Equivalences and refinement

  • Rob J. van Glabbeek
  • Ursula Goltz
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 469)

Abstract

We investigate equivalence notions for concurrent systems. We consider “linear time” approaches where the system behaviour is characterised as the set of possible runs as well as “branching time” approaches where the conflict structure of systems is taken into account. We show that the usual interleaving equivalences, and also the equivalences based on steps (multisets of concurrently executed actions) are not preserved by refinement of actions. We prove that “linear time” partial order semantics, where causality in runs is explicit, is invariant under refinement. Finally, we consider various bisimulation equivalences based on partial orders and show that the strongest one of them is preserved by refinement whereas the others are not.

References

  1. [ADF]
    L. Aceto, R. De Nicola, A. Fantechi: Testing Equivalences for Event Structures, Mathematical Models for the Semantics of Parallelism, LNCS 280, Springer-Verlag, 1987Google Scholar
  2. [AH]
    L. Aceto, M. Hennessy: Towards Action-Refinement in Process Algebras, Proc. LICS'89, IEEE Computer Society Press, Washington, pp 138–145, 1989Google Scholar
  3. [AB]
    D. Austry, G. Boudol: Algébre de processus et synchronisations, Theoretical Computer Science, Vol. 30, No. 1, pp 91–131, 1984Google Scholar
  4. [BT]
    J.A. Bergstra, J.V. Tucker: Top-down Design and the Algebra of Communicating Processes, Science of Computer Programming, Vol. 5, No. 2, pp 171–199, 1985Google Scholar
  5. [BDKP]
    E. Best, R. Devillers, A. Kiehn, L. Pomello: Fully Concurrent Bisimulation, Technical Report LIT 202, Université Libre de Bruxelles, Laboratoire d'Informatique Theorique, 1989Google Scholar
  6. [Boudol a]
    G. Boudol: Atomic Actions (Note), Bulletin of the EATCS 38, pp 136–144, 1989Google Scholar
  7. [Boudol b]
    G. Boudol: Computations of Distributed Systems, Part 1: Flow Event structures and Flow Nets, report INRIA Sophia Antipolis, to appearGoogle Scholar
  8. [BC a]
    G. Boudol, I. Castellani: On the Semantics of Concurrency: Partial Orders and Transition Systems, Proc. TAPSOFT 87, Vol. I, LNCS 249, Springer-Verlag, pp 123–137, 1987Google Scholar
  9. [BC b]
    G. Boudol, I. Castellani: Permutation of Transitions: An Event Structure Semantics for CCS and SCCS, Linear Time, Branching Time and Partial Order in Logics and Models for Concurrency, LNCS 354, Springer-Verlag, pp 411–427, 1989Google Scholar
  10. [BGV]
    W. Brauer, R. Gold, W. Vogler: Behaviour and Equivalence Preserving Refinements of Petri Nets, Report, Institut für Informatik, Technische Universität München, 1990Google Scholar
  11. [BHR]
    S.D. Brookes, C.A.R. Hoare, A.W. Roscoe: A Theory of Communicating Sequential Processes, Journal of the ACM, Vol. 31, No. 3, pp 560–599, 1984Google Scholar
  12. [CDP]
    L. Castellano, G. De Michelis, L. Pomello: Concurrency vs Interleaving: An Instructive Example, Bulletin of the EATCS 31, pp 12–15, 1987Google Scholar
  13. [DD a]
    P. Darondeau, P. Degano: Causal Trees, Proc. ICALP 89, LNCS 372, Springer-Verlag, pp 234–248, 1989Google Scholar
  14. [DD b]
    Ph. Darondeau, P. Degano: Event structures, Causal trees, and Refinements, to appear in Proc. MFCS 90, LNCS, Springer-Verlag, 1990Google Scholar
  15. [DDM a]
    P. Degano, R. De Nicola, U. Montanari: Observational Equivalences for Concurrency Models, Formal Description of Programming Concepts — III, Proc. of the third IFIP WG 2.2 working conference, Elsevier Science Publishers B.V. (North Holland), pp 105–129, 1987Google Scholar
  16. [DDM b]
    P. Degano, R. De Nicola, U. Montanari: A Distributed Operational Semantics for CCS Based on Condition/Event Systems, Acta Informatica, Vol. 26, No. 1/2, pp 59–91, 1988Google Scholar
  17. [DDM c]
    P. Degano, R. De Nicola, U. Montanari: Partial Ordering Descriptions of Nondeterministic Concurrent Processes, Linear Time, Branching Time and Partial Order in Logics and Models for Concurrency, LNCS 354, Springer-Verlag, pp 438–466, 1989Google Scholar
  18. [DH]
    R. De Nicola, M. Hennessy: Testing Equivalences for Processes, Theoretical Computer Science, Vol. 34, pp 83–133, 1984Google Scholar
  19. [Devillers]
    R. Devillers: Maximality Preserving Bisimulation, Technical Report LIT 214, Université Libre de Bruxelles, Laboratoire d' Informatique Theorique, 1990Google Scholar
  20. [van Glabbeek a]
    R.J. van Glabbeek: The Refinement Theorem for ST-Bisimulation Semantics, Report CS-R9002, Centrum voor Wiskunde en Informatica, Amsterdam 1990; to appear in: Proceedings IFIP Working Conference on Programming Concepts and Methods, Israel at sea Gallilee 1990Google Scholar
