Domains of higher-dimensional automata

  • Eric Goubault
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 715)


We carry on the program set up in [GJ92] by giving constructions of “domains of higher-dimensional automata (HDA)” on which we can define the truly-concurrent semantics of parallel languages, much in the style of domain theory (see [GS90]). In [GJ92] we gave a semantics for CCS-like languages. In this article, we show how to extend the technique to languages with real states, while keeping nice algebraic definitions. In particular, we are still able to compute local invariants which can decide a few computational properties of interest. For being used as actual computational definitions, the semantics is denotational (i.e. compositional); for being precise enough when it comes to studying the dynamic behaviour of programs, the denotations are higher-dimensional automata, which are no more than an operational behaviour (in the style of operational semantics, see [Plo81]). We conclude by giving the semantics of a small shared-memory imperative language.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [AL91]
    Andrea Asperti and Giuseppe Longo. Categories, types and structures. The MIT Press, second edition, 1991.Google Scholar
  2. [FS90]
    Peter J. Freyd and Andre Scedrov. Categories, allegories. In North-Holland Mathematical Library, volume 39. North-Holland, 1990.Google Scholar
  3. [GJ92]
    Eric Goubault and Thomas P. Jensen. Homology of higher-dimensional automata. In Proc. of CONCUR'92, Stonybrook, New York, August 1992. Springer-Verlag.Google Scholar
  4. [Gou93]
    Eric Goubault. Higher-dimensional automata. Technical report, Ecole Normale Supérieure, to appear 93.Google Scholar
  5. [GS90]
    CA. Gunther and D.S. Scott. Semantic domains. In Handbook of Theoretical Computer Science. Elsevier, 1990.Google Scholar
  6. [HU79]
    J.E. Hopcroft and J.D. Ullman. Introduction to Automata Theory, Languages and Computation. Addison-Wesley, 1979.Google Scholar
  7. [Lan84]
    Serge Lang. Algebra. Addison Wesley, second edition, 1984.Google Scholar
  8. [Mas78]
    William S. Massey. Homology and cohomology theory. In Monographs and Text-books in Pure and Applied Mathematics, number 46. Marcel DEKKER, INC., 1978.Google Scholar
  9. [ML63]
    Saunders Mac Lane. Homology. In Die Grundlehren der Mathematishen Wissenschaften in Einzeldarstellungen, volume Band 114. Springer Verlag, 1963.Google Scholar
  10. [Plo81]
    Gordon Plotkin. A structural approach to operational semantics. Technical Report DAIMI FN-19, Computer Science Department, Aarhus, 1981.Google Scholar
  11. [Pra91]
    Vaughan Pratt. Modeling concurrency with geometry. In Proc. 18th ACM Symposium on Principles of Programming Languages. ACM Press, 1991.Google Scholar
  12. [Pra92]
    Vaughan Pratt. The duality of time and information. In Proc. of CONCUR'92, Stonybrook, New York, August 1992. Springer-Verlag.Google Scholar
  13. [Win88]
    Glynn Winskel. An introduction to event structures. Lecture notes in computer science, (354), 1988.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Eric Goubault
    • 1
  1. 1.Ecole Normale SupérieureLIENSParis Cedex 05France

Personalised recommendations