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Publié par | Thesee |
Nombre de lectures | 23 |
Langue | English |
Poids de l'ouvrage | 1 Mo |
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tel-00569058, version 1 - 24 Feb 2011tel-00569058, version 1 - 24 Feb 2011Abstract
Arithmetical constraints are widely used in formal languages like regular ex-
pressions, tree grammars and paths. In XML they are used to impose bounds
onthenumberofoccurrencesdescribedbycontentmodelsofschemalanguages
(XML Schema, RelaxNG). In query languages (XPath, XQuery), they allow
selecting nodes that have a bounded number of nodes reachable by a given
path expression. Counting types and paths are thus natural extensions of
their countless counterparts already regarded as the core constructs in XML
languages and type systems.
One of the biggest challenges in XML is to develop automated procedures
for ensuring static-type safety and optimization techniques. To this end, there
is a need to solve some basic reasoning tasks that involve constructions such
as counting XML schemas and XPath expressions. Every compiler of XML
programs will have to routinely solve problems such as type and path type-
checking, for ensuring at compile time that invalid documents can never arise
as the output of XML processing code.
This thesis studies e!cient reasoning frameworks able to express counting
constraints on tree structures. It was recently shown that theµ-calculus, when
extended with counting constraints on immediate successor nodes is undecid-
able over graphs. Here we show that, when interpreted over finite trees, the
logic with counting constraints is decidable in single exponential time. Fur-
thermore, this logic allows more general counting operators. For example, the
logic can pose numerical constraints on number of ancestors or descendants.
We also present linear translations of counting XPath expressions and XML
schemas into the logic.
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tel-00569058, version 1 - 24 Feb 2011tel-00569058, version 1 - 24 Feb 2011R´esum´e
Lescontraintesarithm´etiquessontlargementutilis´eesdansleslangagesformels
comme les expressions, les grammaires d’arbres et les chemins r´eguliers. Ces
contraintessontutilis´eesdanslesmod`elesdecontenudestypes(XMLSchemas)
pour imposer des bornes sur le nombre d’occurrences de nœuds. Dans les lan-
gages de requˆetes (XPath, XQuery), ces contraintes permettent de s´electionner
les nœuds ayant un nombre limit´e de nœuds accessibles par une expression de
chemin donn´ee. Les types et chemins ´etendus avec les contraintes de comp-
tage constituent le prolongement naturel de leurs homologues sans comptage
d´ej`a consid´er´es comme des constructions fondamentales dans les langages de
programmation et les syst`emes de type pour XML.
Un des d´efis majeurs en programmation XML consiste `a d´evelopper des
techniques automatis´ees permettant d’assurer statiquement un typage correct
`et des optimisations de programmes manipulant les donn´ees XML. A cette fin,
ilestn´ecessaireder´esoudrecertainestˆachesderaisonnementquiimpliquentdes
constructions telles que les types et les expressions XPath avec des contraintes
de comptage. Dans un futur proche, les compilateurs de programmes XML
devrontr´esoudredesprobl`emesdebasetelsquelesous-typageafindes’assurer
au moment de la compilation qu’un programme ne pourra jamais g´en´erer de
documents non valides `a l’ex´ecution.
Cetteth`ese´etudieleslogiquescapablesd’exprimerdescontraintesdecomp-
tage sur les structures d’arbres. Il a ´et´e montr´e r´ecemment que le µ-calcul sur
les graphes, lorsqu’il est ´etendu `a des contraintes de comptage portant ex-
clusivement sur les nœuds successeurs imm´ediats est ind´ecidable. Dans cette
th`ese, nous montrons que, sur les arbres finis, la logique avec contraintes de
comptage est d´ecidable en temps exponentiel. En outre, cette logique four-
nit des op´erateurs de comptage selon des chemins plus g´en´eraux. En e"et,
la logique peut exprimer des contraintes num´eriques sur le nombre de nœuds
descendants ou mˆeme ascendants. Nous pr´esentons ´egalement des traductions
lin´eaires d’expressions XPath et de types XML comportant des contraintes de
comptage dans la logique.
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tel-00569058, version 1 - 24 Feb 2011tel-00569058, version 1 - 24 Feb 2011Para Lia Danae
tel-00569058, version 1 - 24 Feb 2011tel-00569058, version 1 - 24 Feb 2011Acknowledgements
Many people contributed to the development of this thesis. I would like to
express my gratitude to all of them.
I would like to thank my supervisors Vincent Quint and Nabil Laya¨ıda.
They first gave me the opportunity to join the WAM team at INRIA as their
student. During the development of my thesis, they also provided me with
excellent research conditions.
In the WAM team, I was fortunate to meet Pierre Genev`es. From the
beginning to the end, this thesis benefited of Pierre’s guidance. I would like to
thank Pierre for his invaluable availability and support.
I have been honoured to have V´eronique Benzaken and Denis Lugiez as
referees for this dissertation. I thank them for their insightful comments and
suggestions, which helped to improve this dissertation document. I am also
grateful to Nils Gesbert for his suggestions.
I would like to also thank Marie-Christine Rousset for taking the role of
examiner and president in the thesis committee.
The results described in this dissertation were benefited of a collaboration
with Alan Schmitt. I am very grateful to Alan for the great moments doing
research.
TothemembersoftheWAMandEXMOteams,inparticulartoMelisachew
Chekol, Freddy Limpens, Chan Le Duc, J´erˆome David, C´assia Trojahn dos
Santos, GiussepePirr`o and Manuel Atencia, thank you for providing me avery
pleasant and friendly atmosphere at INRIA.
To all my family, Luz Mar´ıa, Everardo, Iliana, and Blanca, thank you for
your continuous support.
All my gratitude is for Lia Danae and Cynthia. Thank you for all your
sacrifice and support. I would never be able do it without you.
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tel-00569058, version 1 - 24 Feb 2011tel-00569058, version 1 - 24 Feb 2011