XPath Query Satisfiability is in PTIME for Real-World DTDs

The problem of XPath query satisfiability under DTDs (Document Type Definitions) is to decide, given an XPath query p and a DTD D, whether or not there is some document valid with respect to D on which p returns a nonempty result. Recent studies in the literature have shown the problem to be NP-hard or worse for most fragments of XPath. However, in this paper we show that the satisfiability problem is in PTIME for most DTDs used in real-world applications. Firstly, we report on the details of our investigation of real-world DTDs and define two properties that they typically satisfy: being duplicate-free and being covering. Then we concentrate on the satisfiability problem of XPath queries under such DTDs. We obtain a number of XPath fragments for which the complexity of the satisfiablity problem reduces to PTIME when such real-world DTDs are used.