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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.
@article{TAC_2009_22_a8,
author = {Eric Goubault and Emmanuel Haucourt and Sanjeevi Krishnan},
title = {Covering space theory for directed topology},
journal = {Theory and applications of categories},
pages = {252--268},
publisher = {mathdoc},
volume = {22},
year = {2009},
language = {en},
url = {http://geodesic.mathdoc.fr/item/TAC_2009_22_a8/}
}
TY - JOUR AU - Eric Goubault AU - Emmanuel Haucourt AU - Sanjeevi Krishnan TI - Covering space theory for directed topology JO - Theory and applications of categories PY - 2009 SP - 252 EP - 268 VL - 22 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TAC_2009_22_a8/ LA - en ID - TAC_2009_22_a8 ER -
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/