On the Expressiveness of Infinite Behavior and Name Scoping in Process Calculi

  • Pablo Giambiagi
  • Gerardo Schneider
  • Frank D. Valencia
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2987)


In the literature there are several CCS-like process calculi differing in the constructs for the specification of infinite behavior and in the scoping rules for channel names. In this paper we study various representatives of these calculi based upon both their relative expressiveness and the decidability of divergence. We regard any two calculi as being equally expressive iff for every process in each calculus, there exists a weakly bisimilar process in the other.

By providing weak bisimilarity preserving mappings among the various variants, we show that in the context of relabeling-free and finite summation calculi: (1) CCS with parameterless (or constant) definitions is equally expressive to the variant with parametric definitions. (2) The CCS variant with replication is equally expressive to that with recursive expressions and static scoping. We also state that the divergence problem is undecidable for the calculi in (1) but decidable for those in (2). We obtain this from (un)decidability results by Busi, Gabbrielli and Zavattaro, and by showing the relevant mappings to be computable and to preserve divergence and its negation. From (1) and the well-known fact that parametric definitions can replace injective relabelings, we show that injective relabelings are redundant (i.e., derived) in CCS (which has constant definitions only).


  1. 1.
    Boreale, M., De Nicola, R., Pugliese, R.: Trace and testing equivalence on asynchronous processes. Information and Computation 172(2), 139–164 (2002)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Busi, N., Gabbrielli, M., Zavattaro, G.: The expressive power of replication in CCS. Draft (2003)Google 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.
    Cleaveland, R., Parrow, J., Steffen, B.: The ConcurrencyWorkbench:Asemantics based tool for the verification of concurrent systems. ACM Transactions on Programming Languages and Systems 15(1), 36–72 (1993)CrossRefGoogle Scholar
  5. 5.
    Engberg, U., Nielsen, M.: A calculus of communicating systems with label-passing. Technical report, University of Aarhus (1986)Google Scholar
  6. 6.
    Giambiagi, P., Schneider, G., Valencia, F.D.: On the expressiveness of CCS-like calculi. Technical report, Uppsala University (2004), Postscript available from
  7. 7.
    Maffeis, S., Phillips, I.: On the computational strength of pure ambient calculi. In: EXPRESS 2003 (2003)Google Scholar
  8. 8.
    Milner, R.: Calculi for synchrony and asynchrony. Technical Report CSR-104-82, University of Edinburgh (1982)Google Scholar
  9. 9.
    Milner, R.: Communication and Concurrency. Prentice Hall, Englewood Cliffs (1989)zbMATHGoogle Scholar
  10. 10.
    Milner, R.: Communicating and Mobile Systems: The π-calculus. Cambridge University Press, Cambridge (1999)Google Scholar
  11. 11.
    Palamidessi, C.: Comparing the expressive power of the synchronous and the asynchronous π-calculus. In: POPL 1997, pp. 256–265. ACM Press, New York (1997)CrossRefGoogle Scholar
  12. 12.
    Parrow, J.: An introduction to the π-calculus. In: Handbook of Process Algebra, pp. 479–543. Elsevier, Amsterdam (2001)CrossRefGoogle Scholar
  13. 13.
    Sangiorgi, D., Walker, D.: The π−calculus: A Theory of Mobile Processes. Cambridge University Press, Cambridge (2001)Google Scholar
  14. 14.
    Thomsen, B.: A calculus of higher order communicating systems. In: POPL 1989, pp. 143–154. ACM, New York (1989)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Pablo Giambiagi
    • 1
  • Gerardo Schneider
    • 2
    • 3
  • Frank D. Valencia
    • 3
  1. 1.KTH Royal Institute of Technology, IMITKistaSweden
  2. 2.IRISA/CNRSRennesFrance
  3. 3.Dept. of Computer SystemsUppsala UniversityUppsalaSweden

Personalised recommendations