Covering space theory for directed topology

Details Covering space theory for directed topology Covering space theory for directed topology

2008-12-05

arxiv.org/abs/0812.1157v2

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

Mathematics

Algebraic Topology

14 pages, 2 figures, results partially presented at ATMCS III 2008; deleted false Lem 2.2; corrected proof of Lem 3.7; deleted

Scientific paper

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.

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