On the Expressiveness of ACP

extended abstract
  • Rob van Glabbeek
Part of the Workshops in Computing book series (WORKSHOPS COMP.)


De Simone showed that a wide class of languages, including CCS, SCCS, CSP and ACP, are expressible up to strong bisimulation equivalence in Meije. He also showed that every recursively enumerable process graph is representable by a Meije expression. Meije in turn is expressible in aprACP (ACP with action prefixing instead of sequential composition).

Vaandrager established that both results crucially depend on the use of unguarded recursion, and its noncomputable consequences. Effective versions of CCS, SCCS, Meije and ACP, not using unguarded recursion, are incapable of expressing all effective De Simone languages. And no effective language can denote all computable process graphs.

In this paper I recreate De Simone’s results in aprACP without using unguarded recursion. The price to be payed for this is the use of a partial recursive communication function and—for the second result— a single constant denoting a simple infinitely branching process. Due to the noncomputable communication function, the version of aprACP employed is still not effective.

However, I also define a wide class of De Simone languages that are expressible in an effective version of aprACP. This class includes the effective versions of CCS, SCCS, ACP, Meije and most other languages proposed in the literature, but not CSP. An even wider class, including CSP, turns out to be expressible in an effective version of aprACP to which an effective relational renaming operator has been added.


Recursive Function Communication Function Parallel Composition Label Transition System Process Expression 
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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  1. [1]
    D. Austry & G. Boudol (1984): Algèbre de processus et synchronisations. Theoretical Computer Science 30(1), pp. 91–131. See also [4].MathSciNetMATHCrossRefGoogle Scholar
  2. [2]
    J.C.M. Baeten, J.A. Bergstra & J.W. Klop (1987): On the consistency of Koomen’s fair abstraction rule. Theoretical Computer Science 51(1/2), pp. 129–176.MathSciNetMATHCrossRefGoogle Scholar
  3. [3]
    J.A. Bergstra & J.W. Klop (1984): The algebra of recursively defined processes and the algebra of regular processes. This volume.Google Scholar
  4. [4]
    G. Boudol (1985): Notes on algebraic calculi of processes. In K. Apt, editor: Logics and Models of Concurrent Systems, Springer-Verlag, pp. 261–303. NATO ASI Series F13.Google Scholar
  5. [5]
    S.D. Brookes, C.A.R. Hoare & A.W. Roscoe (1984): A theory of communicating sequential processes. JACM 31(3), pp. 560–599.MathSciNetMATHCrossRefGoogle Scholar
  6. [6.
    J.F. Groote & F.W. Vaandrager (1992): Structured operational semantics and bisimulation as a congruence. Information and Computation 100(2), pp. 202–260.MathSciNetMATHCrossRefGoogle Scholar
  7. [7]
    Yu. I. Manin (1977): A Course in Mathematical Logic, Graduate Texts in Mathematics 53. Springer-Verlag.MATHGoogle Scholar
  8. [8]
    R. Milner (1980): A Calculus of Communicating Systems, LNCS 92. Springer-Verlag.MATHGoogle Scholar
  9. [9]
    R. Milner (1983): Calculi for synchrony and asynchrony. Theoretical Computer Science 25, pp. 267–310.Google Scholar
  10. [10]
    G.D. Plotkin (1981): A structural approach to operational semantics. Report DAIMI FN-19, Computer Science Department, Aarhus University.Google Scholar
  11. [11]
    A. PONSE (1992): Computable processes and bisimulation equivalence. Report CS-R9207, CWI, Amsterdam.Google Scholar
  12. [12]
    R. de Simone (1984): On Meije and SCCS: infinite sum operators vs. non-guarded definitions. Theoretical Computer Science 30, pp. 133–138.Google Scholar
  13. [13]
    R. DE Simone (1985): Higher-level synchronising devices in Meije- SCCS. Theoretical Computer Science 37, pp. 245–267. For more details see [12] and: Calculabilité et Expressivité dans l’Algebra de Processus Parallèles Meije, These de 3e cycle, Univ. Paris 7, 1984.Google Scholar
  14. [14]
    F.W. Vaandrager (1993): Expressiveness results for process algebras. In J.W. de Bakker, W.P. de Roever & G. Rozenberg, editors: Proceedings REX Workshop on Semantics: Foundations and Applications, Beekbergen, The Netherlands, June 1992, LNCS 666, Springer-Verlag, pp. 609–638.Google Scholar

Copyright information

© British Computer Society 1995

Authors and Affiliations

  • Rob van Glabbeek
    • 1
  1. 1.Computer Science DepartmentStanford UniversityStanfordUSA

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