XPath is a language for navigating an XML document and selecting a set of element nodes. XPath expressions are used to query XML data, describe key constraints, express transformations, and reference elements in remote documents. This article studies the containment and equivalence problems for a fragment of the XPath query language, with applications in all these contexts. In particular, we study a class of XPath queries that contain branching, label wildcards and can express descendant relationships between nodes. Prior work has shown that languages that combine any two of these three features have efficient containment algorithms. However, we show that for the combination of features, containment is coNP-complete. We provide a sound and complete algorithm for containment that runs in exponential time, and study parameterized PTIME special cases. While we identify one parameterized class of queries for which containment can be decided efficiently, we also show that even with some bounded parameters, containment remains coNP-complete. In response to these negative results, we describe a sound algorithm that is efficient for all queries, but may return false negatives in some cases.

We study the satisfiability problem associated with XPath in the presence of DTDs. This is the problem of determining, given a query p in an XPath fragment and a DTD D, whether or not there exists an XML document T such that T conforms to D and the answer of p on T is nonempty. We consider a variety of XPath fragments widely used in practice, and investigate the impact of different XPath operators on satisfiability analysis. We first study the problem for negation-free XPath fragments with and without upward axes, recursion and data-value joins, identifying which factors lead to tractability and which to NP-completeness. We then turn to fragments with negation but without data values, establishing lower and upper bounds in the absence and in the presence of upward modalities and recursion. We show that with negation the complexity ranges from PSPACE to EXPTIME. Moreover, when both data values and negation are in place, we find that the complexity ranges from NEXPTIME to undecidable. Finally, we give a finer analysis of the problem for particular classes of DTDs, exploring the impact of various DTD constructs, identifying tractable cases, as well as providing the complexity in the query size alone. 1.

We study structural properties of each of the main sublanguages of XPath [8] commonly used in practice. First, we characterize the expressive power of these language fragments in terms of both logics and tree patterns. Second, we investigate closure properties, focusing on the ability to perform basic Boolean operations while remaining within the fragment. We give a complete picture of the closure properties of these fragments, treating XPath expressions both as functions of arbitrary nodes in a document tree, and as functions that are applied only at the root of the tree. Finally, we provide sound and complete axiom systems and normal forms for several of these fragments. These results are useful for simplification of XPath expressions and optimization of XML queries.

The prevalent use of XML highlights the need for a generic, flexible access-control mechanism for XML documents that supports efficient and secure query access, without revealing sensitive information to unauthorized users. This paper introduces a novel paradigm for specifying XML security constraints and investigates the enforcement of such constraints during XML query evaluation. Our approach is based on the novel concept of security views, which provide for each user group (a) an XML view consisting of all and only the information that the users are authorized to access, and (b) a view DTD that the XML view conforms to. Security views effectively protect sensitive data from access and potential inferences by unauthorized users, and provide authorized users with necessary schema information to facilitate effective query formulation and optimization. We propose an efficient algorithm for deriving security view definitions from security policies (defined on the original document DTD) for different user groups. We also develop novel algorithms for XPath query rewriting and optimization such that queries over security views can be efficiently answered without materializing the views. Our algorithms transform a query over a security view to an equivalent query over the original document, and effectively prune query nodes by exploiting the structural properties of the document DTD in conjunction with approximate XPath containment tests. Our work is the first to study a flexible, DTD-based access-control model for XML and its implications on the XML query-execution engine. Furthermore, it is among the first efforts for query rewriting and optimization in the presence of general DTDs for a rich class of XPath queries. An empirical study based on real-life DTDs verifies the ef...

The advent of XML as a universal exchange format, and of Web services as a basis for distributed computing, has fostered the apparition of a new class of documents: dynamic XML documents. These are XML documents where some data is given explicitly while other parts are given only intensionally by means of embedded calls to web services that can be called to generate the required information. By the sole presence of Web services, dynamic documents already include inherently some form of distributed computation. A higher level of distribution that also allows (fragments of) dynamic documents to be distributed and/or replicated over several sites is highly desirable in today's Web architecture, and in fact is also relevant for regular (non dynamic) documents.

Abstract. Research on information extraction from Web pages (wrapping) has seen much activity recently (particularly systems implementations), but little work has been done on formally studying the expressiveness of the formalisms proposed or on the theoretical foundations of wrapping. In this paper, we first study monadic datalog over trees as a wrapping language. We show that this simple language is equivalent to monadic second order logic (MSO) in its ability to specify wrappers. We believe that MSO has the right expressiveness required for Web information extraction and propose MSO as a yardstick for evaluating and comparing wrappers. Along the way, several other results on the complexity of query evaluation and query containment for monadic datalog over trees are established, and a simple normal form for this language is presented. Using the above results, we subsequently study the kernel fragment Elog − of the Elog wrapping language used in the Lixto system (a visual wrapper generator). Curiously, Elog − exactly captures MSO, yet is easier to use. Indeed, programs in this language can be entirely visually specified.

In this paper, we study the precise complexity of XPath 1.0 query processing. Even though heavily used by its incorporation into a variety of XML-related standards, the precise cost of evaluating an XPath query is not yet wellunderstood. The first polynomial-time algorithm for XPath processing (with respect to combined complexity) was proposed only recently, and even to this day all major XPath engines take time exponential in the size of the input queries. From the standpoint of theory, the precise complexity of XPath query evaluation is open, and it is thus unknown whether the query evaluation problem can be parallelized. In this work, we show that both the data complexity and the query complexity of XPath 1.0 fall into lower (highly parallelizable) complexity classes, but that the combined complexity is PTIME-hard. Subsequently, we study the sources of this hardness and identify a large and practically important fragment of XPath 1.0 for which the combined complexity is LOGCFL-complete and, therefore, in the highly parallelizable complexity class NC2.

Motivated by reasoning tasks for XML languages, the satisfiability problem of logics on data trees is investigated. The nodes of a data tree have a label from a finite set and a data value from a possibly infinite set. It is shown that satisfiability for two-variable first-order logic is decidable if the tree structure can be accessed only through the child and the next sibling predicates and the access to data values is restricted to equality tests. From this main result, decidability of satisfiability and containment for a data-aware fragment of XPath and of the implication problem for unary key and inclusion constraints is concluded.

Monadic query languages over trees currently receive considerable interest in the database community, as the problem of selecting nodes from a tree is the most basic and widespread database query problem in the context of XML. Partly a survey of recent work done by the authors and their group on logical query languages for this problem and their expressiveness, this paper provides a number of new results related to the complexity of such languages over so-called axis relations (such as "child" or "descendant") which are motivated by their presence in the XPath standard or by their utility for data extraction (wrapping).

We study the complexity and expressive power of conjunctive queries over unranked labeled trees, where the tree structures are represented using “axis relations” such as “child”, “descendant”, and “following” (we consider a superset of the XPath axes) as well as unary relations for node labels. (Cyclic) conjunctive queries over trees occur in a wide range of data management scenarios related to XML, the Web, and computational linguistics. We establish a framework for characterizing structures representing trees for which conjunctive queries can be evaluated efficiently. Then we completely chart the tractability frontier of the problem for our axis relations, i.e., we find all subsetmaximal sets of axes for which query evaluation is in polynomial time. All polynomial-time results are obtained immediately using the proof techniques from our framework. Finally, we study the expressiveness of conjunctive queries over trees and compare it to the expressive power of fragments of XPath. We show that for each conjunctive query, there is an equivalent acyclic positive query (i.e., a set of acyclic conjunctive queries), but that in general this query is not of polynomial size.