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)


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.


Sequential Composition Concurrent Execution Trace Theory Concatenation Operation Directed Subset 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

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

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