On Typechecking Top-Down XML Tranformations: Fixed Input or Output   Schemas
  Typechecking consists of statically verifying whether the output of an XML transformation always conforms to an output type for documents satisfying a given input type. In this general setting, both the input and output schema as well as the transformation are part of the input for the problem. However, scenarios where the input or output schema can be considered to be fixed, are quite common in practice. In the present work, we investigate the computational complexity of the typechecking problem in the latter setting. 
Wim Martens, Frank Neven, and Marc Gyssens