Helmut Seidl. **On the Finite Degree of Ambiguity of Finite Tree Automata**. *Acta Inf.*, 26(6):527-542, 1989.

The degree of ambiguity of a finite tree automaton , da(), is the maximal number of different accepting computations of for any possible input tree. We show: it can be decided in polynomial time whether or not da(). We give two criteria characterizing an infinite degree of ambiguity and derive the following fundamental properties of an finite tree automaton with states and rank having a finite degree of ambiguity: for every input tree there is a input tree of depth less than ! having the same number of accepting computations; the degree of ambiguity of is bounded by .