Cubical local partial orders on cubically subdivided spaces - existence and construction

Publikation: Bog/antologi/afhandling/rapportRapportForskning

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Resumé

The geometric models of Higher Dimensional Automata 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.
OriginalsprogEngelsk
Udgivelses stedAalborg
ForlagDepartment of Mathematical Sciences, Aalborg University
Antal sider8
StatusUdgivet - 2004
NavnResearch Report Series
NummerR-2004-31
ISSN1399-2503

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Partial Order
Subdivision
Topological space
N-cube
Geometric Model
Regular hexahedron
Automata
High-dimensional
Imply
Model

Citer dette

Fajstrup, L. (2004). Cubical local partial orders on cubically subdivided spaces - existence and construction. Aalborg: Department of Mathematical Sciences, Aalborg University. Research Report Series, Nr. R-2004-31
Fajstrup, Lisbeth. / Cubical local partial orders on cubically subdivided spaces - existence and construction. Aalborg : Department of Mathematical Sciences, Aalborg University, 2004. 8 s. (Research Report Series; Nr. R-2004-31).
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abstract = "The geometric models of Higher Dimensional Automata 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 M{\"o}bius 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.",
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Fajstrup, L 2004, Cubical local partial orders on cubically subdivided spaces - existence and construction. Research Report Series, nr. R-2004-31, Department of Mathematical Sciences, Aalborg University, Aalborg.

Cubical local partial orders on cubically subdivided spaces - existence and construction. / Fajstrup, Lisbeth.

Aalborg : Department of Mathematical Sciences, Aalborg University, 2004. 8 s.

Publikation: Bog/antologi/afhandling/rapportRapportForskning

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Fajstrup L. Cubical local partial orders on cubically subdivided spaces - existence and construction. Aalborg: Department of Mathematical Sciences, Aalborg University, 2004. 8 s. (Research Report Series; Nr. R-2004-31).