We modified our wrap1.aut based on the bridge verbs and subj-aux inversion automaton from the Wrapping of Trees paper. We attempted to make it more general and allow for a greater number of possible parsed sentences as well as adjusting the head for the 3-dimensional root. We came up with a couple new trees for testing which seemed to work.
Our trees now look like:
wrap1.tree
"Who does Alice think that Carol does like"
CP(~,~,CP[2](~,who[1](Cb(~,that[1](Y(~,does[1](VP(~,like[1](t,~,~),~),~,~),IP(~,Carol[1](Ib,~,~),~)),~,~),Cb[1](~,does[1](Y(~,t2[1](VP(~,think[1](Cb,~,~),~),~,~),IP(~,Alice[1](Ib,~,~),~)),~,~),~)),~,~),~))
wrap1.tree2
"does* Bob like Alice"
CP(~,~,Cb*[1](~,does*[1](Y(~,t2[1](VP(~,like[1](Alice(~,~,~),~,~),~),~,~),IP[0](~,Bob[1](Ib(~,~,~),~,~),~)),~,~),~)
wrap1.tree3
"Carol does like Alice"
CP(~,~,Y[0](~,does[1](VP(~,like[1](Alice(~,~,~),~,~),~),~,~),IP[0](~,Carol[1](Ib(~,~,~),~,~),~)))
And, here's the automaton file
wrap1.aut
3 0 ~
who DPwh ~
does I ~
like Vt ~
Alice DP ~
Carol DP ~
Bob DP ~
think Vb ~
t2 It ~
t DPt ~
Cb Cb ~
Ib Ib ~
VP VP ~
that C ~
CP CP ~
IP IP ~
Cb* Cb* ~
does* I* ~
CP @ CP[2](~,DPwh[1](Cb(~,C[1](Y(~,I[1](VP(~,Vt[1](DPt(~,~,~),~,~),~),~,~),~),~,~),~),~,~),~)
Cb Cb Cb[1](~,I[1](Y(~,It[1](VP(~,Vb[1](Cb(~,~,~),~,~),~),~,~),~),~,~),~)
Y Y IP[0](~,DP[1](Ib(~,~,~),~,~),~)
CP @ CP[2](~,DPwh[1](Cb*(~,I*[1](Y(~,It[1](VP(~,Vt[1](DPt(~,~,~),~,~),~),~,~),~),~,~),~),~,~),~)
CP @ Cb*[1](~,I*[1](Y(~,It[1](VP(~,Vt[1](DP(~,~,~),~,~),~),~,~),~),~,~),~)
CP @ Y[0](~,I[1](VP(~,Vt[1](DP(~,~,~),~,~),~),~,~),~)