Structural and behavioural equivalences of networks

  • Joachim Parrow
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 443)


We define an algebraic language for networks consisting of a finite number of nodes whose ports are interconnected by links. The language contains two types of operations: parallel composition of two networks, and interlinking of two ports within a network. We interpret this language in both a structural way and a behavioural way; in the latter interpretation the networks are regarded as schemas where the nodes can be instantiated to processes communicating over the links. This gives rise to structural and behavioural equivalences; these equivalences are given sound and complete axiomatisations.


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  1. [AB84]
    D Austry and G Boudol. Algèbre de processus et synchronisation. Theoretical Computer Science, 30(1):91–131, 1984.Google Scholar
  2. [BHR84]
    S. Brookes, C.A.R. Hoare, and W. Roscoe. A theory of communicating sequential processes. J. ACM, 31(3):560–599, 1984.Google Scholar
  3. [BT85]
    J. Bergstra and J. Tucker. Top-down design and the algebra of communicating processes. Science of Computer Programming, 5(2):171–199, 1985.Google Scholar
  4. [Jon85]
    Bengt Jonsson. A model and proof system for asynchronous networks. In Proceedings of the 4:th ACM Symposium on Principles of Distributed Computing, pages 49–58, 1985.Google Scholar
  5. [Kah74]
    G Kahn. The semantics of a simple language for parallel programming. In IFIP 74, pages 471–475, 1974.Google Scholar
  6. [KP85]
    R M Keller and P Panangaden. Semantics of networks containing indeterminate operators. In Brookes, Roscoe, and Winskel, editors, Seminar on Concurrency 1984, LNCS 197, pages 479–496, 1985.Google Scholar
  7. [Mil79]
    Robin Milner. Flowgraphs and flow algebras. J. ACM, 26(4):794–818, 1979.Google Scholar
  8. [Mil83]
    Robin Milner. Calculi for synchrony and asynchrony. Theoretical Computer Science, 25:267–310, 1983.Google Scholar
  9. [Mil85]
    George Milne. CIRCAL and the representation of communication, concurrency and time. ACM Transactions on Programming Languages and Systems, 7(2):270–298, 1985.Google Scholar
  10. [Mil89]
    Robin Milner. Communication and Concurrency. Prentice Hall, 1989.Google Scholar
  11. [Par83]
    David Park. The ‘fairness’ problem and nondeterministic computing networks. In de Bakker and van Leeuwen, editors, Foundations of Computer Science IV. Part 2, pages 133–161. Amsterdam, 1983. Mathematical Centre Tracts 159.Google Scholar
  12. [Par87]
    Joachim Parrow. Synchronisation flow algebra. Technical Report LFCS-87-35, Laboratory for Foundations of Computer Science, Department of Computer Science, University of Edinburgh, 1987.Google Scholar
  13. [Par89]
    Joachim Parrow. The expressive power of simple parallelism. In Proceedings of PARLE '89, Vol. II; LNCS 366, pages 389–405, 1989.Google Scholar
  14. [SN85]
    J Staples and V L Nguyen. A fixpoint semantics for nondeterministic data flow. J. ACM, 32(2):411–444, 1985.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1990

Authors and Affiliations

  • Joachim Parrow
    • 1
  1. 1.Swedish Institute of Computer ScienceKistaSweden

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