July 20, 2004
Projections and Rec
We have completed code to implement an n-dimensional tree recognizer which now takes heads into account. We also have coded a projection algorithm which converts an n-dimensional headed tree into an (n-1)-dimensional headed tree. Here are some examples:
Original 3d tree:
S(~,~,S(~,e(~,~,~),S(~,a[1](X(~,~,S(~,Y(c(~,~,~),~,S(~,b[1](S(~,~,~),~,~),S(~,a[1](X(~,~,S(~,Y(c(~
,~,~),~,S(~,b[1](S(~,~,~),~,~),S(~,a[1](X(~,~,S(~,Y(c(~,~,~),~,S(~,b[1](S(~,~,~),~,~),~)),~)),~,~),~))
),~)),~,~),~))),~)),~,~),S(~,a[1](X(~,~,S(~,Y(c(~,~,~),~,S(~,b[1](S(~,~,~),~,~),~)),~)),~,~),~))))
1-d (string) projection:
a0[1](b0[0](a0[0](a0[0](a0[0](b0[0](b0[0](b0[0](e0[0](c0[0](c0[0](c0[0](c0[0](~)))))))))))))
And the n-dimensional recognizer output using the example tree and automaton from our original attempt at an n-dimensional recognizer:
SF[0](~,~,SS[0](~,eE[0](~,~,~),SS[0](~,aA[1](XX[0](~,~,SS[0](~,YY[0](cC[0](~,~,~),~,SS[0](~,bB[1]
(SS[0](~,~,~),~,~),SS[0](~,aA[1](XX[0](~,~,SS[0](~,YY[0](cC[0](~,~,~),~,SS[0](~,bB[1](SS[0](~,~,~)
,~,~),SS[0](~,aA[1](XX[0](~,~,SS[0](~,YY[0](cC[0](~,~,~),~,SS[0](~,bB[1](SS[0](~,~,~),~,~),~)),~)),~
,~),~))),~)),~,~),~))),~)),~,~),SS[0](~,aA[1](XX[0](~,~,SS[0](~,YY[0](cC[0](~,~,~),~,SS[0](~,bB[1]
(SS[0](~,~,~),~,~),~)),~)),~,~),~))))
