Aller à : contenu haut bas recherche
 
 
EN     FR
Vous êtes ici:   UNIL > HEC Inst. > HEC App. > RECHERCHE
 
 

Jacques Duparc

Contact

Full Professor
Department of Information Systems


Contact
Jacques.Duparc@unil.ch
Internef, room 134
Tel 021.692.35.88

Postal address
Université de Lausanne
Quartier UNIL-Chamberonne
Bâtiment Internef
1015 Lausanne


Page personnelle : people.epfl.ch/jacques.duparc

Teaching

bachelor Introduction à la logique
Related programme
Bachelor of Science (BSc) in Management

Research

Research areas

Borel mappings via games and representation theorems
We 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

Gianluca Basso
gianluca.basso@unil.ch



full description
  Alessia Spadini
alessia.spadini@unil.ch



 
Louis Vuilleumier
louis.vuilleumier.1@unil.ch



full description
 

Publications

48 last publications ordered by: publication type  -  year

: Peer Reviewed

Articles

Camerlo Riccardo , Duparc Jacques (2017). Some remarks on Baire's grand theorem. Archive for Mathematical Logic.


Cabessa J. , Duparc J. (2016). Expressive Power of Nondeterministic Recurrent Neural Networks in Terms of their Attractor Dynamics. International Journal of Unconventional Computing, 12, 25-50. Peer Reviewed


Duparc J. (2015). Easy Proofs of Löwenheim-Skolem Theorems by Means of Evaluation Games. CoRR, abs/1507.03665.


Cabessa J. , Duparc J. (2009). A Game Theoretical Approach to The Algebraic Counterpart of The Wagner Hierarchy: Part II. RAIRO: Informatique Théorique et Applications / RAIRO: Theoretical Informatics and Applications, 43, 463-515. Peer Reviewed


Cabessa J. , Duparc J. (2008). The Algebraic Counterpart of the Wagner Hierarchy. Lecture Notes in Computer Science, 5028, 100-109. Peer Reviewed


Duparc J. , Finkel O. (2007). Wadge games and sets of reals recognized by simple machines: An omega power of a finite context-free language which is Borel above Delta^ø_omega. Studies in Logic, 11, 109-122. Peer Reviewed


Duparc J. , Riss M. (2006). The Missing Link for omega-Rational Sets, Automata, and Semigroups. International Journal of Algebra and Computation, 16, 161-185. Peer Reviewed


Duparc J. (2003). The Steel Hierarchy of Ordinal Valued Borel Mappings. Journal of Symbolic Logic, 68, 187-234. Peer Reviewed


Duparc J. (2003). A Hierarchy of Deterministic Context-Free omega-languages. Theoretical Computer Science, 290, 1253-1300. Peer Reviewed


Duparc J. (2001). Wadge Hierarchy and Veblen Hierarchy. Part I: Borel Sets of Finite Rank. Journal of Symbolic Logic, 66, 56-86. Peer Reviewed


Duparc J., Finkel O. ; Ressayre J-P. (2001). Computer Science and the Fine Structure of Borel Sets. Theoretical Computer Science, 257, 85-105. Peer Reviewed


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. Peer Reviewed


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. Peer Reviewed


Books

Duparc J. (2015). La Logique Pas à Pas. Presses polytechniques et universitaires romandes.


Book Sections

Duparc J. (2017). Jeux, Topologie et Automates. Informatique Mathématique: Une photographie en 2017 (pp. 55-79). CNRS Éditions.


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.


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.


In Proceedings

Cabessa J. , Duparc J. (2015, Jan). Expressive Power of Non-deterministic Evolving Recurrent Neural Networks in Terms of Their Attractor Dynamics. Unconventional Computation and Natural Computation: 14th International Conference, UCNC 2015, Auckland, New Zealand, August 30 - September 3, 2015, Proceedings, 9252 (pp. 144-156). Springer, Cham. Peer Reviewed


Duparc J. , Fournier K. (2015, Jan). A Tentative Approach for the Wadge-Wagner Hierarchy of Regular Tree Languages of Index [0, 2]. Descriptional Complexity of Formal Systems: 17th International Workshop, DCFS 2015, Waterloo, ON, Canada, June 25-27, 2015. Proceedings, 9118 (pp. 81-92). Springer, Cham. Peer Reviewed


Duparc J., Finkel O. ; Ressayre J.-P. (2013, Jan). The Wadge Hierarchy of Petri Nets \emph\(\omega\)-Languages. Logical Foundations of Computer Science, International Symposium, LFCS 2013, San Diego, CA, USA, January 6-8, 2013. Proceedings, 7734 (pp. 179-193).


Duparc J., Facchini A. ; Murlak F. (2011, Jan). Definable Operations On Weakly Recognizable Sets of Trees. IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2011, December 12-14, 2011, Mumbai, India, 13 (pp. 363-374).


