Skip to main content
SpringerLink
Log in

Equivalences and refinement

  • Conference paper
  • First Online:
Semantics of Systems of Concurrent Processes (LITP 1990)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 469))

Included in the following conference series:

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.

Notes This is an extended and updated version of our paper [GG a]. The extension consists of considering equivalences and refinement for the domain of flow event structures — instead of the subdomain of prime event structures — and allowing also infinite refinements and refinements with conflicts. This more general refinement operation was introduced in [GG b], however equivalences were not considered there. The results of this paper are also contained in [van Glabbeek b]. The work presented here has partly been carried out within the Esprit Basic Research Action 3148 (DEMON) and the Sonderforschungsbereich 342 of the TU München.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. L. Aceto, R. De Nicola, A. Fantechi: Testing Equivalences for Event Structures, Mathematical Models for the Semantics of Parallelism, LNCS 280, Springer-Verlag, 1987

    Google Scholar 

  2. L. Aceto, M. Hennessy: Towards Action-Refinement in Process Algebras, Proc. LICS'89, IEEE Computer Society Press, Washington, pp 138–145, 1989

    Google Scholar 

  3. D. Austry, G. Boudol: Algébre de processus et synchronisations, Theoretical Computer Science, Vol. 30, No. 1, pp 91–131, 1984

    Google Scholar 

  4. 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, 1985

    Google Scholar 

  5. E. Best, R. Devillers, A. Kiehn, L. Pomello: Fully Concurrent Bisimulation, Technical Report LIT 202, Université Libre de Bruxelles, Laboratoire d'Informatique Theorique, 1989

    Google Scholar 

  6. G. Boudol: Atomic Actions (Note), Bulletin of the EATCS 38, pp 136–144, 1989

    Google Scholar 

  7. G. Boudol: Computations of Distributed Systems, Part 1: Flow Event structures and Flow Nets, report INRIA Sophia Antipolis, to appear

    Google Scholar 

  8. 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, 1987

    Google Scholar 

  9. 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, 1989

    Google Scholar 

  10. W. Brauer, R. Gold, W. Vogler: Behaviour and Equivalence Preserving Refinements of Petri Nets, Report, Institut für Informatik, Technische Universität München, 1990

    Google Scholar 

  11. 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, 1984

    Google Scholar 

  12. L. Castellano, G. De Michelis, L. Pomello: Concurrency vs Interleaving: An Instructive Example, Bulletin of the EATCS 31, pp 12–15, 1987

    Google Scholar 

  13. P. Darondeau, P. Degano: Causal Trees, Proc. ICALP 89, LNCS 372, Springer-Verlag, pp 234–248, 1989

    Google Scholar 

  14. Ph. Darondeau, P. Degano: Event structures, Causal trees, and Refinements, to appear in Proc. MFCS 90, LNCS, Springer-Verlag, 1990

    Google Scholar 

  15. 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, 1987

    Google Scholar 

  16. 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, 1988

    Google Scholar 

  17. 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, 1989

    Google Scholar 

  18. R. De Nicola, M. Hennessy: Testing Equivalences for Processes, Theoretical Computer Science, Vol. 34, pp 83–133, 1984

    Google Scholar 

  19. R. Devillers: Maximality Preserving Bisimulation, Technical Report LIT 214, Université Libre de Bruxelles, Laboratoire d' Informatique Theorique, 1990

    Google Scholar 

  20. 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 1990

    Google Scholar 

  21. R.J. van Glabbeek: Comparative Concurrency Semantics and Refinement of Actions, Ph. D. Thesis, Free University, Amsterdam 1990

    Google Scholar 

  22. 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, 1989

    Google Scholar 

  23. 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, 1990

    Google Scholar 

  24. 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, 1987

    Google Scholar 

  25. 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, 1989

    Google Scholar 

  26. 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, 1988

    Google Scholar 

  27. M. Hennessy, R. Milner: Algebraic Laws for Nondeterminism and Concurrency, Journal of the ACM, Vol. 32, No. 1, pp 137–161, 1985

    Google Scholar 

  28. 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, 1985

    Google Scholar 

  29. R. Milner: A Calculus of Communicating Systems, LNCS 92, Springer-Verlag, 1980

    Google Scholar 

  30. R. Milner: Calculi for Synchrony and Asynchrony, Theoretical Computer Science, Vol. 25, No. 3, pp 267–310, 1983

    Google Scholar 

  31. 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, 1989

    Google Scholar 

  32. 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, 1981

    Google Scholar 

  33. D. Park: Concurrency and Automata on Infinite Sequences, Proc. 5th GI-Conference on Theoretical Computer Science, LNCS 104, Springer-Verlag, pp 167–183, 1981

    Google Scholar 

  34. C.A. Petri: Non-Sequential Processes, Interner Bericht 77-05, GMD, Institut für Informationssystemforschung, 1977

    Google Scholar 

  35. L. Pomello: Some Equivalence Notions for Concurrent Systems. An Overview, in: Advances in Petri Nets 1985, LNCS 222, Springer-Verlag, pp 381–400, 1986

    Google Scholar 

  36. V.R. Pratt: Modelling Concurrency with Partial Orders, International Journal of Parallel Programming, Vol. 15, No. 1, pp 33–71, 1986

    Google Scholar 

  37. W. Reisig: Petri Nets, EATCS Monographs on Theoretical Computer Science 4, Springer-Verlag, 1985

    Google Scholar 

  38. D.A. Taubner, W. Vogler: The Step Failure Semantics, Proc. STACS 87, LNCS 247, Springer-Verlag, pp 348–359, 1987

    Google Scholar 

  39. 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, 1988

    Google Scholar 

  40. F. Vaandrager: An Explicit Representation of Equivalence Classes of the History Preserving Bisimulation, Manuscript, CWI Amsterdam, 1989

    Google Scholar 

  41. W. Vogler: Failure Semantics Based on Interval Semiwords is a Congruence for Refinement, Proc. STACS'90, LNCS 415, Springer-Verlag, pp 285–297, 1990

    Google Scholar 

  42. W. Vogler: Bisimulation and Action Refinement, SFB-Bericht Nr. 342/10/90 A, Institut für Informatik, Technische Universität München, 1990

    Google Scholar 

  43. G. Winskel: Event Structures, Petri Nets: Applications and Relationships to Other Models of Concurrency, LNCS 255, Springer-Verlag, pp 325–392, 1987

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Informatik der TU München, Postfach 20 24 20, D-8000, München 2

    Rob J. van Glabbeek

  2. Gesellschaft für Mathematik und Datenverarbeitung, Postfach 1240, D-5205, Sankt Augustin 1

    Ursula Goltz

Authors
  1. Rob J. van Glabbeek
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ursula Goltz
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Irène Guessarian

Rights and permissions

Reprints and permissions

Copyright information

© 1990 Springer-Verlag

About this paper

Cite this paper

van Glabbeek, R.J., Goltz, U. (1990). Equivalences and refinement. In: Guessarian, I. (eds) Semantics of Systems of Concurrent Processes. LITP 1990. Lecture Notes in Computer Science, vol 469. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-53479-2_13

Download citation

  • DOI: https://doi.org/10.1007/3-540-53479-2_13

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-53479-2

  • Online ISBN: 978-3-540-46897-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation