Jacques Duparc
Coordonnées
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Professeur ordinaire
Département des opérations Contact Jacques.Duparc@unil.ch Anthropole, bureau 3086 Tél 021.692.35.88 Adresse postale Université de Lausanne Quartier UNIL-Chamberonne Bâtiment Anthropole 1015 Lausanne Page personnelle : people.epfl.ch/jacques.duparc |
Enseignements
bachelor Introduction à la logique Formation concernée Baccalauréat universitaire ès Sciences en management |
Recherches
Axes de recherche
Borel mappings via games and representation theoremsWe characterize some classes of Borel functions over the Baire space as strategies in suitable games. This is a way towards both obtaining representation theorems and elaborating a fine classifications of Borel functions. Representation theorems come as a representation of some classes of functions very different from their definitions. For instance, a cornerstone for this type of result is the Baire Grand Theorem which states that the following are equivalent for any function f on a Polish space:
- f is the pointwise limit of countably many continuous functions;
- on every non-empty closed subset f admits a point of continuity.
Continuous Reductions on Quasi-Polish spaces
Quasi-Polish spaces is a novel unifying theory due to Matthew de Brecht. It brings together topological structures that were previously unrelated. It connects closely topology in mathematical analysis -- which is usually Hausdorff (T_2) -- to topology in computer science -- which is rather Kolmogorov} (T_0) -- by offering the Polish spaces as well as the omega-algebraic or omega-continuous domains a common roof. Quasi-Polish spaces are derived from Polish spaces -- which are separable completely metrizable topological spaces -- by simply relaxing the symmetry condition in the definition of a metric.
We propose to design and make use of game theoretical tools to study the reductions between these sets and explore the underlying ordering as well as
the natural hierarchies that would arise. We intend to do this in a similar manner as the way we studied the Wadge hierarchy of Borel subsets of the Cantor space.
Quotients of Projective Fraïssé Limits
The idea of studying infinite structures via approximation by finite structures is a well rooted concept in mathematics. In particular, the Fraïssé limit is an extensively studied tool in many areas of mathematics.
In 2006 T. Irwin and S. Solecki introduced the projective Fraïssé limit of topological structures. Many applications have since been found in continua theory and descriptive dynamics.
We propose to isolate and study the class of all compact metric spaces that are obtainable as a quotient of a projective Fraïssé limit by the interpretation of a binary relation symbol from the language. Our hope is to describe a natural way of obtaining such spaces.
The Wadge Hierarchy
Over a century ago, the modern theory of integration, based on measure theory induced a fundamental interest in the study of well-behaved subsets of the real line or the real plane. Topology, which developed about the same time yielded the mathematical framework for such a study. For instance, the σ-algebra generated by the open subsets proved to be central in measure theory, for the sets it defines bear all desired nice properties.
The most refined classification of these sets is the so-called Wadge hierarchy whose study involves methods from (set theoretical) game theory
Topological Complexity, Games, Logic and Automata
We try to unravel the fine topological structure of omega-regular tree languages which are the infinitary languages of trees recognized by automata. In other words, we exhibit the Wadge hierarchy of non deterministic omega-tree automata.
