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TitleSome collapsing operations for 2-dimensional precubical sets
Author(s)Kahl, Thomas
KeywordsCubical sets
Fundamental bipartite graph
Fundamental category
Trace spaces
Directed homotopy theory
Concurrency theory
Issue date5-Jun-2012
JournalJournal of Homotopy and Related Structures
Abstract(s)In this paper, we consider 2-dimensional precubical sets, which can be used to model systems of two 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 easily verifiable conditions under which it is possible to reduce a 2-dimensional precubical set to an equivalent smaller one by collapsing an edge or eliminating a square and one or two free faces. We also look at some simple standard examples in order to illustrate how our results can be used to construct small models of 2-dimensional precubical sets.
Publisher version
AccessOpen access
Appears in Collections:CMAT - Artigos em revistas com arbitragem / Papers in peer review journals

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