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An Event Structure Model for Probabilistic Concurrent Kleene Algebra

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Logic for Programming, Artificial Intelligence, and Reasoning (LPAR 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8312))

Abstract

We give a new true-concurrent model for probabilistic concurrent Kleene algebra. The model is based on probabilistic event structures, which combines ideas from Katoen’s work on probabilistic concurrency and Varacca’s probabilistic prime event structures. The event structures are compared with a true-concurrent version of Segala’s probabilistic simulation. Finally, the algebraic properties of the model are summarised to the extent that they can be used to derive techniques such as probabilistic rely/guarantee inference rules.

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References

  1. Rabin, M.O.: Probabilistic Algorithms. Technical Report RC 6164 (#26545), IBM Research Division, San Jose, Yorktown, Zurich (August 1976)

    Google Scholar 

  2. Hoare, T., Möller, B., Struth, G., Wehrman, I.: Concurrent Kleene algebra and its foundations. J. Log. Algebr. Program. 80(6), 266–296 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  3. Hayes, I.J., Jones, C.B., Colvin, R.J.: Refining rely-guarantee thinking. Technical report, Newcastle University, United Kingdom (2012)

    Google Scholar 

  4. McIver, A.K., Rabehaja, T.M., Struth, G.: Probabilistic concurrent Kleene algebra. In: Bortolussi, L., Wiklicky, H. (eds.) QAPL. EPTCS, vol. 117, pp. 97–115 (2013)

    Google Scholar 

  5. Katoen, J.P.: Quantitative and qualitative extensions of event structures. PhD thesis, University of Twente (1996)

    Google Scholar 

  6. Langerak, R.: Bundle event structures: a non-interleaving semantics for LOTOS. Memoranda informatica. University of Twente (1992)

    Google Scholar 

  7. Rensink, A., Gorrieri, R.: Action refinement for vertical implementation. In: Wolisz, A., Schieferdecker, I., Rennoch, A. (eds.) FBT. GMD-Studien., vol. 315, pp. 69–78. GMD-Forschungszentrum Informationstechnik GmbH (1997)

    Google Scholar 

  8. Winskel, G.: Event structures. In: Brauer, W., Reisig, W., Rozenberg, G. (eds.) APN 1985. LNCS, vol. 222, pp. 325–392. Springer, Heidelberg (1986)

    Chapter  Google Scholar 

  9. van Glabbeek, R.J., Vaandrager, F.W.: Bundle event structures and CCSP. In: Amadio, R.M., Lugiez, D. (eds.) CONCUR 2003. LNCS, vol. 2761, pp. 57–71. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  10. van Glabbeek, R.J., Plotkin, G.D.: Configuration structures, event structures and petri nets. Theor. Comput. Sci. 410(41), 4111–4159 (2009)

    Article  MATH  Google Scholar 

  11. Varacca, D.: Probability, nondeterminism and concurrency: two denotational models for probabilistic computation. PhD thesis, University of Aarhus (2003)

    Google Scholar 

  12. Segala, R.: A compositional trace-based semantics for probabilistic automata. In: Lee, I., Smolka, S.A. (eds.) CONCUR 1995. LNCS, vol. 962, pp. 234–248. Springer, Heidelberg (1995)

    Chapter  Google Scholar 

  13. Cherief, F.: Back and forth bisimulations on prime event structures. In: Etiemble, D., Syre, J.-C. (eds.) PARLE 1992. LNCS, vol. 605, pp. 843–858. Springer, Heidelberg (1992)

    Google Scholar 

  14. Majster-Cederbaum, M., Roggenbach, M.: Transition systems from event structures revisited. Info. Proc. Letters 67(3), 119–124 (1998)

    Article  MathSciNet  Google Scholar 

  15. McIver, A.K., Rabehaja, T.M., Struth, G.: An event structure model for probabilistic concurrent kleene algebra. CoRR abs/1310.2320 (2013)

    Google Scholar 

  16. Gischer, J.L.: The equational theory of pomsets. Theor. Comput. Sci. 61(23), 199–224 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  17. Jones, C.B.: Development Methods for Computer Programs including a Notion of Interference. PhD thesis, Oxford University (June 1981)

    Google Scholar 

  18. Dingel, J.: A refinement calculus for shared-variable parallel and distributed programming. Formal Asp. Comput. 14(2), 123–197 (2002)

    Article  MATH  Google Scholar 

  19. Fokkink, W., Zantema, H.: Basic process algebra with iteration: Completeness of its equational axioms. Comput. J. 37(4), 259–268 (1994)

    Article  Google Scholar 

  20. Deng, Y., van Glabbeek, R.J., Hennessy, M., Morgan, C., Zhang, C.: Remarks on testing probabilistic processes. ENTCS 172, 359–397 (2007)

    Google Scholar 

  21. McIver, A.K., Weber, T.: Towards automated proof support for probabilistic distributed systems. In: Sutcliffe, G., Voronkov, A. (eds.) LPAR 2005. LNCS (LNAI), vol. 3835, pp. 534–548. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  22. Parma, A., Segala, R.: Axiomatization of trace semantics for stochastic nondeterministic processes. In: Franceschinis, G., Haverkort, B.R., Katoen, J.P., Woodside, M. (eds.) QEST, pp. 294–303. IEEE Computer Society (2004)

    Google Scholar 

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McIver, A., Rabehaja, T., Struth, G. (2013). An Event Structure Model for Probabilistic Concurrent Kleene Algebra. In: McMillan, K., Middeldorp, A., Voronkov, A. (eds) Logic for Programming, Artificial Intelligence, and Reasoning. LPAR 2013. Lecture Notes in Computer Science, vol 8312. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-45221-5_43

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  • DOI: https://doi.org/10.1007/978-3-642-45221-5_43

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-45220-8

  • Online ISBN: 978-3-642-45221-5

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