Advertisement

On the domain of traces and sequential composition

  • Martz Z. Kwiatkowska
CAAP Colloquium On Trees In Algebra And Programming
Part of the Lecture Notes in Computer Science book series (LNCS, volume 493)

Abstract

An enhancement of Mazurkiewicz's trace theory with infinite traces is presented. Infinite traces have been obtained by introducing the trace preorder relation on possibly infinite strings. It is shown that the extension gives rise to the domain of traces in the sense of Scott and a complete metric space. Sequential composition (concatenation) of possibly infinite traces is also considered. The difficulty of finding an appropriate concatenation of infinite traces is a consequence of the concatenation of finite traces being non-uniformly continuous wrt the metric for traces. A natural extension of the concatenation operation for finite traces is proposed; the extended operation is total, yields a generalization of Levi's lemma for infinite traces, but is non-associative.

Keywords

Sequential Composition Concurrent Execution Trace Theory Concatenation Operation Directed Subset 
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.

References

  1. [AaR88]
    Aalbersberg I.J., Rozenberg G., Theory of Traces, Theoretical Computer Science 60 (1988) 1–82.Google Scholar
  2. [BoN80]
    Boasson L., Nivat M., Adherences of Languages, Journal of Computer and System Sciences 20 (1980) 285–309.Google Scholar
  3. [CoP85]
    Cori R, Perrin D., Automates et commutations partielles, RAIRO Theoretical Informatics and Applications 19 (1985) 21–32.Google Scholar
  4. [Die91]
    Diekert V., On the Concatenation of Infinite Traces, to appear in Proceedings, Symposium on Theoretical Aspects of Computer Science (STACS 91), Lecture Notes in Computer Science (Springer, 1991).Google Scholar
  5. [Gas90]
    Gastin P., Infinite Traces, in I. Guessarian, ed., Semantics of Systems of Concurrent Processes, Lecture Notes in Computer Science 469 (Springer, 1990)Google Scholar
  6. [GHK80]
    Gierz G., Hofmann K.H., Keimel K., Lawson J.D., Mislove M., Scott D., A Compendium of Continuous Lattices (Springer, 1980).Google Scholar
  7. [Kwi90m]
    Kwiatkowska M.Z., A Metric for Traces, Information Processing Letters 35, 3 (1990).Google Scholar
  8. [Kwi89e]
    Kwiatkowska M.Z., Event Fairness and Non-Interleaving Concurrency, Formal Aspects of Computing 1 3 (1989).Google Scholar
  9. [Kwi89t]
    Kwiatkowska M.Z., Fairness for Non-Interleaving Concurrency, PhD Thesis, University of Leicester (1989). Also available as Technical Report No. 22, University of Leicester, Department of Computing Studies (1989).Google Scholar
  10. [Kwi90t]
    Kwiatkowska M.Z., On Topological Characterization of Behavioural Properties, to appear in: G.M. Reed & A.W. Roscoe, eds., Topology in Computer Science (Oxford University Press, 1990).Google Scholar
  11. [Kwi90c]
    Kwiatkowska M.Z., Causality and Fairness Properties, submitted.Google Scholar
  12. [Kwi90p]
    Kwiatkowska M.Z., Defining Process Fairness for Non-Interleaving Concurrency, in K.V.Nori and C.E. Madhavan, eds., Foundations of Software Technology and Theoretical Computer Science, Lecture Notes in Computer Science 472 (Springer, 1990).Google Scholar
  13. [Law87]
    Lawson J., The Versatile Continuous Order, in: M. Main et al, eds., Mathematical Foundations of Programming Language Semantics 1987, Lecture Notes in Computer Science 298 (Springer, 1988) 134–160.Google Scholar
  14. [Maz77]
    Mazurkiewicz A., Concurrent Program Schemes and Their Interpretations, DAIMI Report PB-78, Aarhus University (1977).Google Scholar
  15. [Maz84]
    Mazurkiewicz A., Traces, Histories, Graphs: Instances of a Process Monoid, in: Chytil M.P., Koubek V., eds., Mathematical Foundations of Computer Science 1984, Lecture Notes in Computer Science 176 (Springer, 1984).Google Scholar
  16. [Maz89]
    Mazurkiewicz A., Basic Notions of Trace Theory, in: J.W. de Bakker, W.-P. de Roever, G. Rozenberg, eds., Linear Time, Branching time and Partial Order in Logics and Models for Concurrency, Lecture Notes in Computer Science 354 (Springer, 1989) 285–263.Google Scholar
  17. [Pnu86]
    Pnueli A., Applications of temporal logic to the specification and verification of reactive systems: a survey of current trends, in: de Bakker, de Roever, Rozenberg, eds., Current Trends in Concurrency, Lecture Notes in Computer Science 224 (Springer, 1986).Google Scholar
  18. [Shi85]
    Shields M.W., Deterministic Asynchronous Automata, in: Formal Methods in Programming (North-Holland, 1985).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Martz Z. Kwiatkowska
    • 1
  1. 1.Department of Computing StudiesUniversity of LeicesterLeicesterUnited Kingdom

Personalised recommendations