Topological Aspects of Traces

Jaap van Oosten

November 1995


Traces play a major role in several models of concurrency. They arise out of ``independence structures'' which are sets with a symmetric, irreflexive relation. In this paper, independence structures are characterized as certain topological spaces. We show that these spaces are a universal construction known as ``soberification'', a topological generalization of the ideal completion construction in domain theory. We also show that there is an interesting group action connected to this construction. Finally, generalizing the constructions in the first part of the paper, we define a new category of ``labelled systems of posets''. This category includes labelled event structures as a full reflective subcategory, and has moreover a very straightforward notion of bisimulation which restricts on event structures to strong history-preserving bisimulation.

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