Satisfiability of XPath Queries with Sibling Axes

Journal of the ACM, 2008

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 the satisfiability analysis. We first study the problem for negationfree 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. Furthermore, we give a finer analysis of the problem for particular classes of DTDs, exploring the impact of various DTD constructs, identifying Extended abstracts [Benedikt et al. 2005; Geerts and Fan 2005] of this work were presented at the 24th 8:2 M. BENEDIKT ET AL.

This paper aims at finding a subclass of DTDs that covers many of the real-world DTDs while offering a polynomial-time complexity for deciding the XPath satisfiability problem. In our previous work, we proposed RW-DTDs, which cover most of the real-world DTDs (26 out of 27 real-world DTDs and 1406 out of 1407 DTD rules). However, under RW-DTDs, XPath satisfiability with only child, descendant-or-self, and sibling axes is tractable. In this paper, we propose MRW-DTDs, which are slightly smaller than RW-DTDs but have tractability on XPath satisfiability with parent axes or qualifiers. MRW-DTDs are a proper superclass of duplicate-free DTDs proposed by Montazerian et al., and cover 24 out of the 27 real-world DTDs and 1403 out of the 1407 DTD rules. Under MRW-DTDs, we show that XPath satisfiability problems with (1) child, parent, and sibling axes, and (2) child and sibling axes and qualifiers are both tractable, which are known to be intractable under RW-DTDs.

IEICE Transactions on Information and Systems, 2013

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.

2004

In this paper, we investigate the complexity of deciding the satisfiability of XPath 2.0 expressions, ie, whether there is an XML document for which their result is nonempty. Several fragments that allow certain types of expressions are classified as either in PTIME or NP-hard to see which type of expression make this a hard problem. Finally, we establish a link between XPath expressions and partial tree descriptions which are studied in computational linguistics.

2001

XPath is a W3C standard that plays a crucial role in several in uential query, transformation, and schema standards for XML. Motivated by the larger challenge of XML query optimization, we investigate the problem of containment of XPath expressions under integrity constraints that are in turn formulated with the help of XPath expressions. Our core formalism consists of a fragment of XPath that we call simple and a corresponding class of of integrity constraints that we call simple XPath integrity constraints (SXIC). SXIC's can express many database-style constraints, including key and foreign key constraints speci ed in the XML Schema standard proposal, as well as many constraints implied by DTDs. We identify a subclass of bounded SXIC's under which containment of simple XPath expressions is decidable, but we show that even modest use of unbounded SXIC's makes the problem undecidable. In particular, the addition of (unbounded) constraints implied by DTDs leads to undecidability.

2001

XPath is a W3C standard that plays a crucial role in several in uential query, transformation, and schema standards for XML. Motivated by the larger challenge of XML query optimization, we investigate the problem of containment of XPath expressions under integrity constraints that are in turn formulated with the help of XPath expressions. Our core formalism consists of a fragment of XPath that we call simple and a corresponding class of of integrity constraints that we call simple XPath integrity constraints (SXIC). SXIC's can express many database-style constraints, including key and foreign key constraints speci ed in the XML Schema standard proposal, as well as many constraints implied by DTDs. We identify a subclass of bounded SXIC's under which containment of simple XPath expressions is decidable, but we show that even modest use of unbounded SXIC's makes the problem undecidable. In particular, the addition of (unbounded) constraints implied by DTDs leads to undecidability.

2003

XML queries are usually expressed by means of XPath expressions identifying portions of the selected documents. An XPath expression defines a way of navigating an XML tree and returns the set of nodes which are reachable from one or more starting nodes through the paths specified by the expression. The problem of efficiently answering XPath queries is very interesting and has recently received increasing attention by the research community. In particular, an increasing effort has been devoted to define effective optimization techniques for XPath queries. One of the main issues related to the optimization of XPath queries is their minimization. The minimization of XPath queries has been studied for limited fragments of XPath, containing only the descendent, the child and the branch operators. In this work, we address the problem of minimizing XPath queries for a more general fragment, containing also the wildcard operator. We characterize the complexity of the minimization of XPath queries, stating that it is NP-hard, and propose an algorithm for computing minimum XPath queries. Moreover, we identify an interesting tractable case and propose an ad hoc algorithm handling the minimization of this kind of queries in polynomial time.

Proceedings of the twenty-sixth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems - PODS '07, 2007

Variables are the distinguishing new feature of XPath 2.0 which permits to select n-tuples of nodes in trees. It is known that the Core of XPath 2.0 captures n-ary first-order (FO) queries modulo linear time transformations. In this paper, we distinguish a fragment of Core XPath 2.0 that remains FO-complete with respect to n-ary queries while enjoying polynomial-time query answering.

Proceedings of the 12th International Conference on Extending Database Technology Advances in Database Technology - EDBT '09, 2009

The problem of rewriting a query using a materialized view is studied for a well known fragment of XPath that includes the following three constructs: wildcards, descendant edges and branches. In earlier work, determining the existence of a rewriting was shown to be coNP-hard, but no tight complexity bound was given. While it was argued that Σ p 3 is an upper bound, the proof was based on results that have recently been refuted. Consequently, the exact complexity (and even decidability) of this basic problem has been unknown, and there have been no practical rewriting algorithms if the query and the view use all the three constructs mentioned above. It is shown that under fairly general conditions, there are only two candidates for rewriting and hence, the problem can be practically solved by two containment tests. In particular, under these conditions, determining the existence of a rewriting is coNP-complete. The proofs utilize various novel techniques for reasoning about XPath patterns. For the general case, the exact complexity remains unknown, but it is shown that the problem is decidable.

2008

Abstract. In this paper we consider a powerful mechanism, called Regular XPath, for expressing queries and constraints over XML data, including DTDs and existential path constraints and their negation. Regular XPath extends XPath with binary relations over XML nodes specified by means two-way regular path queries. Our first contribution deals with checking satisfiability of Regular XPath constraints.