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I am trying to describe a novel type of DAG's construction algorithm (in computer science). The directed edges of the graph correspond to a partial ordering: i.e. any directed edge $e$ spanning from $f$ to $t$ also observes: $f \preceq t$.

Q: How can I precisely define the main task of edge construction: that is finding the node $f$ for a given $t$?

It is something like this:

find all $f_a \in \{ f_i \}$ s.t. $f_a \preceq t$ $\land \nexists f_j$ s.t. $f_i \preceq f_j$

but I'm not sure if this is sufficient or even understandable?

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  • $\begingroup$ Like a Hasse diagram of the poset? you want the notion of covering? en.wikipedia.org/wiki/Covering_relation $\endgroup$
    – Phicar
    Jan 23 at 11:09
  • $\begingroup$ The graph is a DAG where the edges are added according to a partial ordering of the nodes. It is not the goal to try to visualize the partial ordering using a pre-defined diagram. Maybe I should ask on the cs stackexchange instead :/ $\endgroup$
    – Domi
    Jan 23 at 11:50
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    $\begingroup$ Well, just give us an example, so we know what you are doing. The statement that you have is a little vague and, perhaps, we can help to formalize it. $\endgroup$
    – Phicar
    Jan 23 at 13:39
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    $\begingroup$ Ok, sounds like a en.wikipedia.org/wiki/Dependency_graph to me. Please edit the question when you can give us the "rule set". $\endgroup$
    – Phicar
    Jan 23 at 13:49
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    $\begingroup$ @MishaLavrov I agree. I also came to the conclusion that a short, concise "wordy" version might be more useful than an attempt at pseudo symbolism, or so I think... I will see as I draw up a concept graph etc. A few picture and examples can probably also aid the definition... Or so I hope $\endgroup$
    – Domi
    Jan 23 at 18:46

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