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On the Asynchronous Nature of the Asynchronous π-Calculus

  • Romain Beauxis
  • Catuscia Palamidessi
  • Frank D. Valencia
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5065)

Abstract

We address the question of what kind of asynchronous communication is exactly modeled by the asynchronous π-calculus (π a ). To this purpose we define a calculus \(\pi_\mathfrak{B}\) where channels are represented explicitly as special buffer processes. The base language for \(\pi_\mathfrak{B}\) is the (synchronous) π-calculus, except that ordinary processes communicate only via buffers. Then we compare this calculus with π a . It turns out that there is a strong correspondence between π a and \(\pi_\mathfrak{B}\) in the case that buffers are bags: we can indeed encode each π a process into a strongly asynchronous bisimilar \(\pi_\mathfrak{B}\) process, and each \(\pi_\mathfrak{B}\) process into a weakly asynchronous bisimilar π a process. In case the buffers are queues or stacks, on the contrary, the correspondence does not hold. We show indeed that it is not possible to translate a stack or a queue into a weakly asynchronous bisimilar π a process. Actually, for stacks we show an even stronger result, namely that they cannot be encoded into weakly (asynchronous) bisimilar processes in a π-calculus without mixed choice.

Keywords

Turing Machine Input Action Base Language Asynchronous Communication Synchronous Communication 
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.

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References

  1. 1.
    Amadio, R.M., Castellani, I., Sangiorgi, D.: On bisimulations for the asynchronous π-calculus. Theoretical Computer Science 195(2), 291–324 (1998); An extended abstract appeared in Sassone, V., Montanari, U. (eds.): CONCUR 1996. LNCS, vol. 1119, pp. 147–162. Springer, Heidelberg (1996)Google Scholar
  2. 2.
    Bergstra, J., Klop, J.: Process algebra for synchronous communication. Information and Control 60(1,3), 109–137 (1984)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Bergstra, J.A., Klop, J.W., Tucker, J.V.: Process algebra with asynchronous communication mechanisms. In: Brookes, S.D., Winskel, G., Roscoe, A.W. (eds.) Seminar on Concurrency. LNCS, vol. 197, pp. 76–95. Springer, Heidelberg (1985)Google Scholar
  4. 4.
    Boreale, M., Nicola, R.D., Pugliese, R.: Trace and testing equivalence on asynchronous processes. Information and Computation 172(2), 139–164 (2002)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Boudol, G.: Asynchrony and the π-calculus (note). Rapport de Recherche 1702, INRIA, Sophia-Antipolis (1992)Google Scholar
  6. 6.
    Brookes, S., Hoare, C., Roscoe, A.: A theory of communicating sequential processes. J. ACM 31(3), 560–599 (1984)zbMATHMathSciNetGoogle Scholar
  7. 7.
    Busi, N., Gorrieri, R., Zavattaro, G.: Comparing three semantics for linda-like languages. Theoretical Computer Science 240(1), 49–90 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Cardelli, L., Gordon, A.D.: Mobile ambients. Theoretical Computer Science (TCS) 240(1), 177–213 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    de Boer, F.S., Klop, J.W., Palamidessi, C.: Asynchronous communication in process algebra. In: Scedrov, A. (ed.) Proceedings of the 7th Annual IEEE Symposium on Logic in Computer Science, Santa Cruz, CA, June 1992, pp. 137–147. IEEE Computer Society Press, Los Alamitos (1992)Google Scholar
  10. 10.
    Gorla, D.: On the relative expressive power of asynchronous communication primitives. In: Aceto, L., Ingólfsdóttir, A. (eds.) FOSSACS 2006. LNCS, vol. 3921, pp. 47–62. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  11. 11.
    Gorla, D.: On the criteria for a ‘good’ encoding: a new approach to encodability and separation results. Technical report, Università di Roma “La Sapienza” (2007)Google Scholar
  12. 12.
    He, J., Josephs, M.B., Hoare, C.A.R.: A theory of synchrony and asynchrony. In: Broy, M., Jones, C.B. (eds.) Programming Concepts and Methods, Proc. of the IFIP WG 2.2/2.3, Working Conf. on Programming Concepts and Methods, pp. 459–478. North-Holland, Amsterdam (1990)Google Scholar
  13. 13.
    Hoare, C.A.R.: Communicating Sequential Processes. Prentice-Hall, Englewood Cliffs (1985)zbMATHGoogle Scholar
  14. 14.
    Honda, K., Tokoro, M.: An object calculus for asynchronous communication. In: America, P. (ed.) ECOOP 1991. LNCS, vol. 512, pp. 133–147. Springer, Heidelberg (1991)CrossRefGoogle Scholar
  15. 15.
    Lynch, N.: Distributed Algorithms. Morgan Kaufmann, San Francisco (1996)zbMATHGoogle Scholar
  16. 16.
    Milner, R.: A Calculus of Communication Systems. LNCS, vol. 92. Springer, Heidelberg (1980)Google Scholar
  17. 17.
    Milner, R.: Communication and Concurrency. International Series in Computer Science. Prentice-Hall, Englewood Cliffs (1989)zbMATHGoogle Scholar
  18. 18.
    Milner, R., Parrow, J., Walker, D.: A calculus of mobile processes, I and II. Information and Computation 100(1), 1–40 & 41–77 (1992); A preliminary version appeared as Technical Reports ECF-LFCS-89-85 and -86, University of Edinburgh (1989)Google Scholar
  19. 19.
    Nestmann, U.: What is a ‘good’ encoding of guarded choice? Journal of Information and Computation 156, 287–319 (2000); An extended abstract appeared in the Proceedings of EXPRESS 1997, vol. 7, ENTCS (1997)Google Scholar
  20. 20.
    Palamidessi, C.: Comparing the expressive power of the synchronous and the asynchronous pi-calculus. Mathematical Structures in Computer Science 13(5), 685–719 (2003); A short version of this paper appeared in POPL 1997CrossRefMathSciNetGoogle Scholar
  21. 21.
    Pierce, B.C., Turner, D.N.: Pict: A programming language based on the pi-calculus. In: Plotkin, G., Stirling, C., Tofte, M. (eds.) Proof, Language and Interaction: Essays in Honour of Robin Milner, pp. 455–494. MIT Press, Cambridge (1998)Google Scholar
  22. 22.
    Sangiorgi, D., Walker, D.: The π-calculus: a Theory of Mobile Processes. Cambridge University Press, Cambridge (2001)Google Scholar
  23. 23.
    Saraswat, V.A., Rinard, M., Panangaden, P.: Semantic foundations of concurrent constraint programming. In: Conference Record of the Eighteenth Annual ACM Symposium on Principles of Programming Languages, pp. 333–352. ACM Press, New York (1991)Google Scholar
  24. 24.
    Selinger, P.: First-order axioms for asynchrony. In: Mazurkiewicz, A., Winkowski, J. (eds.) CONCUR 1997. LNCS, vol. 1243, pp. 376–390. Springer, Heidelberg (1997)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Romain Beauxis
    • 1
  • Catuscia Palamidessi
    • 1
  • Frank D. Valencia
    • 1
  1. 1.INRIA Saclay and LIX, École Polytechnique 

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