Abstract
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 Möbius 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.
Original language | English |
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Journal | Theoretical Computer Science |
Volume | 365 |
Issue number | 3 |
Pages (from-to) | 199-205 |
Number of pages | 7 |
ISSN | 0304-3975 |
Publication status | Published - 2006 |