Complexity of data tree patterns over XML documents

We consider Boolean combinations of data tree patterns as a specification and query language for XML documents. Data tree patterns are tree patterns plus variable (in)equalities which express joins between attribute values. Data tree patterns are a simple and natural formalism for expressing properties of XML documents. We consider first the model checking problem (query evaluation), we show that it, is DP-complete(1) in general and already NP-complete when we consider a, single pattern. We then consider the satisfiability problem in the presence of a DTD. We show that it is in general undecidable and we identify several decidable fragments.