11 Encoding second order string ACG with deterministic tree walking transducers

In this paper we study the class of string languages represen ted by second order Abstract Categorial Grammar. We prove that this class is the sa me as the class of output languages of determistic tree walking automata. Together w ith the result of de Groote and Pogodalla (2004) this shows that the higher-order opera tions involved in the definition of second order ACGs can always be represented by oper ations that are at most fourth order.

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