  21. [van Glabbeek b]
    R.J. van Glabbeek: Comparative Concurrency Semantics and Refinement of Actions, Ph. D. Thesis, Free University, Amsterdam 1990Google Scholar
  22. [GG a]
    R.J. van Glabbeek, U. Goltz: Equivalence Notions for Concurrent Systems and Refinement of Actions, Arbeitspapiere der GMD 366, February 1989, Extended Abstract in Proc. MFCS 89, LNCS 379, Springer-Verlag, pp 237–248, 1989Google Scholar
  23. [GG b]
    R.J. van Glabbeek, U. Goltz: Refinement of Actions in Causality Based Models, Stepwise Refinement of Distributed Systems: Models, Formalism, Correctness, LNCS 430, Springer-Verlag, pp 267–300, 1990Google Scholar
  24. [GV]
    R.J. van Glabbeek, F.W. Vaandrager: Petri Net Models for Algebraic Theories of Concurrency, Proc. PARLE, Vol. II, LNCS 259, Springer-Verlag, pp 224–242, 1987Google Scholar
  25. [GW]
    R.J. van Glabbeek, W.P. Weijland: Refinement in Branching Time Semantics, Report CS-R8922, Centrum voor Wiskunde en Informatica, Amsterdam 1989; in: J.W. de Bakker, 25 jaar semantiek, liber amicorum, Centrum voor Wiskunde en Informatica, Amsterdam 1989, pp 247–252; and in: Proceedings AMAST Conference, Iowa City, USA, pp 197–201, 1989Google Scholar
  26. [GMM]
    R. Gorrieri, S. Marchetti, U. Montanari: A 2 CCS: A Simple Extension of CCS for Handling Atomic Actions, Proc. CAAP'88, LNCS 299, Springer-Verlag, pp 258–270, 1988Google Scholar
  27. [HM]
    M. Hennessy, R. Milner: Algebraic Laws for Nondeterminism and Concurrency, Journal of the ACM, Vol. 32, No. 1, pp 137–161, 1985Google Scholar
  28. [Milne]
    G.J. Milne: CIRCAL and the Representation of Communication, Concurrency and Time, Transactions on Programming languages and Systems (ACM), Vol. 7, No. 2, pp 270–298, 1985Google Scholar
  29. [Milner a]
    R. Milner: A Calculus of Communicating Systems, LNCS 92, Springer-Verlag, 1980Google Scholar
  30. [Milner b]
    R. Milner: Calculi for Synchrony and Asynchrony, Theoretical Computer Science, Vol. 25, No. 3, pp 267–310, 1983Google Scholar
  31. [NEL]
    M. Nielsen, U. Engberg, K.S. Larsen: Fully Abstract Models for a Process Language with Refinement, Linear Time, Branching Time and Partial Order in Logics and Models for Concurrency, LNCS 354, Springer-Verlag, pp 523–548, 1989Google Scholar
  32. [NPW]
    M. Nielsen, G.D. Plotkin, G. Winskel: Petri Nets, Event Structures and Domains, Part I, Theoretical Computer Science, Vol. 13, No. 1, pp 85–108, 1981Google Scholar
  33. [Park]
    D. Park: Concurrency and Automata on Infinite Sequences, Proc. 5th GI-Conference on Theoretical Computer Science, LNCS 104, Springer-Verlag, pp 167–183, 1981Google Scholar
  34. [Petri]
    C.A. Petri: Non-Sequential Processes, Interner Bericht 77-05, GMD, Institut für Informationssystemforschung, 1977Google Scholar
  35. [Pomello]
    L. Pomello: Some Equivalence Notions for Concurrent Systems. An Overview, in: Advances in Petri Nets 1985, LNCS 222, Springer-Verlag, pp 381–400, 1986Google Scholar
  36. [Pratt]
    V.R. Pratt: Modelling Concurrency with Partial Orders, International Journal of Parallel Programming, Vol. 15, No. 1, pp 33–71, 1986Google Scholar
  37. [Reisig]
    W. Reisig: Petri Nets, EATCS Monographs on Theoretical Computer Science 4, Springer-Verlag, 1985Google Scholar
  38. [TV]
    D.A. Taubner, W. Vogler: The Step Failure Semantics, Proc. STACS 87, LNCS 247, Springer-Verlag, pp 348–359, 1987Google Scholar
  39. [TRH]
    B.A. Trakhtenbrot, A. Rabinovich, J. Hirshfeld: Nets of Processes, Technical Report 97/88, Tel Aviv Univ., 1988, see also: A Rabinovich, B.A. Trakhtenbrot: Behavior Structures and Nets, Fundamenta Informaticae, Vol. XI, No. 4, pp 357–404, 1988Google Scholar
  40. [Vaandrager]
    F. Vaandrager: An Explicit Representation of Equivalence Classes of the History Preserving Bisimulation, Manuscript, CWI Amsterdam, 1989Google Scholar
  41. [Vogler a]
    W. Vogler: Failure Semantics Based on Interval Semiwords is a Congruence for Refinement, Proc. STACS'90, LNCS 415, Springer-Verlag, pp 285–297, 1990Google Scholar
  42. [Vogler b]
    W. Vogler: Bisimulation and Action Refinement, SFB-Bericht Nr. 342/10/90 A, Institut für Informatik, Technische Universität München, 1990Google Scholar
  43. [Winskel]
    G. Winskel: Event Structures, Petri Nets: Applications and Relationships to Other Models of Concurrency, LNCS 255, Springer-Verlag, pp 325–392, 1987Google Scholar

Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • Rob J. van Glabbeek
    • 1
  • Ursula Goltz
    • 2
  1. 1.Institut für Informatik der TU MünchenMünchen 2
  2. 2.Gesellschaft für Mathematik und DatenverarbeitungSankt Augustin 1

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