In this thesis we introduce alpha and beta tree acceptors,
generalizations of tree automata. The alpha tree acceptors recognize
a tree by final symbol and the beta tree acceptors by final state. We
show that alpha and beta tree acceptors recognize the same sets of
Gorn trees and demonstrate that there are sets of Gorn trees not
recognizably by any alpha tree acceptor. The tree automata are
equivalent to the one state alpha tree acceptors. We show that the
languages of alpha tree acceptors are exactly those of matrix grammars
and the derivation trees of matrix grammars are recognized by
alpha tree acceptors. Finally we show that nondeterministic alpha
tree acceptors are no more powerful than deterministic alpha tree
acceptors
