Deciding Equivalence of Finite Tree Automata

We s h o w : f o r mJe~j constant m i t can be decided i n p o l y n o m i a l t ime whether or not two m-ambiguous finite tree automata are equivalent. In general, inequivalence for finite tree automata is DEXPTIfdE-complete v).r.t, logspace reductions, and PSPACE-complete w.r.t, logspace reductions, i f the automata in question are supposed to accept only finite languages. For finite tree automata u i t h coefficients in a field R we give a polynomial time algorithm for deciding ambiguity-equivalence provided R-operations and R-tests for 0 can be perfor,ned in constant time. We apply this algorithm for deciding ambiguityinequivalence of f inite tree automata in randomized polynomial time. FUrthermore, for every constant m we show that it can be decided in polynomial time whether or not a given finite tree automaton is m-ambiguous.