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.
Supported by SERC grant GR/F 93050.
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Kwiatkowska, M.Z. (1991). On the domain of traces and sequential composition. In: Abramsky, S., Maibaum, T.S.E. (eds) TAPSOFT '91. CAAP 1991. Lecture Notes in Computer Science, vol 493. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-53982-4_3
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DOI: https://doi.org/10.1007/3-540-53982-4_3
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