Schemas for Unordered XML on a DIME

We investigate schema languages for unordered XML having no relative order among siblings. First, we propose unordered regular expressions (UREs), essentially regular expressions with unordered concatenation instead of standard concatenation, that define languages of unordered words to model the allowed content of a node (i.e., collections of the labels of children). However, unrestricted UREs are computationally too expensive as we show the intractability of two fundamental decision problems for UREs: membership of an unordered word to the language of a URE and containment of two UREs. Consequently, we propose a practical and tractable restriction of UREs, disjunctive interval multiplicity expressions (DIMEs). Next, we employ DIMEs to define languages of unordered trees and propose two schema languages: disjunctive interval multiplicity schema (DIMS), and its restriction, disjunction-free interval multiplicity schema (IMS). We study the complexity of the following static analysis problems: schema satisfiability, membership of a tree to the language of a schema, schema containment, as well as twig query satisfiability, implication, and containment in the presence of schema. Finally, we study the expressive power of the proposed schema languages and compare them with yardstick languages of unordered trees (FO, MSO, and Presburger constraints) and DTDs under commutative closure. Our results show that the proposed schema languages are capable of expressing many practical languages of unordered trees and enjoy desirable computational properties.Comment: Theory of Computing System

Efficient asymmetric inclusion of regular expressions with interleaving and counting for XML type-checking

The inclusion of Regular Expressions (REs) is the kernel of any type-checking algorithm for XML manipulation languages. XML applications would benefit from the extension of REs with interleaving and counting, but this is not feasible in general, since inclusion is EXPSPACE-complete for such extended REs. In Colazzo et al. (2009) [1] we introduced a notion of ?conflict-free REs?, which are extended REs with excellent complexity behaviour, including a polynomial inclusion algorithm [1] and linear membership (Ghelli et al., 2008 [2]). Conflict-free REs have interleaving and counting, but the complexity is tamed by the ?conflict-free? limitations, which have been found to be satisfied by the vast majority of the content models published on the Web.However, a type-checking algorithm needs to compare machine-generated subtypes against human-defined supertypes. The conflict-free restriction, while quite harmless for the human-defined supertype, is far too restrictive for the subtype. We show here that the PTIME inclusion algorithm can be actually extended to deal with totally unrestricted REs with counting and interleaving in the subtype position, provided that the supertype is conflict-free.This is exactly the expressive power that we need in order to use subtyping inside type-checking algorithms, and the cost of this generalized algorithm is only quadratic, which is as good as the best algorithm we have for the symmetric case (see [1]). The result is extremely surprising, since we had previously found that symmetric inclusion becomes NP-hard as soon as the candidate subtype is enriched with binary intersection, a generalization that looked much more innocent than what we achieve here

Regular Rooted Graph Grammars

In dieser Arbeit wir ein pragmatischer Ansatz zur Typisierung, statischen Analyse und Optimierung von Web-Anfragespachen, speziell Xcerpt, untersucht. Pragmatisch ist der Ansatz in dem Sinne, dass dem Benutzer keinerlei Einschränkungen aus Entscheidbarkeits- oder Effizienzgründen auf modellierbare Typen gestellt werden. Effizienz und Entscheidbarkeit werden stattdessen, falls nötig, durch Vergröberungen bei der Typprüfung erkauft. Eine Typsprache zur Typisierung von Graph-strukturierten Daten im Web wird eingeführt. Modellierbare Graphen sind so genannte gewurzelte Graphen, welche aus einem Spannbaum und Querreferenzen aufgebaut sind. Die Typsprache basiert auf reguläre Baum Grammatiken, welche um typisierte Referenzen erweitert wurde. Neben wie im Web mit XML üblichen geordneten strukturierten Daten, sind auch ungeordnete Daten, wie etwa in Xcerpt oder RDF üblich, modellierbar. Der dazu verwendete Ansatz---ungeordnete Interpretation Regulärer Ausdrücke---ist neu. Eine operationale Semantik für geordnete wie ungeordnete Typen wird auf Basis spezialisierter Baumautomaten und sog. Counting Constraints (welche wiederum auf presburgerarithmetische Ausdrücke) basieren. Es wird ferner statische Typ-Prüfung und -Inferenz von Xcerpt Anfrage- und Konstrukttermen, wie auch Optimierung von Xcerpt Anfragen auf Basis von Typinformation eingeführt.This thesis investigates a pragmatic approach to typing, static analysis and static optimization of Web query languages, in special the Web query language Xcerpt. The approach is pragmatic in the sense, that no restriction on the types are made for decidability or efficiency reasons, instead precision is given up if necessary. Pragmatics on the dynamic side means to use types not only to ensure validity of objects operating on, but also influencing query selection based on types. A typing language for typing of graph structured data on the Web is introduced. The Graphs in mind are based on spanning trees with references, the typing languages is based on regular tree grammars with typed reference extensions. Beside ordered data in the spirit of XML, unordered data (i.e. in the spirit of the Xcerpt data model or RDF) can be modelled using regular expressions under unordered interpretation – this approach is new. An operational semantics for ordered and unordered types is given based on specialized regular tree automata and counting constraints (them again based on Presburger arithmetic formulae). Static type checking of Xcerpt query and construct terms is introduced, as well as optimization of Xcerpt query terms based on schema information

