Validity of Tree Pattern Queries with Respect to Schema Information.

We prove that various containment and validity problems for tree pattern queries with respect to a schema are EXPTIME-complete. When one does not require the root of a tree pattern query to match the root of a tree, validity of a non-branching tree pattern query with respect to a Relax NG schema or W3C XML Schema is already EXPTIME-hard when the query does not branch and uses only child axes. These hardness results already hold when the alphabet size is fixed. Validity with respect to a DTD is proved to be EXPTIME-hard already when the query only uses child axes and is allowed to branch only once.