Geodesic
Covering space theory for directed topology
Theory and applications of categories, Tome 22 (2009), pp. 252-268.

Voir la notice de l'article provenant de la source Theory and Applications of Categories website

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.
Classification : 54E99, 54F05, 68N30, 68Q85
Keywords: pospace, covering space, directed topology 
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     author = {Eric Goubault and Emmanuel Haucourt and Sanjeevi Krishnan},
     title = {Covering space theory for directed topology},
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     pages = {252--268},
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     volume = {22},
     year = {2009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2009_22_a8/}
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Eric Goubault; Emmanuel Haucourt; Sanjeevi Krishnan. Covering space theory for directed topology. Theory and applications of categories, Tome 22 (2009), pp. 252-268. http://geodesic.mathdoc.fr/item/TAC_2009_22_a8/