An Inflationary Fixed Point Operator in XQuery

We introduce a controlled form of recursion in XQuery, inflationary fixed points, familiar in the context of relational databases. This imposes restrictions on the expressible types of recursion, but we show that inflationary fixed points nevertheless are sufficiently versatile to capture a wide range of interesting use cases, including the semantics of Regular XPath and its core transitive closure construct. While the optimization of general user-defined recursive functions in XQuery appears elusive, we will describe how inflationary fixed points can be efficiently evaluated, provided that the recursive XQuery expressions exhibit a distributivity property. We show how distributivity can be assessed both, syntactically and algebraically, and provide experimental evidence that XQuery processors can substantially benefit during inflationary fixed point evaluation.Comment: 11 pages, 10 figures, 2 table

Alternating register automata on finite words and trees

We study alternating register automata on data words and data trees in relation to logics. A data word (resp. data tree) is a word (resp. tree) whose every position carries a label from a finite alphabet and a data value from an infinite domain. We investigate one-way automata with alternating control over data words or trees, with one register for storing data and comparing them for equality. This is a continuation of the study started by Demri, Lazic and Jurdzinski. From the standpoint of register automata models, this work aims at two objectives: (1) simplifying the existent decidability proofs for the emptiness problem for alternating register automata; and (2) exhibiting decidable extensions for these models. From the logical perspective, we show that (a) in the case of data words, satisfiability of LTL with one register and quantification over data values is decidable; and (b) the satisfiability problem for the so-called forward fragment of XPath on XML documents is decidable, even in the presence of DTDs and even of key constraints. The decidability is obtained through a reduction to the automata model introduced. This fragment contains the child, descendant, next-sibling and following-sibling axes, as well as data equality and inequality tests

Satisfiability of Downward XPath with Data Equality Tests

International audienceIn this work we investigate the satisfiability problem for the logic XPath(↓*, ↓, =), that includes all downward axes as well as equality and inequality tests. We address this problem in the absence of DTDs and the sibling axis. We prove that this fragment is decidable, and we nail down its complexity, showing the problem to be ExpTime-complete. The result also holds when path expressions allow closure under the Kleene star operator. To obtain these results, we introduce a new automaton model over data trees that captures XPath(↓*, ↓, =) and has an ExpTime emptiness problem. Furthermore, we give the exact complexity of several downward-looking fragments

Web and Semantic Web Query Languages

A number of techniques have been developed to facilitate powerful data retrieval on the Web and Semantic Web. Three categories of Web query languages can be distinguished, according to the format of the data they can retrieve: XML, RDF and Topic Maps. This article introduces the spectrum of languages falling into these categories and summarises their salient aspects. The languages are introduced using common sample data and query types. Key aspects of the query languages considered are stressed in a conclusion

Model Theory of XPath on Data Trees: Part I: Bisimulation and Characterization

We investigate model theoretic properties of XPath with data (in)equality tests over the class of data trees, i.e., the class of trees where each node contains a label from a finite alphabet and a data value from an infinite domain.We provide notions of (bi)simulations for XPath logics containing the child, descendant, parent and ancestor axes to navigate the tree. We show that these notions precisely characterize the equivalence relation associated with each logic. We study formula complexity measures consisting of the number of nested axes and nested subformulas in a formula; these notions are akin to the notion of quantifier rank in first-order logic. We show char- acterization results for fine grained notions of equivalence and (bi)simulation that take into account these complexity measures. We also prove that positive fragments of these logics correspond to the formulas preserved under (non-symmetric) simulations. We show that the logic including the child axis is equivalent to the fragment of first-order logic invariant under the corresponding notion of bisimulation. If upward navigation is allowed the characterization fails but a weaker result can still be established. These results hold both over the class of possibly infinite data trees and over the class of finite data trees.Besides their intrinsic theoretical value, we argue that bisimulations are useful tools to prove (non)expressivity results for the logics studied here, and we substantiate this claim with examples.Fil: Figueira, Diego. Centre National de la Recherche Scientifique; FranciaFil: Figueira, Santiago. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; ArgentinaFil: Areces, Carlos Eduardo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentin

Relative Expressive Power of Navigational Querying on Graphs

Motivated by both established and new applications, we study navigational query languages for graphs (binary relations). The simplest language has only the two operators union and composition, together with the identity relation. We make more powerful languages by adding any of the following operators: intersection; set difference; projection; coprojection; converse; and the diversity relation. All these operators map binary relations to binary relations. We compare the expressive power of all resulting languages. We do this not only for general path queries (queries where the result may be any binary relation) but also for boolean or yes/no queries (expressed by the nonemptiness of an expression). For both cases, we present the complete Hasse diagram of relative expressiveness. In particular the Hasse diagram for boolean queries contains some nontrivial separations and a few surprising collapses.Comment: An extended abstract announcing the results of this paper was presented at the 14th International Conference on Database Theory, Uppsala, Sweden, March 201

A General Approach for Securely Querying and Updating XML Data

Over the past years several works have proposed access control models for XML data where only read-access rights over non-recursive DTDs are considered. A few amount of works have studied the access rights for updates. In this paper, we present a general model for specifying access control on XML data in the presence of update operations of W3C XQuery Update Facility. Our approach for enforcing such updates specifications is based on the notion of query rewriting where each update operation defined over arbitrary DTD (recursive or not) is rewritten to a safe one in order to be evaluated only over XML data which can be updated by the user. We investigate in the second part of this report the secure of XML updating in the presence of read-access rights specified by a security views. For an XML document, a security view represents for each class of users all and only the parts of the document these users are able to see. We show that an update operation defined over a security view can cause disclosure of sensitive data hidden by this view if it is not thoroughly rewritten with respect to both read and update access rights. Finally, we propose a security view based approach for securely updating XML in order to preserve the confidentiality and integrity of XML data.Comment: No. RR-7870 (2012

Complete Axiomatizations of Fragments of Monadic Second-Order Logic on Finite Trees

We consider a specific class of tree structures that can represent basic structures in linguistics and computer science such as XML documents, parse trees, and treebanks, namely, finite node-labeled sibling-ordered trees. We present axiomatizations of the monadic second-order logic (MSO), monadic transitive closure logic (FO(TC1)) and monadic least fixed-point logic (FO(LFP1)) theories of this class of structures. These logics can express important properties such as reachability. Using model-theoretic techniques, we show by a uniform argument that these axiomatizations are complete, i.e., each formula that is valid on all finite trees is provable using our axioms. As a backdrop to our positive results, on arbitrary structures, the logics that we study are known to be non-recursively axiomatizable