2003 | OriginalPaper | Buchkapitel
Recognizing Boolean Closed A-Tree Languages with Membership Conditional Rewriting Mechanism
verfasst von : Hitoshi Ohsaki, Hiroyuki Seki, Toshinori Takai
Erschienen in: Rewriting Techniques and Applications
Verlag: Springer Berlin Heidelberg
Enthalten in: Professional Book Archive
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This paper provides an algorithm to compute the complement of tree languages recognizable with A-TA (tree automata with associativity axioms [16]). Due to this closure property together with the previously obtained results, we know that the class is boolean closed, while keeping recognizability of A-closures of regular tree languages. In the proof of the main result, a new framework of tree automata, called sequence-tree automata, is introduced as a generalization of Lugiez and Dal Zilio’s multi-tree automata [14] of an associativity case. It is also shown that recognizable A-tree languages are closed under a one-step rewrite relation in case of ground A-term rewriting. This result allows us to compute an under-approximation of A-rewrite descendants of recognizable A-tree languages with arbitrary accuracy.