We have implemented an embed function which converts d-dimensional n-branching automata into d-dimensional 2-branching automata. This may be useful to simplify deduction rules for CKY as well as creating a method of accessing rules in the automaton. We tested this using rec and project on automaton and trees from the Wrapping of Trees paper.
wrap1.aut
3 0 ~
who DPi ~
does I ~
does2 Ij ~
like V ~
Alice DP ~
Carol DP ~
think V ~
t2 Ij ~
t DPi ~
Cb Cb ~
Ib Ib ~
VP VP ~
that C ~
CP CP ~
IP IP ~
S S CP(~,DPi[1](Cb(~,C[1](Y(~,I[1](VP(~,V[1](DPi(~,~,~),~,~),~),~,~),~),~,~),~),~,~),~)
Cb Cb Cb(~,Ij[1](Y(~,Ij[1](VP(~,V[1](Cb(~,~,~),~,~),~),~,~),~),~,~),~)
Y Y IP(~,DP[1](Ib(~,~,~),~,~),~)
after using the embed() function:
wrap1.embed.aut
3 0 ~
does2 Ij ~
like V ~
that C ~
does I ~
IP IP ~
Alice DP ~
who DPi ~
Cb Cb ~
CP CP ~
Ib Ib ~
think V ~
Carol DP ~
t DPi ~
VP VP ~
t2 Ij ~
Cb' Cb' Cb[0](~,C[1](Y'[0](~,~,~),~,~),~)
VP' VP' VP[0](~,V[1](DPi[0](~,~,~),~,~),~)
Y Y IP[0](~,DP[1](Ib[0](~,~,~),~,~),~)
S S CP[0](~,DPi[1](Cb'[0](~,~,~),~,~),~)
VP' VP' VP[0](~,V[1](Cb[0](~,~,~),~,~),~)
Y' Y' Y[0](~,Ij[1](VP'[0](~,~,~),~,~),~)
Cb Cb Cb[0](~,Ij[1](Y'[0](~,~,~),~,~),~)
Y' Y' Y[0](~,I[1](VP'[0](~,~,~),~,~),~)
wrap2.aut
4
0 ~
that C ~
Alice DP ~
does I ~
like V ~
Bob DP ~
seem V ~
it DP ~
Y Y ~
CP CP ~
Cb Cb ~
IP IP ~
Ib Ib ~
DP DP ~
VP VP ~
S S ~
T T S(~,~,CP[2](~,DP[1](Cb(~,C[1](Y(~,I[1](VP(~,V[1](DP,~,~,~),~,~),~,~,~),IP[0](~,DP[1](Ib,~,~,~),~,~),~),~,~,~),~,~),~,~,~),~,~),~)
Cb Cb Cb(~,~,Cb[3](~,DP[1](Y(~,I[1](VP(~,V[1](Cb,~,~,~),~,~),~,~,~),IP[0](~,DP[1](Ib,~,~,~),~,~),~),~,~,~),~,~),~)
after embed():
wrap2.embed.aut
4
0 ~
tau tau ~
Y'' Y'' Y'[0](~,~,IP[0](~,DP[1](Ib[0](~,~,~,~),~,~,~),~,~),~)
does I ~
Y'' Y'' Y'[0](~,~,IP[0](~,DP[1](Ib[0](~,~,~,~),~,~,~),~,~),~)
Cb' Cb' tau[0](~,~,Cb[0](~,C[1](Y''[0](~,~,~,~),~,~,~),~,~),~)
T T S[0](~,~,CP[1](~,DP[1](Cb'[0](~,~,~,~),~,~,~),~,~),~)
like V ~
DP DP ~
that C ~
Cb Cb ~
VP VP ~
IP IP ~
VP' VP' tau[0](~,~,VP[0](~,V[1](DP[0](~,~,~,~),~,~,~),~,~),~)
Alice DP ~
S S ~
Cb Cb Cb[0](~,~,Cb[1](~,DP[1](Y''[0](~,~,~,~),~,~,~),~,~),~)
Bob DP ~
Y' Y' tau[0](~,~,Y[0](~,I[1](VP'[0](~,~,~,~),~,~,~),~,~),~)
it DP ~
seem V ~
Y' Y' tau[0](~,~,Y[0](~,I[1](VP'[0](~,~,~,~),~,~,~),~,~),~)
Y Y ~
VP' VP' tau[0](~,~,VP[0](~,V[1](Cb[0](~,~,~,~),~,~,~),~,~),~)
CP CP ~
Ib Ib ~