Abstract
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 a 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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References
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© 1996 Springer-Verlag Berlin Heidelberg
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van Oosten, J. (1996). Topological aspects of traces. In: Billington, J., Reisig, W. (eds) Application and Theory of Petri Nets 1996. ICATPN 1996. Lecture Notes in Computer Science, vol 1091. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61363-3_26
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DOI: https://doi.org/10.1007/3-540-61363-3_26
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