Reducing cubical set models of concurrent systems

Details Reducing cubical set models of concurrent systems Reducing cubical set models of concurrent systems

2010-05-29

arxiv.org/abs/1005.5443v1

Mathematics

Algebraic Topology

21 pages, 4 figures

Scientific paper

Precubical sets, i.e., cubical sets without degeneracies, can be used to model systems of concurrently executing processes. From the point of view of concurrency theory, two precubical sets can be considered equivalent if their geometric realizations have the same directed homotopy type relative to the extremal elements in the sense of P. Bubenik. We give conditions under which it is possible to collapse an edge or to eliminate a cube and a free face in a 2-dimensional precubical set to obtain an equivalent smaller one. We use our results to construct small models of some simple precubical sets.

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