Containment of Shape Expression Schemas for RDF

International audienceWe study the problem of containment of shape expression schemas (ShEx) for RDF graphs. We identify a subclass of ShEx that has a natural graphical representation in the form of shape graphs and whose semantics is captured with a tractable notion of embedding of an RDF graph in a shape graph. When applied to pairs of shape graphs, an embedding is a sufficient condition for containment, and for a practical subclass of deterministic shape graphs, it is also a necessary one, thus yielding a subclass with tractable containment. Containment for general shape graphs is EXP-complete. Finally , we show that containment for arbitrary ShEx is decid-able. CCS CONCEPTS • Information systems → Graph-based database models ; Resource Description Framework (RDF); • Theory of computation → Database theory; Database interoper-ability

: Méthodes d'Inférence Symbolique pour les Bases de Données

This dissertation is a summary of a line of research, that I wasactively involved in, on learning in databases from examples. Thisresearch focused on traditional as well as novel database models andlanguages for querying, transforming, and describing the schema of adatabase. In case of schemas our contributions involve proposing anoriginal languages for the emerging data models of Unordered XML andRDF. We have studied learning from examples of schemas for UnorderedXML, schemas for RDF, twig queries for XML, join queries forrelational databases, and XML transformations defined with a novelmodel of tree-to-word transducers.Investigating learnability of the proposed languages required us toexamine closely a number of their fundamental properties, often ofindependent interest, including normal forms, minimization,containment and equivalence, consistency of a set of examples, andfinite characterizability. Good understanding of these propertiesallowed us to devise learning algorithms that explore a possibly largesearch space with the help of a diligently designed set ofgeneralization operations in search of an appropriate solution.Learning (or inference) is a problem that has two parameters: theprecise class of languages we wish to infer and the type of input thatthe user can provide. We focused on the setting where the user inputconsists of positive examples i.e., elements that belong to the goallanguage, and negative examples i.e., elements that do not belong tothe goal language. In general using both negative and positiveexamples allows to learn richer classes of goal languages than usingpositive examples alone. However, using negative examples is oftendifficult because together with positive examples they may cause thesearch space to take a very complex shape and its exploration may turnout to be computationally challenging.Ce mémoire est une courte présentation d’une direction de recherche, à laquelle j’ai activementparticipé, sur l’apprentissage pour les bases de données à partir d’exemples. Cette recherches’est concentrée sur les modèles et les langages, aussi bien traditionnels qu’émergents, pourl’interrogation, la transformation et la description du schéma d’une base de données. Concernantles schémas, nos contributions consistent en plusieurs langages de schémas pour les nouveaumodèles de bases de données que sont XML non-ordonné et RDF. Nous avons ainsi étudiél’apprentissage à partir d’exemples des schémas pour XML non-ordonné, des schémas pour RDF,des requêtes twig pour XML, les requêtes de jointure pour bases de données relationnelles et lestransformations XML définies par un nouveau modèle de transducteurs arbre-à-mot.Pour explorer si les langages proposés peuvent être appris, nous avons été obligés d’examinerde près un certain nombre de leurs propriétés fondamentales, souvent souvent intéressantespar elles-mêmes, y compris les formes normales, la minimisation, l’inclusion et l’équivalence, lacohérence d’un ensemble d’exemples et la caractérisation finie. Une bonne compréhension de cespropriétés nous a permis de concevoir des algorithmes d’apprentissage qui explorent un espace derecherche potentiellement très vaste grâce à un ensemble d’opérations de généralisation adapté àla recherche d’une solution appropriée.L’apprentissage (ou l’inférence) est un problème à deux paramètres : la classe précise delangage que nous souhaitons inférer et le type d’informations que l’utilisateur peut fournir. Nousnous sommes placés dans le cas où l’utilisateur fournit des exemples positifs, c’est-à-dire deséléments qui appartiennent au langage cible, ainsi que des exemples négatifs, c’est-à-dire qui n’enfont pas partie. En général l’utilisation à la fois d’exemples positifs et négatifs permet d’apprendredes classes de langages plus riches que l’utilisation uniquement d’exemples positifs. Toutefois,l’utilisation des exemples négatifs est souvent difficile parce que les exemples positifs et négatifspeuvent rendre la forme de l’espace de recherche très complexe, et par conséquent, son explorationinfaisable

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

Theory of traces

AbstractThe theory of traces, originated by A. Mazurkiewicz in 1977, is an attempt to provide a mathematical description of the behavior of concurrent systems. Its aim is to reconcile the sequential nature of observations of the system behavior on the one hand and the nonsequential nature of causality between the actions of the system on the other hand.One can see the theory of traces to be rooted in formal string language theory with the notion of partial commutativity playing the central role. Alternatively one can see the theory of traces to be rooted in the theory of labeled acyclic directed graphs (or even in the theory of labeled partial orders).This paper attempts to present a major portion of the theory of traces in a unified way. However, it is not a survey in the sense that a number of new notions are introduced and a number of new results are proved. Although traditionally most of the development in the theory of traces follows the string-language-theoretic line, we try to demonstrate to the reader that the graph-theoretic point of view may be more appropriate.The paper essentially consists of two parts. The first one (Sections 1 through 4) is concerned with the basic theory of traces. The second one (Section 5) presents applications of the theory of traces to the theory of the behavior of concurrent systems, where the basic system model we have chosen is the condition/event system introduced by C.A. Petri