Data exchange is the problem of finding an instance of a target schema, given an instance of a source schema and a specification of the relationship between the source and the target. Theoretical foundations of data exchange have recently been investigated for relational data. In this paper, we start looking into the basic properties of XML data exchange, that is, restructuring of XML documents that conform to a source DTD under a target DTD, and answering queries written over the target schema. We define XML data exchange settings in which source-totarget dependencies refer to the hierarchical structure of the data. Combining DTDs and dependencies makes some XML data exchange settings inconsistent. We investigate the consistency problem and determine its exact complexity. We then move to query answering, and prove a dichotomy theorem that classifies data exchange settings into those over which query answering is tractable, and those over which it is coNP-complete, depending on classes of regular expressions used in DTDs. Furthermore, for all tractable cases we give polynomial-time algorithms that compute target XML documents over which queries can be answered. 1.

Abstract. We give two sufficient conditions on XPath like languages for having first order expressivity, meaning that every first order definable set of paths in an ordered node-labeled tree is definable in that XPath language. They are phrased in terms of expansions of navigational (sometimes called “Core”) XPath. Adding either complementation, or the more elegant conditional paths is sufficient. A conditional path is an axis relation of the form (one step axis::n[F]) +, denoting the transitive closure of the relation expressed by one step axis::n[F]. As neither is expressible in navigational XPath we also give characterizations in terms of first order logic of the answer sets and the sets of paths navigational XPath can define. The first in terms of a suitable two variable fragment, the second in terms of unions of conjunctive queries. 1

Abstract. XPath 1.0 is a variable free language designed to specify paths between nodes in XML documents. Such paths can alternatively be specified in first-order logic. The logical abstraction of XPath 1.0, usually called Navigational or Core XPath, is not powerful enough to express every first-order definable path. In this paper we show that there exists a natural expansion of Core XPath in which every first-order definable path in XML document trees is expressible. This expansion is called Conditional XPath. It contains additional axis relations of the form (child::n[F])+, denoting the transitive closure of the path expressed by child::n[F]. The difference with XPath’s descendant::n[F] is that the path (child::n[F])+ is conditional on the fact that all nodes in between should be labeled by n and should make the predicate F true. This result can be viewed as the XPath analogue of the expressive completeness of the relational algebra with respect to first-order logic. 1

We present the Lixto project, which is both a research project in database theory and a commercial enterprise that develops Web data extraction (wrapping) and Web service definition software. We discuss the project's main motivations and ideas, in particular the use of a logic-based framework for wrapping. Then we present theoretical results on monadic datalog over trees and on Elog, its close relative which is used as the internal wrapper language in the Lixto system. These results include both a characterization of the expressive power and the complexity of these languages. We describe the visual wrapper specification process in Lixto and various practical aspects of wrapping. We discuss work on the complexity of query languages for trees that was inseminated by our theoretical study of logic-based languages for wrapping. Then we return to the practice of wrapping and the Lixto Transformation Server, which allows for streaming integration of data extracted from Web pages. This is a natural requirement in complex services based on Web wrapping. Finally, we discuss industrial applications of Lixto and point to open problems for future study.

As a simple XML query language but with enough expressive power, XPath has become very popular. To expedite evaluation of XPath queries, we consider the problem of rewriting XPath queries using materialized XPath views. This problem is very important and arises not only from query optimization in server side but also from semantic caching in client side. We consider the problem of deciding whether there exists a rewriting of a query using XPath views and the problem of finding minimal rewritings. We first consider those two problems for a very practical XPath fragment containing the descendent, child, wildcard and branch features. We show that the rewriting existence problem is coNP-hard and the problem of finding minimal rewritings is 3 . We also consider those two rewriting problems for three subclasses of this XPath fragment, each of which contains child feature and two of descendent, wildcard and branch features, and show that both rewriting problems can be polynomially solved. Finally, we give an algorithm for finding minimal rewritings, which is sound for the XPath fragment, but is also complete and runs in polynomial time for its three subclasses.

The logical foundations of the standard web ontology languages are provided by expressive Description Logics (DLs), such as SHIQ and SHOIQ. In the Semantic Web and other domains, ontologies are increasingly seen also as a mechanism to access and query data repositories. This novel context poses an original combination of challenges that has not been addressed before: (i) sufficient expressive power of the DL to capture common data modelling constructs; (ii) well established and flexible query mechanisms such as those inspired by database technology; (iii) optimisation of inference techniques with respect to data size, which typically dominates the size of ontologies. This calls for investigating data complexity of query answering in expressive DLs. While the complexity of DLs has been studied extensively, few tight characterisations of data complexity were available, and the problem was still open for most DLs of the SH family and for standard query languages like conjunctive queries and their extensions. We tackle this issue and prove a tight coNP upper bound for positive existential queries without transitive roles in SHOQ, SHIQ,andSHOI. We thus establish that, for a whole range of sublogics of SHOIQ that contain AL, answering such queries has coNP-complete

This survey gives an overview of formal results on the XML query language XPath. We identify several important fragments of XPath, focusing on subsets of XPath 1.0. We then give results on the expressiveness of XPath and its fragments compared to other formalisms for querying trees, algorithms and complexity bounds for evaluation of XPath queries, and static analysis of XPath queries.

This paper describes a method for transforming any given set of Datalog rules into an efficient specialized implementation with guaranteed worst-case time and space complexities, and for computing the complexities from the rules. The running time is optimal in the sense that only useful combinations of facts that lead to all hypotheses of a rule being simultaneously true are considered, and each such combination is considered exactly once. The associated space usage is optimal in that it is the minimum space needed for such consideration modulo scheduling optimizations that may eliminate some summands in the space usage formula. The transformation is based on a general method for algorithm design that exploits fixed-point computation, incremental maintenance of invariants, and combinations of indexed and linked data structures. We apply the method to a number of analysis problems, some with improved algorithm complexities and all with greatly improved algorithm understanding and greatly simplified complexity analysis.

We give semantic characterizations of the expressive power of navigational XPath (a.k.a. Core XPath) in terms of first order logic. XPath can be used to specify sets of nodes and sets of paths in an XML document tree. We consider both uses. For sets of nodes, XPath is equally expressive as first order logic in two variables. For paths, XPath can be defined using four simple connectives, which together yield the class of first order definable relations which are safe for bisimulation. Furthermore, we give a characterization of the XPath expressible paths in terms of conjunctive queries. 1

(full version, including appendices, of the PODS’07 paper)