master Computational Complexity I Formations concernées Maîtrise universitaire ès Sciences en management, Orientation stratégie, organisation et leadership Maîtrise universitaire ès Sciences en management, Orientation marketing Maîtrise universitaire ès Sciences en management, Orientation comportement, économie et évolution Maîtrise universitaire ès Sciences en management, Orientation business analytics

bachelor Introduction à la logique Formations concernées Baccalauréat universitaire ès Sciences en management Baccalauréat universitaire en sciences économiques

Axes de recherche

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.

	Alexis Breschan alexis.breschan@unil.ch Bureau: ANT 3091			Louis Vuilleumier louis.vuilleumier.1@unil.ch Tél: (021 692) 6110 Bureau: ANT 3061 page personnelle

45 dernières publications

: Revue avec comité de lecture

2020

	Basso Gianluca, Duparc Jacques , Camerlo Riccardo (Dir.) (2020). COMPACT METRIZABLE STRUCTURES VIA PROJECTIVE FRAÏSSÉ THEORY WITH AN APPLICATION TO THE STUDY OF FENCES. Université de Lausanne, Faculté des hautes études commerciales.

2018

	CAVALLARI Filippo, Duparc Jacques , Motto-Ros Luca (Dir.) (2018). Regular tree languages in the first two levels of the Borel hierarchy. Université de Lausanne, Faculté des hautes études commerciales.

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

2015

	Cabessa J. , Duparc J. (2015). Expressive Power of Non-deterministic Evolving Recurrent Neural Networks in Terms of Their Attractor Dynamics. Unconventional Computation and Natural Computation, 12, 144-156.

	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, 9252 (pp. 144-156). Springer, Cham.

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

	Duparc J. (2015, Jan). Easy Proofs of Löwenheim-Skolem Theorems by Means of Evaluation Games. Proceedings of the Fourth International Conference on Tools for Teaching Logic, abs/1507.03665 (pp. 27-34). Schloss Dagstuhl.

	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, 9118 (pp. 81-92). Springer, Cham.

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

	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, January 6-8, 2013. Proceedings, 7734 (pp. 179-193).

2011

	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).

2010

	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.

2009

	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.

	Cabessa J., Duparc J., Facchini A. ; Murlak F. (2009, Déc). 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.

	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.

	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.

	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.

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.

	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.

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

	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.

	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.

	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.

	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.

	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.

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

	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.

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

	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.

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

	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.

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.

Compétences

Cours donnés à l'EPFL

• Mathematical logic


• Set theory

Logique mathématique
Fondement des mathématiques (théorie des ensembles) et fondement de l'informatique (informatique théorique).

Formations

Doctorat de mathématiques
Université Paris VII-Denis Diderot, (1995)