Acta Informatica

, Volume 24, Issue 5, pp 491–511 | Cite as

Order and metric in the stream semantics of elemental concurrency

  • J. W. de Bakker
  • J. -J. Ch. Meyer


Two denotational semantics for a language with simple concurrency are presented. The language has parallel composition in the form of the shuffle operation, in addition to the usual sequential concepts including full recursion. Two linear time models, both involving sets of finite and infinite streams, are given. The first model is order-theoretic and based on the Smyth order. The second model employs complete metric spaces. Various technical results are obtained relating the order-theoretic and metric notions. The paper culminates in the proof that the two semantics for the language considered coincide. The paper completes previous investigations of the same language, establishing the equivalence of altogether four semantic models for it.


Operating System Data Structure Communication Network Information Theory Computational Mathematic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Back, R.J.: A continuous semantics for unbounded nondeterminism. Theor. Comput. Sci. 23, 187–210 (1983)MathSciNetCrossRefGoogle Scholar
  2. 2.
    de Bakker, J.W., Bergstra, J.A., Klop, J.W., Meyer, J.-J.Ch.: Linear time and branching time semantics for recursion with merge. Theor. Comput. Sci. 34, 135–156 (1984)MathSciNetCrossRefGoogle Scholar
  3. 3.
    de Bakker, J.W., Kok, J.N., Meyer, J.-J.Ch., Olderog, E.-R., Zucker, J.I.: Contrasting themes in the semantics of imperative concurrency. In: Current Trends in Concurrency: Overviews and Tutorials (J.W. de Bakker, W.P. de Roever, G. Rozenberg, eds.), LNCS 224, pp. 51–121. Berlin-Heidelberg-New York: Springer 1986CrossRefGoogle Scholar
  4. 4.
    de Bakker, J.W., Meyer, J.-J.Ch., Olderog, E.-R.: Infinite streams and finite observations in the semantics of uniform concurrency. In: Proceedings 12th ICALP (W. Brauer, ed.), LNCS 194, pp. 149–157. Berlin-Heidelberg-New York: Springer 1985Google Scholar
  5. 5.
    de Bakker, J.W., Meyer, J.-J.Ch., Olderog, E.-R.: Infinite streams and finite observations in the semantics of uniform concurrency. Report CS-R8512, Centre for Mathematics and Computer Science, 1985 (full version of [4], to appear in Theor. Comput. Sci.)Google Scholar
  6. 6.
    de Bakker, J.W., Meyer, J.-J.Ch., Olderog, E.-R., Zucker, J.I.: Transition systems, infinitary languages and the semantics of uniform concurrency. In: Proceedings 17th ACM STOC, pp. 252–262. ACM-Publications: Providence, R.I. 1985Google Scholar
  7. 7.
    de Bakker, J.W., Meyer, J.-J.Ch., Olderog, E.-R., Zucker, J.I.: Transition systems, metric spaces and ready sets in the semantics of uniform concurrency. Report CS-R 8601, Centre for Mathematics and, Computer Science 1986 (full version of [6])Google Scholar
  8. 8.
    de Bakker, J.W., Zucker, J.I.: Processes and the denotational semantics of concurrency. Inf. Control 54, 70–120 (1982)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Bergstra, J.A., Klop, J.W.: Process algebra for synchronous communication. Inf. Control 60, 109–137 (1984)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Broy, M.: Fixed point theory for communication and concurrency. IFIP TC 2 Working Conference '82, Garmisch-Partenkirchen (D. Bjørner, ed.). Amsterdam: North-Holland 1983Google Scholar
  11. 11.
    Broy, M.: A theory for nondeterminism, parallelism, communication and concurrency. Theor. Comput. Sci. 45, 1–62 (1986)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Dugundji, J.: Topology. Rockleigh, N.J.: Allen and Bacon 1966zbMATHGoogle Scholar
  13. 13.
    Engelking, R.: General topology. Polish Scientific Publishers 1977Google Scholar
  14. 14.
    Hahn, H.: Reelle Funktionen. New York: Chelsea 1948zbMATHGoogle Scholar
  15. 15.
    Hennessy, M., Plotkin, G.D.: Full abstraction for a simple parallel programming language. In: Proceedings 8th MFCS (J. Becvar, ed.), LNCS 74, pp. 108–120. Berlin-Heidelberg-New York: Springer 1979Google Scholar
  16. 16.
    Joshi, K.D.: Introduction to General Topology. New Delhi: Wiley Eastern 1983zbMATHGoogle Scholar
  17. 17.
    Kuiper, R.: An operational semantics for bounded nondeterminism equivalent to a denotational one. IFIP TC2-MC Symp. on Algorithmic Languages (J.W. de Bakker, J.C. van Vliet, eds.), pp. 373–398. Amsterdam: North-Holland 1981Google Scholar
  18. 18.
    Meyer, J.-J.Ch.: Programming calculi based on fixed point transformations: semantics and applications. Dissertation, Free University of Amsterdam, 1985Google Scholar
  19. 19.
    Meyer, J.-J.Ch.: Merging regular processes by means of fixed point theory. Theor. Comput. Sci. 45, 193–260 (1986)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Meyer, J.-J.Ch., de Vink, E.P.: Applications of compactness in the Smyth power domain of streams. Report IR-110, Free University, Amsterdam, 1986; extended abstract in Proceedings TAPSOFT/CAAP'87 (H. Ehrig, R. Kowalski, G. Levi, U. Montanari, eds.), Pisa, LNCS 249, pp. 241–255. Berlin-Heidelberg-New York-Tokyo: Springer 1987Google Scholar
  21. 21.
    Nivat, M.: Infinite words, infinite trees, infinite computations, Foundations of Computer Science III.2. Math. Centre Tracts 109, 3–52 (1979)Google Scholar
  22. 22.
    Olderog, E.-R., Hoare, C.A.R.: Specification-oriented semantics for communicating processes. Acta Inf. 23, 9–66 (1986)MathSciNetCrossRefGoogle Scholar
  23. 23.
    Plotkin, G.D.: A structural approach to operational semantics, Report DAIMI FN-19, Comp. Sci. Dept., Aarhus Univ. 1981Google Scholar
  24. 24.
    Rounds, W.C.: On the relationship between Scott domains, synchronization trees and metric spaces. Report Univ. of Michigan CRL-TR-25-83, 1983Google Scholar

Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • J. W. de Bakker
    • 1
  • J. -J. Ch. Meyer
    • 2
  1. 1.Centre for Mathematics and Computer ScienceAB AmsterdamThe Netherlands
  2. 2.Department of Mathematics and Computer ScienceFree University of AmsterdamThe Netherlands

Personalised recommendations