A notion of refinement for automata

  • N. Sabadini
  • S. Vigna
  • R. F. C. Walters
Part of the Workshops in Computing book series (WORKSHOPS COMP.)


The notion of refinement of concurrent and distributed systems is a crucial one in any concurrency model. There are (at least) two distinct notions under the name of refinement, namely refinement of specifications and refinement of machines (automata). It is important to keep these two concepts distinct since their properties, and their mathematical formulation, are, or should be, quite different. A specification describes a whole class of machines and refinement here yields a smaller class of models, whereas a refinement of a machine yields a new, more complex, machine. It is not always clear which of these two notions is under consideration, because sometimes a mixture of the two approaches is appropriate and even because some formalisms allow different interpretations [1], [4], [16].


State Space Full Subcategory Transition Category Atomic Action Abstract Machine 
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  1. [1]
    M. Abadi and L. Lamport. Composing specifications. In Stepwise Refinement of Distributed Systems, number 430 in LNCS, pages 1–41, 1987.Google Scholar
  2. [2]
    K.M. Chandy and J. Misra. Parallel Program Design: A Foundation. Addison-Wesley, 1988.Google Scholar
  3. [3]
    I. Czaja, Ft. von Glabbeek, and U. Golz. Interleaving semantics and action refinement with atomic choice. Preprint.Google Scholar
  4. [4]
    P. Degano, R. Gorrieri, and G. Rosolini. A categorical view of process refinement. In Semantics: Foundations and Applications, number 666 in LNCS.Google Scholar
  5. [5]
    C. Elgot. Monadic computation and iterative algebraic theories. Studies in Logic and the Foundations of Mathematics, 80:175–230, 1975.CrossRefMathSciNetGoogle Scholar
  6. [6]
    P. Godefroid, D. Pirottin. Refining dependencies improves partial order verification methods. In C. Courcoubetis, editor, CAV 93, number 697 in LNCS, 1993.Google Scholar
  7. [7]
    A. Heller. An existence theorem for recursion categories. Journal of Symbolic Logic, 55(3):1252–1268, 1990.CrossRefMATHMathSciNetGoogle Scholar
  8. [8]
    W. Janssen, M. Poel, J. Zwiers. Action systems and action refinement in the development of parallel systems. In J.C.M. Baeten, J.F. Groote, editors, CONCUR 91, number 527 in LNCS, 1991.Google Scholar
  9. [9]
    D.E. Knuth. The Art of Computer Programming. Addison-Wesley, 1973.Google Scholar
  10. [10]
    W. Khalil and R.F.C. Walters. An imperative language based on distributive categories H. RAIRO Informatique Théorique et Applications.To appear.Google Scholar
  11. [11]
    W. Khalil, E.G. Wagner, and R.F.C. Walters. Fixed-point semantics for programs in distributive categories. In preparation.Google Scholar
  12. [12]
    N.A. Lynch. Multivalued possibility mappings. In Stepwise Refinement of Distributed Systems, number 430 in LNCS, pages 519–543, 1987.Google Scholar
  13. [13]
    R. Milner. An algebraic definition of simulation between programs. In Proc. of the 2nd Joint Conference on Artificial Intelligence, pages 481–489. BCS, 1971.Google Scholar
  14. [14]
    J. Meseguer and U. Montanari. Petri nets are monoids. Info, and Co., 88:105–155, 1990.CrossRefMATHMathSciNetGoogle Scholar
  15. [15]
    N. Sabadini and R.F.C. Walters. On functions and processors: an automata theoretic approach to concurrency through distributive categories. Mathematics Report 93–97, Sydney University, 1993.Google Scholar
  16. [16]
    W. Vogler. Modular construction and partial order semantics of Petri nets. Number 625 in LNCS, 1992.Google Scholar
  17. [17]
    R.F.C. Walters. Categories and Computer Science. Carslaw Publications (1991), Cambridge University Press (1992).Google Scholar

Copyright information

© British Computer Society 1994

Authors and Affiliations

  • N. Sabadini
    • 1
  • S. Vigna
    • 1
  • R. F. C. Walters
    • 2
  1. 1.Dipartimento di Scienze dell’InformazioneUniversità di MilanoMilanoItaly
  2. 2.School of Mathematics and StatisticsUniversity of SydneyAustralia

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