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Covering space theory for directed topology

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Eric Goubault, Emmanuel Haucourt, Sanjeevi Krishnan

The state space of a machine admits the structure of time. For example,
the geometric realization of a precubical set, a generalization of an
unlabeled asynchronous transition system, admits a ``local preorder''
encoding control flow. In the case where time does not loop, the ``locally
preordered'' state space splits into causally distinct components. The set
of such components often gives a computable invariant of machine behavior.
In the general case, no such meaningful partition could exist. However, as
we show in this note, the locally preordered geometric realization of a
precubical set admits a ``locally monotone'' covering from a state space
in which time does not loop. Thus we hope to extend geometric techniques
in static program analysis to looping processes.

Keywords:
pospace, covering space, directed topology

2000 MSC:
54E99, 54F05, 68N30, 68Q85

*Theory and Applications of Categories,*
Vol. 22, 2009,
No. 9, pp 252-268.

http://www.tac.mta.ca/tac/volumes/22/9/22-09.pdf

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/22/9/22-09.pdf

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