High level tree transducers and iterated pushdown tree transducers

Abstract

n-level tree transducers (n≧0) combine the features ofn-level tree grammars and of top-down tree transducers in the sense that the derivations of the tree grammars are syntax-directed by input trees. For runningn, the sequence ofn-level tree transducers starts with top-down tree transducers (n=0) and macro tree transducers (n=1). In this paper the class of tree-to-tree translations computed byn-level tree transducers is characterized byn-iterated pushdown tree transducers. Such a transducer can be considered as a regular tree grammar of which the derivations are syntax-directed byn-iterated pushdowns of trees; ann-iterated pushdown of trees is a pushdown of pushdowns of ... of pushdowns (n times) of trees. In particular, we investigate the total deterministic case, which is relevant for syntax-directed semantics of programming languages.