Advertisement

Semantics of networks containing indeterminate operators

  • Robert M. Keller
  • Prakash Panangaden
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 197)

Abstract

We discuss a denotational semantics for networks containing indeterminate operators. Our approach is based on modelling a network by the set of all its possible behaviors. Our notion of behavior is a sequence of computational actions. The primitive computational action is an event: the appearance or consumption of a token on a data path. A sequence of such events is called a history and a set of such histories is called an archive. We give composition rules that allow us to derive an archive for a network from the archive of its constituents. Causal and operational constraints on network behavior are encoded into the definitions of archives. We give a construction that allows us to obtain the denotation of networks containing loops by a process of successive approximations. This construction is not carried out in the traditional domain-theoretic setting, but rather resembles the category theoretic notion of limit. By using this construction, we avoid having to impose any closure conditions on the set of behaviors, as are typically necessary in powerdomain constructions. The resulting theory is general and compositional, but is also close to operational ideas making it a useful and flexible tool for modelling systems.

Keywords

Output Event Composition Rule Input Event Denotational Semantic Serial Composition 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

6. References

  1. [Abramsky 83]
    Abramsky, S. Semantic Foundations of Applicative Multiprogramming. In Diaz, J. (editor), Automata, Languages and Programming, pages 1–14. Springer-Verlag, July, 1983.Google Scholar
  2. [Brock 81]
    Brock J.D., W.B. Ackermann. Scenarios: A Model of Non-Determinate Computation. In J. Diaz, I. Ramos (editor), Formalization of Programming Concepts, LNCS 107, pages 252–259. Springer-Verlag, New York, 1981.Google Scholar
  3. [Broy 81]
    Broy M. A Fixed Point Approach to Applicative Multiprogramming. In Lectures at the International Summer School on Theoretical Foundations of Programming Methodology. July, 1981.Google Scholar
  4. [Davis 82]
    A.L. Davis and R.M. Keller. Dataflow program graphs. Computer 15(2):26–41, February, 1982.Google Scholar
  5. [Hennessey 82]
    Hennessey, M. Synchronous and Asynchronous Experiments on Processes. Technical Report, University of Edinburgh, September, 1982.Google Scholar
  6. [Karp 69]
    Karp R. M., Miller R. Parallel program schemata. JCSS, May, 1969.Google Scholar
  7. [Keller 78]
    Keller R.M. Denotational Models for Parallel Programs With Indeterminate Operators. In E.J. Neuhold (editor), Formal Descriptions of Programming Concepts, pages 337–365. North-Holland, Amsterdam, 1978.Google Scholar
  8. [Keller 83]
    R.M. Keller. Unpublished presentation on archives. June, 1983. Massachusetts Institute Technology, Applicative Languages Workshop, Endicott House.Google Scholar
  9. [Plotkin 76]
    Plotkin G. A Powerdomain Construction. SIAM J. of Computing 5(3), September, 1976.Google Scholar
  10. [Pratt 82]
    Pratt V. On the Composition of Processes. In Ninth Annual ACM Symposium on Principles of Programming Languages, pages 213–223. ACM, January, 1982.Google Scholar
  11. [Riddle 79]
    Riddle W.E. An Approach to Software System Behavior Description. Computer Languages 4:29–47, 1979.Google Scholar
  12. [Scott 70]
    Scott D.S. Outline of a Mathematical Theory of Computation. In Proceedings of the Fourth Annual Princeton Conference on Information Sciences and Systems, pages 169–176. 1970.Google Scholar
  13. [Scott 71]
    Scott D.S., Strachey C. Towards a Mathematical Semantics for Computer Languages. Technical Report PRG-6, University of Oxford, 1971.Google Scholar
  14. [Smythe 78]
    Smythe M.B. Power Domains. J. CSS 16:23–36, 1978.Google Scholar
  15. [Winskel 80]
    Winskel G. Events in Computation. PhD thesis, University of Edinburgh, 1980.Google Scholar

Copyright information

© Springer-Verlag 1985

Authors and Affiliations

  • Robert M. Keller
    • 1
  • Prakash Panangaden
    • 1
  1. 1.Department of Computer ScienceUniversity of UtahSait Lake City

Personalised recommendations