Advertisement

Causality and Replication in Concurrent Processes

  • Pierpaolo Degano
  • Fabio Gadducci
  • Corrado Priami
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2890)

Abstract

The replication operator was introduced by Milner for obtaining a simplified description of recursive processes. The standard interleaving semantics denotes the replication of a process P, written ! P, a shorthand for its unbound parallel composition, operationally equivalent to the process P| P| ... , with P repeated as many times as needed.

Albeit the replication mechanism has become increasingly popular, investigations on its causal semantics has been scarce. In our work we consider the interleaving semantics for the operator proposed by Sangiorgi and Walker, and we show how to refine it in order to capture causality.

Furthermore, we prove that a basic property usually associated to these semantics, the so-called concurrency diamond, does hold in our framework, and we sketch a correspondence between our proposal and the standard causal semantics for recursive process studied in the literature, for processes defined through constant invocations.

Keywords

Causal semantics process calculi replication operator 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Boreale, M., Sangiorgi, D.: A fully abstract semantics for causality in the π- calculus. Acta Informatica 35, 353–400 (1998)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Boudol, G., Castellani, I.: A non-interleaving semantics for CCS based on proved transitions. Fundamenta Informaticae 11, 433–452 (1988)zbMATHMathSciNetGoogle Scholar
  3. 3.
    Busi, N., Gabbrielli, M., Zavattaro, G.: Replication vs. recursive definitions in channel based calculi. In: Baeten, J.C.M., Lenstra, J.K., Parrow, J., Woeginger, G.J. (eds.) ICALP 2003. LNCS, vol. 2719, pp. 133–144. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  4. 4.
    Darondeau, P., Degano, P.: Causal trees. In: Ronchi Della Rocca, S., Ausiello, G., Dezani-Ciancaglini, M. (eds.) ICALP 1989. LNCS, vol. 372, pp. 234–248. Springer, Heidelberg (1989)CrossRefGoogle Scholar
  5. 5.
    Degano, P., De Nicola, R., Montanari, U.: Partial ordering derivations for CCS. In: Budach, L. (ed.) FCT 1985. LNCS, vol. 199, pp. 520–533. Springer, Heidelberg (1985)CrossRefGoogle Scholar
  6. 6.
    Degano, P., Gadducci, F., Priami, C.: A concurrent semantics for CCS via rewriting logic. Theoret. Comput. Sci. 275, 259–282 (2002)zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Degano, P., Priami, C.: Proved trees. In: Kuich, W. (ed.) ICALP 1992. LNCS, vol. 623, pp. 629–640. Springer, Heidelberg (1992)Google Scholar
  8. 8.
    Degano, P., Priami, C.: Non interleaving semantics for mobile processes. Theoret. Comput. Sci. 216, 237–270 (1999)zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Degano, P., Priami, C.: Enhanced operational semantics: A tool for describing and analysing concurrent systems. ACM Computing Surveys 33, 135–176 (2001)CrossRefGoogle Scholar
  10. 10.
    Engelfriet, J.: A multiset semantics for the pi-calculus with replication. Theoret. Comput. Sci. 153, 65–94 (1996)zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Kiehn, A.: Comparing causality and locality based equivalences. Acta Informatica 31, 697–718 (1994)zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Milner, R.: Communication and Concurrency. Prentice-Hall, Englewood Cliffs (1989)zbMATHGoogle Scholar
  13. 13.
    Milner, R.: The polyadic π-calculus: A tutorial. In: Bauer, F.L., Brauer, W., Schwichtenberg, H. (eds.) Logic and Algebra of Specification. Nato ASI Series F, vol. 94, pp. 203–246. Springer, Heidelberg (1993)Google Scholar
  14. 14.
    Milner, R., Parrow, J., Walker, D.: A calculus of mobile processes. Part I and II. Information and Computation 100, 1–77 (1992)zbMATHMathSciNetGoogle Scholar
  15. 15.
    Sangiorgi, D.: Locality and interleaving semantics in calculi for mobile processes. Theoret. Comput. Sci. 155, 39–83 (1996)zbMATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Sangiorgi, D., Walker, D.: The π-calculus: A Theory of Mobile Processes. Cambridge University Press, Cambridge (2001)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Pierpaolo Degano
    • 1
  • Fabio Gadducci
    • 1
  • Corrado Priami
    • 2
  1. 1.Dipartimento di InformaticaUniversità di PisaPisaItalia
  2. 2.Dipartimento di Informatica e TelecomunicazioniUniversità di TrentoPovoItalia

Personalised recommendations