Deciding Equivalence of Finite Tree Automata
Helmut Seidl · SIAM Journal on Computing · 1990
It is shown that for every constant m it can be decided in polynomial time whether or not two m-ambiguous finite tree automata are equivalent. In general, inequivalence for finite tree automata is DEXPTIME-complete with respect to logspace reductions, and PSPACE-complete with respect to logspace reductions, if the automata in question are supposed to accept only finite languages. For finite tree automata with weights in a field R, a polynomial time algorithm is presented for deciding ambiguity-equivalence, provided R-operations and R-tests for 0 can be performed in constant time. This result is used to construct an algorithm deciding ambiguity-inequivalence of finite tree automata in randomized polynomial time. Finally, for every constant m it is shown that it can be decided in polynomial time whether or not a given finite tree automaton is m-ambiguous.