Abstract
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.
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Plünnecke, H. (1985). K-density, N-density, and finiteness properties. In: Rozenberg, G. (eds) Advances in Petri Nets 1984. Lecture Notes in Computer Science, vol 188. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-15204-0_22
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DOI: https://doi.org/10.1007/3-540-15204-0_22
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