Luc Segoufin

Two-Variable Logic on Words with Data

In a data word each position carries a label from a finite alphabet and a data value from some infinite domain. These models have been already considered in the realm of semistructured data, timed automata and extended temporal logics. It is shown that satisfiability for the two-variable first-order logic FO2(~,<,+1) is decidable over finite and over infinite data words, where ~ is a binary predicate testing the data value equality and +1,< are the usual successor and order predicates. The complexity of the problem is at least as hard as Petri net reachability. Several extensions of the logic are considered, some remain decidable while some are undecidable

Validating streaming XML documents

This paper investigates the on-line validation of streaming XML documents with respect to a DTD, under memory constraints. We first consider validation using constant memory, formalized by a finite-state automaton (FSA). We examine two flavors of the problem, depending on whether or not the XML document is assumed to be well-formed. The main results of the paper provide conditions on the DTDs under which validation of either flavor can be done using an FSA. For DTDs that cannot be validated by an FSA, we investigate two alternatives. The first relaxes the constant memory requirement by allowing a stack bounded in the depth of the XML document, while maintaining the deterministic, one-pass requirement. The second approach consists in refining the DTD to provide additional information that allows validation by an FSA.

Automata and logics for words and trees over an infinite alphabet

In a data word or a data tree each position carries a label from a finite alphabet and a data value from some infinite domain. These models have been considered in the realm of semistructured data, timed automata and extended temporal logics. This paper survey several know results on automata and logics manipulating data words and data trees, the focus being on their relative expressive power and decidability.

Representing and querying XML with incomplete information

We study the representation and querying of XML with incomplete information. We consider a simple model for XML data and their DTDs, a very simple query language, and a representation system for incomplete information in the spirit of the representations systems developed by Imielinski and Lipski [1984] for relational databases. In the scenario we consider, the incomplete information about an XML document is continuously enriched by successive queries to the document. We show that our representation system can represent partial information about the source document acquired by successive queries, and that it can be used to intelligently answer new queries. We also consider the impact on complexity of enriching our representation system or query language with additional features. The results suggest that our approach achieves a practically appealing balance between expressiveness and tractability.

The DEDALE system for complex spatial queries

This paper presents DEDALE, a spatial database system intended to overcome some limitations of current systems by providing an abstract and non-specialized data model and query language for the representation and manipulation of spatial objects. DEDALE relies on a logical model based on linear constraints, which generalizes the constraint database model of [KKR90]. While in the classical constraint model, spatial data is always decomposed into its convex components, in DEDALE holes are allowed to fit the need of practical applications. The logical representation of spatial data although slightly more costly in memory, has the advantage of simplifying the algorithms. DEDALE relies on nested relations, in which all sorts of data (thematic, spatial, etc.) are stored in a uniform fashion. This new data model supports declarative query languages, which allow an intuitive and efficient manipulation of spatial objects. Their formal foundation constitutes a basis for practical query optimization. We describe several evaluation rules tailored for geometric data and give the specification of an optimizer module for spatial queries. Except for the latter module, the system has been fully implemented upon the O2 DBMS, thus proving the effectiveness of a constraint-based approach for the design of spatial database systems.

When is the evaluation of conjunctive queries tractable

The evaluation of conjunctive queries is hard both with respect to its combined complexity (NP-complete) and its parameterized complexity (W[1]-complete). It becomes tractable (PTIME for combined complexity, FPT for parameterized complexity), when the underlying graphs of the conjunctive queries have bounded tree-width [2]. We show that, in some sense, this is optimal both with respect to combined and parameterized complexity: For every class C of graphs, the evaluation of all conjunctive queries whose underlying graph is in C is tractable if, and only if, C has bounded tree-width. A technical result of independent interest is that the colored grid homomorphism problem is NP-complete and, if parameterized by the grid size, W[1]-complete.

Two-variable logic on data words

In a data word each position carries a label from a finite alphabet and a data value from some infinite domain. This model has been already considered in the realm of semistructured data, timed automata, and extended temporal logics. This article shows that satisfiability for the two-variable fragment FO2(∼,<,+1) of first-order logic with data equality test ∼ is decidable over finite and infinite data words. Here +1 and < are the usual successor and order predicates, respectively. The satisfiability problem is shown to be at least as hard as reachability in Petri nets. Several extensions of the logic are considered; some remain decidable while some are undecidable.

Views and queries: Determinacy and rewriting

We investigate the question of whether a query Q can be answered using a set V of views. We first define the problem in information-theoretic terms: we say that V determines Q if V provides enough information to uniquely determine the answer to Q. Next, we look at the problem of rewriting Q in terms of V using a specific language. Given a view language V and query language Q, we say that a rewriting language R is complete for V-to-Q rewritings if every Q ∈ Q can be rewritten in terms of V ∈ V using a query in R, whenever V determines Q. While query rewriting using views has been extensively investigated for some specific languages, the connection to the information-theoretic notion of determinacy, and the question of completeness of a rewriting language have received little attention. In this article we investigate systematically the notion of determinacy and its connection to rewriting. The results concern decidability of determinacy for various view and query languages, as well as the power required of complete rewriting languages. We consider languages ranging from first-order to conjunctive queries.

Spatio-temporal data handling with constraints

Most spatial information systems are limited to a fixed dimension (generally 2) which is not extensible. On the other hand, the emerging paradigm of constraint databases allows the representation of data of arbitrary dimension, together with abstract query languages. The complexity of evaluating queries though might be costly if the dimension of the objects is really arbitrary. In this paper, we present a data model, based on linear constraints, dedicated to the representation and manipulation of multidimensional data. In order to preserve a low complexity for query evaluation, we restrict the orthographic dimension of an object O, defined as the dimension of the components O1 ,..., On such that O=O1×...× On. This allows to process queries independently on each component, therefore achieving a satisfying trade-off between design simplicity, expressive power of the query language and efficiency of query evaluation. We illustrate these concepts in the context of spatio-temporal databases where space and time are the natural components. This data model has been implemented in the DEDALE system and a spatio-temporal application, with orthographic dimension 2, is currently running, thus showing the practical relevance of the approach.

Two-variable logic on data trees and XML reasoning

Motivated by reasoning tasks in the context of 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.