The use of tree transducers to compute translations between graph algebras

Abstract

The power of top-down, bottom-up, and tree-to-graph- to-tree transducers (tgt transducers) to compute translations from hyperedge-replacement algebras into edge-replacement algebras is investigated. Compositions of top-down and bottom-up tree transducers are too weak if the operations in the target algebra are powerful enough to define all series-parallel graphs, 2-trees, or related types of graphs. Tgt transducers are shown to be more powerful. These are able to compute translations into ER algebras whose operations are so-called 2tree* operations, which are generalizations of the well-known operations to generate 2-trees.