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# Can our parser parse any projective dependency tree?

#1

A counterexample would be if in the first example, Nadia pointed to dexterity instead of with. Obviously that’s not the correct parse of the sentence, but a sentence like that could exist (or maybe it couldn’t and no similar situation can occur and this is moot). In that situation, rode’s child is Nadia, but it can’t remove Nadia until Nadia removes dexterity, which can’t happen while rode is in between them. However, there is no crossing of edges when drawn out.

#2

graph is projective. Informally, this means no crossed lines
in the dependency graph.
More formally, if i -> j and j -> k, then:
if i > j (left-ark), i > k
if i < j (right-ark), i < k

#3

The graph you described is not projective. @despresf gave the correct, formal definition.

It’s not immediately obvious why the graph you described isn’t projective because none of the edges cross. But remember that you need to consider the sentence including ROOT. Add ROOT in and you won’t be able to do what you’re suggesting without crossing edges.