Cubical local partial orders on cubically subdivided spaces - Existence and construction
The geometric models of higher dimensional automata (HDA) and Dijkstra's PV-model are cubically subdivided topological spaces with a local partial order. If a cubicalization of a topological space is free of immersed cubic Mobius bands, then there are consistent choices of direction in all cubes, such that any n-cube in the cubic subdivision is dihomeomorphic to [0, 1](n) with the induced partial order from R-n. After subdivision once, any cubicalized space has a cubical local partial order. In particular, all triangularized spaces have a cubical local partial order. This implies in particular that the underlying geometry of an HDA may be quite complicated. (C) 2006 Elsevier B.V. All rights reserved.
cubicalization local partial order higher dimensional automaton cubical complex