Cabessa J., Duparc J., Facchini A. ; Murlak F. (2009, Dec). The Wadge Hierarchy of Max-Regular Languages. IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2009), 4 (pp. 121-132). Schloss Dagstuhl-Leibniz-Zentrum für Informatik. Peer Reviewed


Duparc J. , Facchini A. (2009, Jan). A Playful Glance at Hierarchical Questions for Two-Way Alternating Automata. Selected Papers of the International Conference Infinity in Logic and Computation, Cape Town, South Africa, November 2007, 5489 (pp. 46-55). Springer. Peer Reviewed


Duparc J., Facchini A. ; Murlak F. (2009, Jan). Linear Game Automata: Decidable Hierarchy Problems for Stripped-Down Alternating Tree Automata. Computer Science Logic: 23rd International Workshop, CSL 2009, 18th Annual Conference of the EACSL, Coimbra, Portugal, September 7-11, 2009, Proceedings, 5771 (pp. 225-239). Springer. Peer Reviewed


Duparc J. , Facchini A. (2008, Jan). Describing the Wadge Hierarchy for the Alternation Free Fragment of μ -Calculus (I) The Levels Below ω 1. Logic and Theory of Algorithms : Fourth Conference on Computability in Europe, CiE 2008, Athens, Greece, June 2008, Proceedings, 5028 (pp. 186-195). Springer. Peer Reviewed


Cabessa J. , Duparc J. (2007, Jan). An infinite game on omega-semigroups. Infinite Games, Papers of the conference Foundations of the Formal Sciences V, held in Bonn, November 26-29, 2004, 11 (pp. 63-78). College Publications, London. Peer Reviewed


Duparc J. , Finkel O. (2007, Jan). An ω-power of a finite context-free language which is Borel above ∆0ω. Infinite Games, Papers of the conference Foundations of the Formal Sciences V, held in Bonn, November 26-29, 2004, 11 (pp. 109-122). College Publications, London. Peer Reviewed


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. Peer Reviewed


Duparc J. , Murlak F. (2007, Jan). On the Topological Complexity of Weakly Recognizable Tree Languages. Fundamentals of Computation Theory : 16th International Symposium, FCT 2007, Budapest, Hungary, August 27-30, 2007. Proceedings, 4639 (pp. 261-273). Springer. Peer Reviewed


Bradfield J., Duparc J. ; Quickert S. (2005, Jan). Transfinite extension ot the mu-calculus. Computer Science Logic : 19th International Workshop, CSL 2005, 14th Annual Conference of the EACSL, Oxford, UK, August 22-25, 2005. Proceedings, 3634 (pp. 384-396). Springer Berlin / Heidelberg. Peer Reviewed


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. Peer Reviewed


Cachat T., Duparc J. ; Thomas W. (2002, Jan). Solving Pushdown Games with a ∑3 Winning Condition. Computer Science Logic : 11th Annual Conference of the EACSL Edinburgh, Scotland, UK, September 22–25, 2002 Proceedings, 2471 (pp. 322-336). Springer. Peer Reviewed


Duparc J., Finkel O. ; Ressayre J-P. (2000, Jan). Infinite Games, Finite Machines. Proceedings of the Joint Conference of the 5th Barcelona Logic Meeting and the 6th Kurt Gödel colloquium, Collegium Logicum, Annals of the Kurt-Gödel-Society Vol 4, 2000. Peer Reviewed


Duparc J. (1994, Jan). The Normal Form of Borel Sets of Finite Rank. Contributed Papers of the Logic Colloquium'94. Peer Reviewed


Technical Reports

Duparc J. , Facchini A. (2009). The Topological Complexity of Models of the Modal μ-Calculus: On The Alternation Free Fragment and Beyond. Laboratoire Bordelais de Recherche en Informatique et Université de Lausanne.


Thesis

Fournier K., Duparc J. (Dir.) (2016). The Wadge Hierarchy: Beyond Borel Sets. Université de Lausanne, Faculté des hautes études commerciales.


Carroy R., Duparc J. , Finkel O. (Dir.) (2013). Fonctions de première classe de Baire. Université de Lausanne, Faculté des hautes études commerciales.


Bach C. W., Jacques D. , Hans P. (Dir.) (2010). Interactive Epistemology and Reasoning: On the Foundations of Game Theory. Université de Lausanne, Faculté des hautes études commerciales.


Facchini A., Duparc J. (Dir.) (2010). A study on the expressive power of some fragments of the modal µ-Calculus. Université de Lausanne, Faculté des hautes études commerciales.


Cabessa J., Duparc J. (Dir.) (2007). A game theoretical approach to the algebraic counterpart of the Wagner hierarchy. Université de Lausanne, Faculté des hautes études commerciales.


Duparc J. (1995). La Forme Normale des Boréliens de Rang fini. University Paris 7.


Unpublished

Duparc J. (In Press). A Coarsification of the Wagner Hierarchy.


Duparc J. (In Press). Wadge Degrees of Louveau's (Wadge) Classes.


Duparc J. (In Press). A Normal Form for Borel Sets.


Duparc J. (In Press). Wadge Hierarchy and Veblen Hierarchy. Part II: Borel Sets of Infinite Rank.


Duparc J. (In Press). Anti-Chains of Mappings from omega^omega on some BQO.


Duparc J. (2008). A Normal Form of Borel Sets of Finite Rank.


Miscellaneous

Duparc J. , Cabessa J. (2004). Games on Semigroups.


Curriculum

Competences



Cours donnés à l'EPFL


Mathematical logic
Foundations of mathematics (set theory) and foundations of computer science (theoretical computer science).

Education

PhD in mathematics
University Paris VII-Denis Diderot, (1995)

Keywords

  • descriptive set theory
  • mathematical logic
  • theoretical computer science

 
 
Search


Internef - CH-1015 Lausanne - Suisse  -   Tél. +41 21 692 33 00  -   Fax +41 21 692 33 05
Swiss University