We present an algorithm to solve XPath decision problems under regular tree type constraints and show its use to statically type-check XPath queries. To this end, we prove the decidability of a logic with converse for finite ordered trees whose time complexity is a simple exponential of the size of a formula. The logic corresponds to the alternation free modal µ-calculus without greatest fixpoint, restricted to finite trees, and where formulas are cycle-free. Our proof method is based on two auxiliary results. First, XML regular tree types and XPath expressions have a linear translation to cycle-free formulas. Second, the least and greatest fixpoints are equivalent for finite trees, hence the logic is closed under negation. Building on these results, we describe a practical, effective system for solving the satisfiability of a formula. The system has been experimented with some decision problems such as XPath emptiness, containment, overlap, and coverage, with or without type constraints. The benefit of the approach is that our system can be effectively used in static analyzers for programming languages

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.

Abstract not found

On an abstract level, XML Schema increases the limited expressive power of Document Type Definitions (DTDs) by extending them with a recursive typing mechanism. However, an investigation of the XML Schema Definitions (XSDs) occurring in practice reveals that the vast majority of them are structurally equivalent to DTDs. This might be due to the complexity of the XML Schema specification and the difficulty to understand the effect of constraints on typing and validation of schemas. To shed some light on the actual expressive power of XSDs this paper studies the impact of the Element Declarations Consistent (EDC) and the Unique Particle Attribution (UPA) rule. An equivalent formalism based on contextual patterns rather than on recursive types is proposed which might serve as a light-weight front end for XML Schema. Finally, the effect of EDC and UPA on the way XML documents can be typed is discussed. It is argued that a cleaner, more robust, stronger but equally efficient class is obtained by replacing these constraints with the notion of 1-pass preorder typing: schemas that allow to determine the type of an element of a streaming document when its opening tag is met. This notion can be defined in terms of restrained competition regular expressions and there is again an equivalent syntactical formalism based on contextual patterns. 1.

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

Abstract. We study the satisfiability problem for XPath fragments supporting the following-sibling and preceding-sibling axes. Although this problem was recently studied for XPath fragments without sibling axes, little is known about the impact of the sibling axes on the satisfiability analysis. To this end we revisit the satisfiability problem for a variety of XPath fragments with sibling axes, in the presence of DTDs, in the absence of DTDs, and under various restricted DTDs. In these settings we establish complexity bounds ranging from NLOGSPACE to undecidable. Our main conclusion is that in many cases, the presence of sibling axes complicates the satisfiability analysis. Indeed, we show that there are XPath satisfiability problems that are in PTIME and PSPACE in the absence of sibling axes, but that become NP-hard and EXPTIME-hard, respectively, when sibling axes are used instead of the corresponding vertical modalities (e.g., the wildcard and the descendant axis). 1

This survey article introduces into the essential concepts and methods underlying rule-based query languages. It covers four complementary areas: declarative semantics based on adaptations of mathematical logic, operational semantics, complexity and expressive power, and optimisation of query evaluation. The treatment of these areas is foundation-oriented, the foundations having resulted from over four decades of research in the logic programming and database communities on combinations of query languages and rules. These results have later formed the basis for conceiving, improving, and implementing several Web and Semantic Web technologies, in particular query languages such as XQuery or SPARQL for querying relational, XML, and RDF data, and rule languages like the “Rule Interchange Framework (RIF) ” currently being developed in a working group of the W3C. Coverage of the article is deliberately limited to declarative languages in a classical setting: issues such as query answering in F-Logic or in description logics, or the relationship of query answering to reactive rules and events, are not addressed.

XPath is the standard language for navigating XML documents and returning a set of matching nodes. We present a sound and complete decision procedure for containment of XPath queries, as well as other related XPath decision problems such as satisfiability, equivalence, overlap, and coverage. The considered XPath fragment covers most of the language features used in practice. Specifically, we propose a unifying logic for XML, namely, the alternation-free modal μ-calculus with converse. We show how to translate major XML concepts such as XPath and regular XML types (including DTDs) into this logic. Based on these embeddings, we show how XPath decision problems, in the presence or absence of XML types, can be solved using a decision procedure for μ-calculus satisfiability. We provide a complexity analysis of our system together with practical experiments to illustrate the efficiency of the approach for realistic scenarios.

We show that problems arising in static analysis of XML specifications and transformations can be dealt with using techniques similar to those developed for static analysis of programs. Many properties of interest in the XML context are related to navigation, and can be formulated in temporal logics for trees. We choose a logic that admits a simple single-exponential translation into unranked tree automata, in the spirit of the classical LTL-to-Büchi automata translation. Automata arising from this translation have a number of additional properties; in particular, they are convenient for reasoning about unary node-selecting queries, which are important in the XML context. We give two applications of such reasoning: one deals with a classical XML problem of reasoning about navigation in the presence of schemas, and the other relates to verifying security properties of XML views.

In this paper we present Regular XPath (RXPath), which is a natural extension of XPath with regular expressions over paths that has the same computational properties as XPath: linear-time query evaluation and exponential-time reasoning. To establish these results, we devise a unifying automata-theoretic framework based on two-way weak alternating tree automata. Specifically, we consider automata that have infinite runs on finite trees. This enables us to leverage and simplify existing automata-theoretic machinery and develop algorithms both for query evaluation and for reasoning over queries. With respect to the latter problem, we consider RXPath as a constraint language, and study constraint satisfiability, and query satisfiability and containment under constraints in the setting of RXPath.