I have written two three dimensional automata and provided tree strings for them. One is the automaton representing the grammar posted earlier on the blog. The other is a 3d adaptation of the balanced parenthesis automaton we used in the 2d recognizer.3
balparen3d.aut
-----------------
0 ~
[ L 0 0 0
] R 0 0 0
X S 0 0 0
S S X L R
S S S S S
Y Y X L X
Z Z X X R
S S X Y R
S S X L Z
3d.aut
--------
3
0 ~
Y 3 S B S
X 2 S Y C
S 1 S A X
S 0 S E 0
e E 0 0 0
a A 0 0 0
c C 0 0 0
b B 0 0 0