Frontiers of tractability for typechecking simple XML transformations

AbstractTypechecking consists of statically verifying whether the output of an XML transformation is always conform to an output type for documents satisfying a given input type. We focus on complete algorithms which always produce the correct answer. We consider top–down XML transformations incorporating XPath expressions and abstract document types by grammars and tree automata. By restricting schema languages and transformations, we identify several practical settings for which typechecking can be done in polynomial time. Moreover, the resulting framework provides a rather complete picture as we show that most scenarios cannot be enlarged without rendering the typechecking problem intractable. So, the present research sheds light on when to use fast complete algorithms and when to reside to sound but incomplete ones

Distributed XML Design

A distributed XML document is an XML document that spans several machines. We assume that a distribution design of the document tree is given, consisting of an XML kernel-document T[f1,...,fn] where some leaves are "docking points" for external resources providing XML subtrees (f1,...,fn, standing, e.g., for Web services or peers at remote locations). The top-down design problem consists in, given a type (a schema document that may vary from a DTD to a tree automaton) for the distributed document, "propagating" locally this type into a collection of types, that we call typing, while preserving desirable properties. We also consider the bottom-up design which consists in, given a type for each external resource, exhibiting a global type that is enforced by the local types, again with natural desirable properties. In the article, we lay out the fundamentals of a theory of distributed XML design, analyze problems concerning typing issues in this setting, and study their complexity.Comment: "56 pages, 4 figures

Flexible query processing of SPARQL queries

SPARQL is the predominant language for querying RDF data, which is the standard model for representing web data and more specifically Linked Open Data (a collection of heterogeneous connected data). Datasets in RDF form can be hard to query by a user if she does not have a full knowledge of the structure of the dataset. Moreover, many datasets in Linked Data are often extracted from actual web page content which might lead to incomplete or inaccurate data. We extend SPARQL 1.1 with two operators, APPROX and RELAX, previously introduced in the context of regular path queries. Using these operators we are able to support exible querying over the property path queries of SPARQL 1.1. We call this new language SPARQLAR. Using SPARQLAR users are able to query RDF data without fully knowing the structure of a dataset. APPROX and RELAX encapsulate different aspects of query flexibility: finding different answers and finding more answers, respectively. This means that users can access complex and heterogeneous datasets without the need to know precisely how the data is structured. One of the open problems we address is how to combine the APPROX and RELAX operators with a pragmatic language such as SPARQL. We also devise an implementation of a system that evaluates SPARQLAR queries in order to study the performance of the new language. We begin by defining the semantics of SPARQLAR and the complexity of query evaluation. We then present a query processing technique for evaluating SPARQLAR queries based on a rewriting algorithm and prove its soundness and completeness. During the evaluation of a SPARQLAR query we generate multiple SPARQL 1.1 queries that are evaluated against the dataset. Each such query will generate answers with a cost that indicates their distance with respect to the exact form of the original SPARQLAR query. Our prototype implementation incorporates three optimisation techniques that aim to enhance query execution performance: the first optimisation is a pre-computation technique that caches the answers of parts of the queries generated by the rewriting algorithm. These answers will then be reused to avoid the re-execution of those sub-queries. The second optimisation utilises a summary of the dataset to discard queries that it is known will not return any answer. The third optimisation technique uses the query containment concept to discard queries whose answers would be returned by another query at the same or lower cost. We conclude by conducting a performance study of the system on three different RDF datasets: LUBM (Lehigh University Benchmark), YAGO and DBpedia

Complexity of decision problems for simple regular expressions

We study the complexity of the inclusion, equivalence, and intersection problem for simple regular expressions arising in practical XML schemas. These basically consist of the concatenation of factors where each factor is a disjunction of strings possibly extended with ‘∗ ’ or ‘?’. We obtain lower and upper bounds for various fragments of simple regular expressions. Although we show that inclusion and intersection are already intractable for very weak expressions, we also identify some tractable cases. For equivalence, we only prove an initial tractability result leaving the complexity of more general cases open. The main motivation for this research comes from database theory, or more specifically XML and semi-structured data. We namely show that all lower and upper bounds for inclusion and equivalence, carry over to the corresponding decision problems for extended context-free grammars and single-type tree grammars, which are abstractions of DTDs and XML Schemas, respectively. For intersection, we show that the complexity only carries over for DTDs