiv.1202.3484.
  10. Y. Feng, R. Duan, and M. Ying. Bisimulation for Quantum Processes. ACM Trans. Program. Lang. Syst., 34(4):17:1-17:43, 2012. URL: https://doi.org/10.1145/2400676.2400680.
  11. C. Fournet and G. Gonthier. The Reflexive CHAM and the Join-Calculus. In Proc. of POPL, pages 372-385. ACM, 1996. URL: https://doi.org/10.1145/237721.237805.
  12. Y. Fu. Theory of Interaction. Theoretical Computer Science, 611:1-49, 2016. URL: https://doi.org/10.1016/j.tcs.2015.07.043.
  13. Y. Fu and H. Lu. On the expressiveness of interaction. Theoretical Computer Science, 411(11-13):1387-1451, 2010. URL: https://doi.org/10.1016/j.tcs.2009.11.011.
  14. D. Gorla. Towards a Unified Approach to Encodability and Separation Results for Process Calculi. In Proc. of CONCUR, volume 5201, pages 492-507. Springer, 2008. URL: https://doi.org/10.1007/978-3-540-85361-9_38.
  15. D. Gorla. Towards a Unified Approach to Encodability and Separation Results for Process Calculi. Information and Computation, 208(9):1031-1053, 2010. URL: https://doi.org/10.1016/j.ic.2010.05.002.
  16. D. Gorla and U. Nestmann. Full abstraction for expressiveness: history, myths and facts. Mathematical Structures in Computer Science, pages 1-16, 2014. URL: https://doi.org/10.1017/S0960129514000279.
  17. M. Hatzel, C. Wagner, K. Peters, and U. Nestmann. Encoding CSP into CCS. In Proc. of EXPRESS/SOS, volume 7, pages 61-75, 2015. URL: https://doi.org/10.4204/EPTCS.190.5.
  18. C. Jou and S.A. Smolka. Equivalences, Congruences, and Complete Axiomatizations for Probabilistic Processes. In Proc. of CONCUR, pages 367-383, 1990. URL: https://doi.org/10.1007/BFb0039071.
  19. M. Kwiatkowska, G. Norman, D. Parker, and M.G. Vigliotti. Probabilistic Mobile Ambients. Theoretical Computer Science, 410:1272-1303, 2009. URL: https://doi.org/10.1016/j.tcs.2008.12.058.
  20. K.G. Larsen and A. Skou. Bisimulation through Probabilistic Testing. Information and Computation, 94(1):1-28, 1991. URL: https://doi.org/10.1016/0890-5401(91)90030-6.
  21. R. Milner. Communication and Concurrency. Prentice-Hall, Inc., 1989. Google Scholar
  22. R. Milner. Communicating and mobile systems - the Pi-calculus. Cambridge University Press, 1999. Google Scholar
  23. R. Milner and D. Sangiorgi. Barbed Bisimulation. In Automata, Languages and Programming, pages 685-695, 1992. Google Scholar
  24. C. Palamidessi. Comparing the Expressive Power of the Synchronous and the Asynchronous π-calculi. Mathematical Structures in Computer Science, 13(5):685-719, 2003. URL: https://doi.org/10.1017/S0960129503004043.
  25. J. Parrow. Expressiveness of Process Algebras. Electronic Notes in Theoretical Computer Science, 209:173-186, 2008. URL: https://doi.org/10.1016/j.entcs.2008.04.011.
  26. J. Parrow. General conditions for full abstraction. Mathematical Structures in Computer Science, 26(4):655-657, 2014. URL: https://doi.org/10.1017/S0960129514000280.
  27. J. Parrow and P. Sjödin. Multiway Synchronization Verified with Coupled Simulation. In Proc. of CONCUR, volume 630 of LNCS, pages 518-533, 1992. URL: https://doi.org/10.1007/BFb0084813.
  28. K. Peters. Translational Expressiveness. PhD thesis, TU Berlin, 2012. URL: http://opus.kobv.de/tuberlin/volltexte/2012/3749/.
  29. K. Peters. Comparing Process Calculi Using Encodings. In Proc. of EXPRESS/SOS, EPTCS, pages 19-38, 2019. URL: https://doi.org/10.48550/arXiv.1908.08633.
  30. K. Peters and R. van Glabbeek. Analysing and Comparing Encodability Criteria. In Proc. of EXPRESS/SOS, volume 190 of EPTCS, pages 46-60, 2015. URL: https://doi.org/10.4204/EPTCS.190.4.
  31. G.D. Plotkin. A structural approach to operational semantics. Log. Algebraic Methods Program., 60-61:17-139, 2004. Google Scholar
  32. D. Sangiorgi. π-Calculus, internal mobility, and agent-passing calculi. Theoretical Computer Science, 167(1):235-274, 1996. URL: https://doi.org/10.1016/0304-3975(96)00075-8.
  33. Anna Schmitt and Kirstin Peters. Probabilistic Operational Correspondence (Technical Report). Technical report, TU Darmstadt and Augsburg University, 2023. URL: https://doi.org/10.48550/arXiv.2307.05218.
  34. R. Segala and N. Lynch. Probabilistic Simulations for Probabilistic Processes. In Proc. of CONCUR, pages 481-496, 1994. URL: https://doi.org/10.1007/978-3-540-48654-1_35.
  35. P. Sylvain and C. Palamidessi. Expressiveness of Probabilistic π-calculus. Electronic Notes in Theoretical Computer Science, 164:119-136, 2006. URL: https://doi.org/10.1016/j.entcs.2006.07.015.
  36. R. van Glabbeek. Musings on Encodings and Expressiveness. In Proc. of EXPRESS/SOS, volume 89, pages 81-98, 2012. URL: https://doi.org/10.4204/EPTCS.89.7.
  37. R. van Glabbeek. A Theory of Encodings and Expressiveness (Extended Abstract). In Proc. of FOSSACS, volume 10803, pages 183-202. Springer, 2018. URL: https://doi.org/10.1007/978-3-319-89366-2_10.
  38. D. Varacca and N. Yoshida. Probabilistic pi-Calculus and Event Structures. Electronic Notes in Theoretical Computer Science, 190(3):147-166, 2007. URL: https://doi.org/10.1016/j.entcs.2007.07.009.
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