Assistants
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Gianluca Basso
gianluca.basso@unil.ch Tél: (021 692) 6110 Bureau: ANT 3061 |
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Louis Vuilleumier
louis.vuilleumier.1@unil.ch Tél: (021 692) 6110 Bureau: ANT 3061 |
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Publications
44 dernières publications classées par:
type de publication
-
année
: Revue avec comité de lecture
2018
![]() | CAVALLARI Filippo (2018). Regular tree languages in the first two levels of the Borel hierarchy. Université de Lausanne, Faculté des hautes études commerciales. Duparc Jacques , Motto-Ros Luca (Dir.) |
2017
![]() | Camerlo R. , Duparc J. (2017). Some remarks on Baire's grand theorem. Archive for Mathematical Logic, 1-7. ![]() |
![]() | Duparc J. (2017). Jeux, Topologie et Automates. Informatique Mathématique: Une photographie en 2017 (pp. 55-79). CNRS Editions. |
2016
![]() | Fournier K. (2016). The Wadge Hierarchy: Beyond Borel Sets. Université de Lausanne, Faculté des hautes études commerciales. Duparc J. (Dir.) |
2015
![]() | Duparc J. (2015). La Logique Pas à Pas. Presses polytechniques et universitaires romandes. |
2014
![]() | Duparc J., Finkel O. ; Ressayre J-P. (2014). The Wadge Hierarchy of Petri Nets omega-Languages. Logic, Computation, Hierarchies (Vol. 4, pp. 109-138). De Gruyter, Berlin, Germany. |
2013
![]() | Carroy R. (2013). Fonctions de première classe de Baire. Université de Lausanne, Faculté des hautes études commerciales. Duparc J. , Finkel O. (Dir.) |
2011
2010
![]() | Bach C. W. (2010). Interactive Epistemology and Reasoning: On the Foundations of Game Theory. Université de Lausanne, Faculté des hautes études commerciales. Jacques D. , Hans P. (Dir.) |
![]() | Facchini A. (2010). A study on the expressive power of some fragments of the modal µ-Calculus. Université de Lausanne, Faculté des hautes études commerciales. Duparc J. (Dir.) |
2009
2008
![]() | Cabessa J. , Duparc J. (2008). The Algebraic Counterpart of the Wagner Hierarchy. Lecture Notes in Computer Science, 5028, 100-109. ![]() |
![]() | Duparc J. (2008). A Normal Form of Borel Sets of Finite Rank. |
2007
![]() | Arnold A., Duparc J., Murlak F. ; Niwiński D. (2007). On the topological complexity of tree languages. Logic and Automata: History and Perspectives (Vol. 2, pp. 9-28). Amsterdam University Press. |
![]() | Cabessa J. (2007). A game theoretical approach to the algebraic counterpart of the Wagner hierarchy. Université de Lausanne, Faculté des hautes études commerciales. Duparc J. (Dir.) |
![]() | Duparc J. , Henzinger T.A. (2007, Sep). Computer Science Logic. 21st International Workshop, CSL 2007 16th Annual Conference of the EACSL Lausanne, Switzerland, 4646. Springer. ![]() |
2006
![]() | Duparc J. , Riss M. (2006). The Missing Link for omega-Rational Sets, Automata, and Semigroups. International Journal of Algebra and Computation, 16, 161-185. ![]() |
2005
2004
![]() | Duparc J. , Cabessa J. (2004). Games on Semigroups. |
2003
![]() | Duparc J. (2003). A Hierarchy of Deterministic Context-Free omega-languages. Theoretical Computer Science, 290, 1253-1300. ![]() |
![]() | Duparc J. (2003). The Steel Hierarchy of Ordinal Valued Borel Mappings. Journal of Symbolic Logic, 68, 187-234. ![]() |
![]() | Duparc J. (2003, Jan). Positive Games and persistent Strategies. 12th Annual Conference of the European Association for Computer Science Logic, 2803 (pp. 183-196). Springer. ![]() |
2002
2001
![]() | Duparc J. (2001). Wadge Hierarchy and Veblen Hierarchy. Part I: Borel Sets of Finite Rank. Journal of Symbolic Logic, 66, 56-86. ![]() |
![]() | Duparc J., Finkel O. ; Ressayre J-P. (2001). Computer Science and the Fine Structure of Borel Sets. Theoretical Computer Science, 257, 85-105. ![]() |
2000
1999
![]() | Duparc J. (1999). The Normal Form of Borel Sets. Part II: Borel Sets of Infinite Rank. Comptes Rendus de l'Académie des Sciences - Series I - Mathematics, 328, 735-740. ![]() |
1995
![]() | Duparc J. (1995). The Normal Form of Borel Sets. Part I: Borel Sets of Finite Rank. Comptes Rendus de l'Académie des Sciences - Series I - Mathematics, 320, 651-656. ![]() |
![]() | Duparc J. (1995). La Forme Normale des Boréliens de Rang fini. University Paris 7. |
1994
![]() | Duparc J. (1994, Jan). The Normal Form of Borel Sets of Finite Rank. Contributed Papers of the Logic Colloquium'94. ![]() |
Curriculum
Compétences
Cours donnés à l'EPFL
Logique mathématique
Fondement des mathématiques (théorie des ensembles) et fondement de l'informatique (informatique théorique).
Formations
Doctorat de mathématiquesUniversité Paris VII-Denis Diderot, (1995)
Mots-clés
- informatique théorique
- logique mathématique
- théorie descriptive des ensembles