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Some collapsing operations for 2-dimensional precubical sets

Authors
  • Kahl, Thomas
Type
Preprint
Publication Date
May 07, 2012
Submission Date
May 29, 2010
Identifiers
arXiv ID: 1005.5443
Source
arXiv
License
Yellow
External links

Abstract

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.

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