Tree transducers with external functions

Abstract

In this paper we investigate the computational power of particular tree transducers, viz., macro tree transducers and attributed tree transducers. The former tree transducers formalize the idea of syntax-directed translation, with the possibility of handling context; the latter tree transducers can serve as a formal model for the reduction semantics of attribute grammars. Here we generalize these tree transducers by allowing the invocation of external functions during the usual rewriting process. The main result of this paper is the characterization of macro tree transducers with external function calls in terms of attributed tree transducers with external function calls. Furthermore, such tree transducers with external function calls induce, in an obvious way, two operators on the set of all classes of tree functions. According to this point of view, we define two classes of tree functions inductively in the same way as the class PREC of primitive recursive tree functions, except that the closure under the scheme of primitive recursion is replaced by the closure under macro tree transducers with external function calls and attributed tree transducers with external function calls, respectively. As a second result of this paper we prove that these two classes are equal to PREC.