In this paper, we consider the XPath satisfiability problem under restricted DTDs called “duplicate free”. For an XPath expression q and a DTD D, q is satisfiable under D if there exists an XML document t such that t is valid against D and that the answer of q on t is nonempty. Evaluating an unsatisfiable XPath expression is meaningless, since such an expression can always be replaced by an empty set without evaluating it. However, it is shown that the XPath satisfiability problem is intractable for a large number of XPath fragments. In this paper, we consider simple XPath fragments under two restrictions: (i) only a label can be specified as a node test and (ii) operators such as qualifier ([]) and path union (∪) are not allowed. We first show that, for some small XPath fragments under the above restrictions, the satisfiability problem is NP-complete under DTDs without any restriction. Then we show that there exist XPath fragments, containing the above small fragments, for which the satisfiability problem is in PTIME under duplicate-free DTDs.

Finding an appropriate data transformation between two schemas has been an important problem. In this paper, assuming that an update script between original and updated DTDs is available, we consider inferring a transformation algorithm from the original DTD and the update script such that the algorithm transforms each document valid against the original DTD into a document valid against the updated DTD. We first show a transformation algorithm inferred from a DTD and an update script. We next show a sufficient condition under which the transformation algorithm inferred from a DTD d and an update script is unambiguous, i.e., for any document t valid against d, elements to be deleted/inserted can unambiguously be determined. Finally, we show a polynomial-time algorithm for testing the sufficient condition.