Monotone AC-Tree Automata

We consider several questions about monotone AC-tree automata, a class of equational tree automata whose transition rules correspond to rules in Kuroda normal form of context-sensitive grammars. Whereas it has been proved that this class has a decision procedure to determine if, given a monotone AC-tree automaton, it accepts no terms, other important decidability or complexity results have not been well-investigated yet. In the paper, we prove that the membership problem for monotone AC-tree automata is PSPACE-complete. We then study the expressiveness of monotone AC-tree automata: precisely, we prove that the family of AC-regular tree languages is strictly subsumed in that of AC-monotone tree languages. The proof technique used in obtaining the above result yields the answers to two different questions, specifically that the family of monotone AC-tree languages is not closed under complementation, and that the inclusion problem for monotone AC-tree automata is undecidable.

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