Tree Automata with Generalized Transition Relations

Finite tree automata consist of a set of states and a set of transitions. Input trees are accepted if it is possible to label the tree with states such that the relationship between the state at every node and the state at its child nodes conforms to a transition. Thus, the transitions only define how a state must be labeled with respect to its children or vice versa. This work investigates how finite tree automata behave when transitions are made more expressive. Two extensions are considered: a new finite tree automaton model with transitions of arbitrary size and a model where a regular tree language defines the set of transitions. The first extension allows transitions in the shape of trees to have any size. The main difference to conventional tree automata is that larger transitions can overlap. Nevertheless, the new tree automaton model has the same expressive power as conventional tree automata models. The main challenge of the provided proof is eliminating overlappings. The second extension contains a separate tree automaton called the transition automaton. The language recognized by the transition automaton defines the set of transitions. Consequently, transitions are no longer bounded in size and amount. Nevertheless, this second tree automaton model is not more expressive than conventional models. A constructive proof is provided that uses a conventional tree automaton for simulating the extended tree automaton together with its transition automaton.