The Translation Power of Top-Down Tree-to-Graph Transducers

We introduce a new syntax-directed translation device called top-down tree-to-graph transducer. Such transducers are very similar to the usual (total deterministic) top-down tree transducers except that the right-hand sides of their rules are hypergraphs rather than trees. Since we are aiming at a device which also allows us to translate trees into objects different from graphs, we focus our attention on so-called tree-generating top-down tree-to-graph transducers. Then the result of every computation is a hypergraph which represents a tree, and in its turn the tree can be interpreted in any algebra of appropriate signature. Although for both devices, top-down tree transducers and tree-generating top-down tree-to-graph transducers, the translation of a subtree of an input tree does not depend on its context, the latter transducers have much more transformational power than the former. In this paper we prove that tree-generating top-down tree-to-graph transducers are equivalent to (total deterministic) macro tree transducers, which are transducers for which the translation of a subtree may depend upon its context. We also prove that tree-generating top-down tree-to-graph transducers are closed under regular look-ahead. © 1994 Academic Press, Inc.