Typechecking Top-Down Uniform Unranked Tree Transducers

We investigate the typechecking problem for XML queries: statically verifying that every answer to a query conforms to a given output schema, for inputs satisfying a given input schema. As typechecking quickly turns undecidable for query languages capable of testing equality of data values, we return to the limited framework where we abstract XML documents as labeled ordered trees. We focus on simple top-down recursive transformations motivated by XSLT and structural recursion on trees. We parameterize the problem by several restrictions on the transformations (deleting, non-deleting, bounded width) and consider both tree automata and DTDs as output schemas. The complexity of the typechecking problems in this scenario range from ptime to exptime.