Jan Van den Bussche

DTDs versus XML schema: a practical study

Among the various proposals answering the shortcomings of Document Type Definitions (DTDs), XML Schema is the most widely used. Although DTDs and XML Schema Definitions (XSDs) differ syntactically, they are still quite related on an abstract level. Indeed, freed from all syntactic sugar, XML Schemas can be seen as an extension of DTDs with a restricted form of specialization. In the present paper, we inspect a number of DTDs and XSDs harvested from the web and try to answer the following questions: (1) which of the extra features/expressiveness of XML Schema not allowed by DTDs are effectively used in practice; and, (2) how sophisticated are the structural properties (i.e. the nature of regular expressions) of the two formalisms. It turns out that at present real-world XSDs only sparingly use the new features introduced by XML Schema: on a structural level the vast majority of them can already be defined by DTDs. Further, we introduce a class of simple regular expressions and obtain that a surprisingly high fraction of the content models belong to this class. The latter result sheds light on the justification of simplifying assumptions that sometimes have to be made in XML research.

An overview of GOOD

GOOD is an acronym, standing for Graph-Oriented Object Database. GOOD is being developed as a joint research effort of Indiana University and the University of Antwerp. The main thrust behind the project is to indicate general concepts that are fundamental to any graph-oriented database user-interface. GOOD does not restrict its attention to well-considered topics such as ad-hoc query facilities, but wants to cover the full spectrum of database manipulations. The idea of graph-pattern matching as a uniform object manipulation primitive offers a uniform framework in which this can be accomplished.

On the completeness of object-creating database transformation languages

Object-oriented applications of database systems require database transformations involoving nonstandard functionalities such as set manipulation and object creation, that is, the introduction of new domain elements. To deal with thse functionalities, Abiteboul and Kanellakis [1989] introduced the “determinate” transformations as a generalization of the standard domain-preserving transformations. The obvious extensions of complete standard database programming languages, however, are not complete for the determinate transformations. To remedy this mismatch, the “constructive” transformations are proposed. It is shown that the constructive transformations are precisely the transformations that can be expressed in said extensions of complete standard languages. Thereto, a close correspondence between object creation and the construction of hereditarily finite sets is established. A restricted version of the main completeness result for the case where only list manipulations are involved is also presented.

On Topological Elementary Equivalence of Spatial Databases

We consider spatial databases and queries definable using first-order logic and real polynomial inequalities. We are interested in topological queries: queries whose result only depends on the topological aspects of the spatial data. Two spatial databases are called topologically elementary equivalent if they cannot be distinguished by such topological first-order queries. Our contribution is a natural and effective characterization of topological elementary equivalence of closed databases in the real plane. As far as topological elementary equivalence is concerned, it does not matter whether we use first-order logic with full polynomial inequalities, or first-order logic with simple order comparisons only.

Simulation of the nested relational algebra by the flat relational algebra, with an application to the complexity of evaluating powerset algebra expressions

Paredaens and Van Gucht proved that the flat relational algebra has the same expressive power as the nested relational algebra, as far as queries over flat relations and with flat results are concerned. We provide a new, very direct proof of this fact using a simulation technique. Our technique is also applied to partially answer a question posed by Suciu and Paredaens regarding the complexity of evaluating powerset algebra expressions. Specifically, we show that when only unary flat relations are into play, any powerset algebra expression is either equivalent to a nested algebra expression, or its evaluation will produce intermediate results of exponential size.

A Formal Account of the Open Provenance Model

On the Web, where resources such as documents and data are published, shared, transformed, and republished, provenance is a crucial piece of metadata that would allow users to place their trust in the resources they access. The open provenance model (OPM) is a community data model for provenance that is designed to facilitate the meaningful interchange of provenance information between systems. Underpinning OPM is a notion of directed graph, where nodes represent data products and processes involved in past computations and edges represent dependencies between them; it is complemented by graphical inference rules allowing new dependencies to be derived. Until now, however, the OPM model was a purely syntactical endeavor. The present article extends OPM graphs with an explicit distinction between precise and imprecise edges. Then a formal semantics for the thus enriched OPM graphs is proposed, by viewing OPM graphs as temporal theories on the temporal events represented in the graph. The original OPM inference rules are scrutinized in view of the semantics and found to be sound but incomplete. An extended set of graphical rules is provided and proved to be complete for inference. The article concludes with applications of the formal semantics to inferencing in OPM graphs, operators on OPM graphs, and a formal notion of refinement among OPM graphs.

Complete Geometric Query Languages

We extend Chandra and Harels seminal work on computable queries for relational databases to a setting in which also spatial data may be present, using a constraint-based data model. Concretely, we introduce both coordinate-based and point-based query languages that are complete in the sense that they can express precisely all computable queries that are generic with respect to certain classes of transformations of space, corresponding to certain geometric interpretations of spatial data. The languages we introduce are obtained by augmenting basic languages with a “while” construct. We also show that the respective basic point-based languages are complete, relative to the subclass of the corresponding generic queries consisting of those that are expressible in the relational calculus with real polynomial constraints.

Expressiveness of structured document query languages based on attribute grammars

Structured document databases can be naturally viewed as derivation trees of a context-free grammar. Under this view, the classical formalism of attribute grammars becomes a formalism for structured document query languages. From this perspective, we study the expressive power of BAGs: Boolean-valued attribute grammars with propositional logic formulas as semantic rules, and RAGs: relation-valued attribute grammars with first-order logic formulas as semantic rules. BAGs can express only unary queries; RAGs can express queries of any arity. We first show that the (unary) queries expressible by BAGs are precisely those definable in monadic second-order logic. We then show that the queries expressible by RAGs are precisely those definable by first-order inductions of linear depth, or, equivalently, those computable in linear time on a parallel machine with polynomially many processors. Further, we show that RAGs that only use synthesized attributes are strictly weaker than RAGs that use both synthesized and inherited attributes. We show that RAGs are more expressive than monadic second-order logic for queries of any arity. Finally, we discuss relational attribute grammars in the context of BAGs and RAGs. We show that in the case of BAGs this does not increase the expressive power, while different semantics for relational RAGs capture the complexity classes NP, coNP and UP ∩ coUP.

First-order queries on databases embedded in an infinite structure

Abstract We consider “generic” (isomorphism-invariant) queries on relational databases embedded in an infinite background structure. Assume a generic query is expressible by a first-order formula over the embedded domain that may involve both the relations of the database and the relations and functions of the background structure. Then this query is already expressible by a first-order formula involving just an auxiliary linear ordering as background structure. We present an elementary proof of this fact.

The Semijoin Algebra and the Guarded Fragment

In the 1970s Codd introduced the relational algebra, with operators selection, projection, union, difference and product, and showed that it is equivalent to first-order logic. In this paper, we show that if we replace in Codd’s relational algebra the product operator by the “semijoin” operator, then the resulting “semijoin algebra” is equivalent to the guarded fragment of first-order logic. We also define a fixed point extension of the semijoin algebra that corresponds to μGF.