Decidability and Closure Properties of Equational Tree Languages

Authors:
Hitoshi Ohsaki;Toshinori Takai
Affiliations:
-;-
Venue:
RTA '02 Proceedings of the 13th International Conference on Rewriting Techniques and Applications
Year:
2002

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Abstract

Equational tree automata provide a powerful tree language framework that facilitates to recognize congruence closures of tree languages. In the paper we show the emptiness problem for AC-tree automata and the intersection-emptiness problem for regular AC-tree automata, each of which was open in our previous work, are decidable, by a straightforward reduction to the reachability problem for ground AC-term rewriting. The newly obtained results generalize decidability of so-called reachable property problem of Mayr and Rusinowitch. We then discuss complexity issue of AC-tree automata. Moreover, in order to solve some other questions about regular A- and AC-tree automata, we recall the basic connection between word languages and tree languages.