A theory of testing for ACP

  • Luca Aceto
  • Anna Ingólfsdóttir
Selected Presentations
Part of the Lecture Notes in Computer Science book series (LNCS, volume 527)


This paper introduces a process algebra which incorporates the auxiliary operators of ACP, [BK85], and is tailored towards algebraic verifications in the theory of testing equivalence. The process algebra we consider is essentially a version of ACP with the empty process in which the nondeterministic choice operators familiar from TCSP, [BHR84], and TCCS, [DH87], are used in lieu of the internal action τ and the single choice operator favoured by CCS, [Mil89], and ACP. We present a behavioural semantics for the language based upon a natural notion of testing equivalence, [DH84], and show that, contrary to what happens in a setting with the internal action τ, the left-merge operator is compatible with it. A complete equational characterization of the behavioural semantics is given for finite processes, thus providing an algebraic theory supporting the use of the auxiliary operators of ACP in algebraic verifications for testing equivalence. Finally we give a fully-abstract denotational model for finite processes with respect to the testing preorder based on a variation on Hennessy's Acceptance Trees suitable for our language.


Normal Form Composition Operator Operational Semantic Axiom System Label Transition System 
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6 References

  1. [AB84]
    D. Austry and G. Boudol, Algebre de Processus et synchronisations, TCS 30(1), pp. 91–131Google Scholar
  2. [Ace90]
    L. Aceto, A theory of Testing for ACP, Report 3/90, Dept. of Computer Science, University of Sussex, May 1990Google Scholar
  3. [AH88]
    L. Aceto and M. Hennessy, Termination, Deadlock and Divergence, Report 6/88, Dept. of Computer Science, University of Sussex, 1988. To appear in the Journal of the ACM.Google Scholar
  4. [BG87]
    J. C. M. Baeten and R. J. van Glabbeek, Abstraction and Empty Process in Process Algebra, Report CS-R8721, CWI Amsterdam, 1987 (to appear in Fundamenta Informaticae)Google Scholar
  5. [BHR84]
    S. D. Brookes, C. A. R. Hoare and A. W. Roscoe, A Theory of Communicating Sequential Processes, JACM 31,3, pp. 560–599, 1984Google Scholar
  6. [BK85]
    J. A. Bergstra and J. W. Klop, Algebra of Communicating Processes with Abstraction, TCS 37, 1, pp. 77–121, 1985Google Scholar
  7. [BKO87]
    J. A. Bergstra, J. W. Klop and E.-R. Olderog, Failures Without Chaos: a New Process Semantics for Fair Abstraction, Formal Description of Programming Concepts-III (M. Wirsing ed.), North-Holland, 1987Google Scholar
  8. [BV89]
    J. C. M. Baeten and F. Vaandrager, An Algebra for Process Creation, Report CS-R8907, CWI, Amsterdam, 1989Google Scholar
  9. [CH89]
    I. Castellani and M. Hennessy, Distributed Bisimulations, JACM, October 1989Google Scholar
  10. [DeN85]
    R. de Nicola, Two Complete Sets of Axioms for a Theory of Communicating Sequential Processes, Information and Control 64(1–3), pp. 136–176, 1985Google Scholar
  11. [DH84]
    R. De Nicola and M. Hennessy, Testing Equivalences for Processes, TCS 34,1, pp. 83–134, 1987Google Scholar
  12. [DH87]
    R. de Nicola and M. Hennessy, CCS without r's, in Proceedings TAPSOFT 87, LNCS 249, pp. 138–152, Springer-Verlag, 1987Google Scholar
  13. [GIV88]
    R. van Glabbeek and F. Vaandrager, Modular Specifications in Process Algebra-with Curious Queues, Report CS-R8821, CIW, Amsterdam, 1988Google Scholar
  14. [Gue81]
    I. Guessarian, Algebraic Semantics, LNCS 99, Springer-Verlag, 1981Google Scholar
  15. [H88]
    M. Hennessy, Algebraic Theory of Processes, MIT Press, 1988Google Scholar
  16. [HI89]
    M. Hennessy and A. Ingólfsdóttir, A Theory of Communicating Processes with Value Passing, Report 3/89, University of Sussex, 1989Google Scholar
  17. [HM85]
    M. Hennessy and R. Milner, Algebraic Laws for Nondeterminism and Concurrency, JACM 32,1, pp. 137–161, 1985Google Scholar
  18. [Hoare85]
    C. A. R. Hoare, Communicating Sequential Processes, Prentice-Hall, 1985Google Scholar
  19. [Kel76]
    R. Keller, Formal Verification of Parallel Programs, C. ACM 19,7, pp. 561–572, 1976Google Scholar
  20. [Mil89]
    R. Milner, Communication and Concurrency, Prentice-Hall, 1989Google Scholar
  21. [Mol89]
    F. Moller, Axioms for Concurrency, Ph. D. Thesis, University of Edinburgh, 1989Google Scholar
  22. [Pa81]
    D. Park, Concurrency and Automata on Infinite Sequences, Lecture Notes in Computer Science vol. 104, Springer-Verlag, 1981Google Scholar
  23. [Pl81]
    G. Plotkin, A Structural Approach to Operational Semantics, Report DAIMI FN-19, Computer Science Dept., Aarhus University, 1981Google Scholar
  24. [Va90a]
    F. Vaandrager, Process Algebra Semantics of POOL, to appear in Applications of Process Algebra (J.C.M. Baeten ed.), pp. 173–236, 1990Google Scholar
  25. [Va90b]
    F. Vaandrager, Two Simple Protocols, to appear in Applications of Process Algebra (J.C.M. Baeten ed.), pp. 237–260, 1990Google Scholar
  26. [Vra86]
    J. L. M. Vrancken, The Algebra of Communicating Processes with Empty Process, Report FVI 86-01, Dept. of Computer Science, University of Amsterdam, 1986Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Luca Aceto
    • 1
  • Anna Ingólfsdóttir
    • 2
  1. 1.INRIA-Sophia AntipolisValbonne CedexFrance
  2. 2.Aalborg University CentreAalborgDenmark

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