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Axiomatization Without Prefix Combinator

Conference paper
Part of the Semantic Structures in Computation book series (SECO, volume 1)

Abstract

The chi calculus proposed several years ago enjoys some properties unknown from the experience with pi calculus, one of which is the ability to model concurrent computation without the use of prefix combinator. The atomic chi calculus studied in this paper is obtained from polyadic chi calculus by leaving out the prefix operator. This omission is impossible in the pi framework because it would render the input actions of pi useless. This paper focuses on complete systems of strong equivalence relations on finite atomic chi processes. The two equivalence relations investigated in this paper are strong bisimilarity and strong asynchronous bisimilarity. These bisimilarities are required to be closed under substitution on each bisimulation step. By exploring some properties enjoyed by the atomic chi calculus, it is shown that they coincide respectively with their ground counterparts. In the definitions of strong ground bisimilarity and strong asynchronous ground bisimilarity closure under substitution is not explicitly required. Based upon this fact complete systems are given for both relations. The axiomatic systems are novel in that they use none of the prefix, choice and match combinators.

Keywords

Process Algebra Bisimulation Axiomatization 

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References

  1. 1.
    S. Abramsky, Proofs as Processes, Theoretical Computer Science, 135, 5–9, 1994.CrossRefGoogle Scholar
  2. 2.
    R. Amadio, I. Castellani, D. Sangiorgi. On Bisimulation for the Asynchronous ir-Calculus. CONCUR’96, Lecture Notes in Computer Science 1119, Springer, 1996.Google Scholar
  3. 3.
    G. Boudol. Asynchrony and the 7r-calculus. Research Report 1702, INRIA, Sophia-Antipolis, 1992.Google Scholar
  4. 4.
    Y. Fu. The x-Calculus. Proceedings of the International Conference on Advances in Parallel and Distributed Computing, 74–81, March 19th-21th, Shanghai, IEEE Computer Society Press, 1997.Google Scholar
  5. 5.
    Y. Fu. A Proof Theoretical Approach to Communications. ICALP’97, 325–335, July 7th-11th, Bologna, Italy, Lecture Notes in Computer Science 1256, Springer, 1997.Google Scholar
  6. 6.
    Y. Fu. Symmetric 7-Calculus. Journal of Computer Science and Technology, 13: 202–208, 1998.CrossRefGoogle Scholar
  7. 7.
    Y. Fu. Reaction Graphs. Journal of Computer Science and Technology, 13: 510–530, 1998.CrossRefGoogle Scholar
  8. 8.
    Y. Fu. Bisimulation Lattice of Chi Processes. ASIAN’98, December 8–10, Manila, The Philippines, Lecture Notes in Computer Science 1538, Springer, 245–262, 1998.Google Scholar
  9. 9.
    Y. Fu. Variations on Mobile Processes. Theoretical Computer Science, Vol. 221, 327–368, 1999.CrossRefGoogle Scholar
  10. 10.
    Y. Fu. Open Bisimulations of Chi Processes. CONCUR’99, Eindhoven, The Netherlands, August 24–27, Lecture Notes in Computer Science 1664, 304–319, Springer, 1999.Google Scholar
  11. 11.
    Y. Fu, Z. Yang. Chi Calculus with Mismatch. CONCUR 2000, 2225 August, Pennsylvenia, USA, Lecture Notes in Computer Science 1877, 596–610, Springer, 2000.Google Scholar
  12. 12.
    Y. Fu, Z. Yang. The Ground Congruence for Chi Calculus. FST&TCS 2000, December, India, Lecture Notes in Computer Science, Springer, 2000.Google Scholar
  13. 13.
    J. Girard. Linear Logic, Theoretical Computer Science, 50, 1–102, 1987.CrossRefGoogle Scholar
  14. 14.
    M. Hennessy, R. Milner. Algebraic Laws for Nondeterminism and Concurrency. Journal of ACM, 67: 137–161, 1985.CrossRefGoogle Scholar
  15. 15.
    K. Honda, M. Tokoro. An Object Calculus for Asynchronous Communication. Proc. ECOOP ’91, Geneve, 1991.Google Scholar
  16. 16.
    C. Laneve, B. Victor. Solos in Concert. ICALP’99, July 11th-15th, Prague, Hungary, Lecture Notes in Computer Science, Springer, 1999.Google Scholar
  17. 17.
    R. Milner. Communication and Concurrency. Prentice Hall, 1989.Google Scholar
  18. 18.
    R. Milner, The Polyadic it-Calculus: a Tutorial, Proceedings of the 1991 Marktoberdorf Summer School on Logic and Algebra of Specification, NATO ASI, Series F, Springer, 1993.Google Scholar
  19. 19.
    R. Milner, J. Parrow, D. Walker. A Calculus of Mobile Processes. Information and Computation, 100: 1–40 (Part I), 41–77 (Part II), Academic Press.Google Scholar
  20. 20.
    M. Merro, D. Sangiorgi. On Asynchrony in Name-Passing Calculi. ICALP’98, Lecture Notes in Computer Science 1443, Springer, 1998.Google Scholar
  21. 21.
    J. Parrow, B. Victor. The Update Calculus. AMAST’97, Sydney, December 13–17, 1997.Google Scholar
  22. 22.
    J. Parrow, B. Victor. The Fusion Calculus: Expressive and Symmetry in Mobile Processes. LICS’98, 1998.Google Scholar
  23. 23.
    J. Parrow, B. Victor. The Tau-Laws of Fusion. CONCUR’98, Lecture Notes in Computer Science, 1998.Google Scholar
  24. 24.
    B. Victor, J. Parrow. Concurrent Constraints in the Fusion Calculus. ICALP ’98, Lecture Notes in Computer Science 1443, 455–469, Springer, 1998.Google Scholar

Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  1. 1.Department of Computer ScienceShanghai Jiaotong UniversityShanghaiChina

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