K-density, N-density, and finiteness properties

  • Helmut Plünnecke
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 188)


Modelling non-sequential processes by partially ordered sets (posets) leads to the concept of K-density which says that every cut and every line have (exactly) one point in common. The “simplest” example of non-K-density is given by a four-element poset the underlying graph of wich is “N-shaped”; a poset is called N-dense iff every (four-element) N-shaped subposet can be extended to an K-dense subposet by addition of one point. K-density implies N-density; for finite non-empty posets also the converse implication is true. It turns out that much weaker properties are sufficient; especially, it will be proved that an N-dense non-empty poset is K-dense if all cuts are finite.


Maximal Chain Infinite Chain Preceding Theorem Finiteness Property Causal Dependency 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1985

Authors and Affiliations

  • Helmut Plünnecke
    • 1
  1. 1.Gesellschaft für Mathematik und Datenverarbeitung Institut für Methodische GrundlagenSt. Augustin 1

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