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Deciding equivalence of finite tree automata. (English) Zbl 0699.68075

Summary: 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.

MSC:

68Q25 Analysis of algorithms and problem complexity
68Q45 Formal languages and automata
68Q70 Algebraic theory of languages and automata
20M35 Semigroups in automata theory, linguistics, etc.
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