Les lundis, à partir de 14h - UPEC CMC - Salle P2-131

22 avril 2024

TBA

Federico Olimpieri (University of Leeds)

TBA

25 mars 2024

TBA

Gabriel Le Bouder (LMF, Université Paris-Saclay)

TBA

25 mars 2024

TBA

Djamel Eddine Amir (LORIA, Université de Lorraine)

TBA

18 mars 2024

Mathematical informatics

Thomas Seiller (CNRS, LIPN)

What is a model of computation? What is a program, an algorithm? While theoretical computer science has been founded on computability theory, the latter does not answer these questions. Indeed, it is a mathematical theory of computable functions, and does not account for computation itself. A symptomatic consequence is the notion of Turing-completeness. This standard (sole?) equivalence between models of computation is purely extensional: it does only care about what is computed and not how, blind to complexity aspects and the question of algorithmic completeness. More importantly, the theory of computation is continuously growing further from how actual machines compute.

I will present a proposal for alternative foundations more faithful to computer science practice and interests. This mathematisation of computer science is grounded within the theory of dynamical systems, focussing on *how* computation is performed rather than only on *what* is computed. I will argue that it generalises computability theory while still allowing to recover standard results.

If time permits, I can then explain how this theory can be used to (I will let he audience decide which items will be discussed):
• provide a uniform account of several lower bounds from algebraic complexity and strengthen them
• define static analysis methods which can be implemented in usable tools
• define families of linear realisability models (realisability models for linear logic)
• lead to a semantic approach of implicit computational complexity
• propose a formal definition of the notion of algorithm

18 mars 2024

Languages of Higher Dimensional Timed Automata

Emily Clément (IRIF, Université Paris-Cité)

Higher Dimensional Automata (HDA) are a very powerful tool to represent non-interleaving concurrency (i.e. a || b =/= a.b + b.a). They generalise numerous models, such as Petri nets. Languages of HDA are sets of ipomsets, which represent the possible order on the events.
In recent years, interest in HDAs has increased and has led to numerous new results (e.g. 2021 Fahrenberg et al., 2023: Fahrenberg et al.). Recently, an extension of both Timed Automata and HDA were defined, called Higher Dimensional Timed Automata, to obtain a more refined information on posets: rather than only the precedence order, we are interested in the time intervals in which events are active.
In our work, we define languages of HDTAs as sets of interval-timed pomsets with interfaces. As an application, we show that language inclusion of HDTAs is undecidable. On the other hand, using a region construction, we can show that untimings of HDTA languages have enough regularity so that untimed language inclusion is decidable.

11 mars 2024

Lambda-Calculus, Taylor Expansion and (Tropical) Quantitative Semantics: an overview

Davide Barbarossa (University of Bath)

The plan of the talk will be, first, to give an overview of the Taylor expansion of the lambda-calculus and, then, to give an overview of some aspects of quantitative categorical semantics.
I will in particular highlight some results obtained for a semantics based on the tropical semiring, which appeared in a recent CSL paper, where programs can be seen as locally Lipschitz functions, and the lambda-calculus Taylor expansion gives local approximants of the Lipschitz constants.
Depending on the interest and the common knowledge of the audience, I will spend more time on one topic or another.

4 mars 2024

Computability of extender sets in multidimensional subshifts

Léo Paviet Salomon (GREYC, Université Caen Normandie)

Un résultat classique dans l’étude des langages formels est le théorème de Myhill-Nerode, qui donne des conditions nécessaires et suffisantes en terme de langages résiduels pour qu’un langage soit régulier. Dans cet exposé, on essaiera de montrer comment cet outil a été adapté à l’étude des espaces de pavages, où les configurations ne sont plus des mots finis mais des coloriages multidimensionnels infinis. En particulier, on étudiera l’/entropie d’extension/, introduite par R.Pavlov et T.French, qui représente le taux de croissance de cet équivalent aux langages résiduels. On donnera plusieurs caractérisations obtenus sur cette entropie grâce à la théorie de la calculabitlité, sur plusieurs clases de pavages mono- et multidimensionnels.

26 février 2024

Ingredients for a BSP library

Wijnand Suijlen (Huawei Technologies)

The Bulk Synchronous Parallel (BSP) model is a cost model for parallel computation, which algorithm designers can use to estimate how much time their parallel algorithm will take when using multiple processors on their computer simultaneously. Indirectly, it therefore aids also in design of parallel algorithms. The implementation of such a BSP algorithms may be much more complicated, however, because strange interactions inside middle-ware and hardware may unexpectedly ruin the carefully proven complexity bounds. For that reason, various BSP libraries have been proposed and developed, which programmers can use to implement BSP algorithms. This talk presents some of the techniques that such BSP libraries employ in order to present an ordinary computer as a highly reliable and efficient BSP computer.

5 février 2024

Performance Paradox for Matching models with greedy disciplines

Jean Michel Fourneau (DAVID, UVSQ)

A matching model is a triple based on a compatibility graph, a set of Poisson processes and a matching discipline. Each node of the graph is associated with a type of objects and the compatibility graph shows which objects interact. The interaction is the immediate deletion of some objects. If an arriving objet does not interact, it enters the system and wait until it can interact with someone. One of the possible applications of matching models is the kidney exchange system organized in many countries. In this talk I will show a performance paradox: adding more flexibility in the compatibility graph (i.e. adding new edges) will, for some graphs and arrival rates, lead to an increase of the total average sojourn time in the system. And this is proved for any greedy disciplines. We show this property holds for some family of graphs and is lifted for some modular constructions of graphs. As this result is mostly based on strong aggregation of Markov chains, I will begin by a short introduction of this property which is used in general to decrease the size of the models.

29 janvier 2024

Analog characterization of complexity classes

Riccardo Gozzi (LACL)

The purpose of this talk is to characterize complexity classes from standard computational complexity theory using systems of ordinary differential equations. We start by recalling concepts related to the general research field of analog computing, from a physical, theoretical, and abstraction level. We then proceed to provide historical context to the main model of the talk, the GPAC from C. Shannon, which describes the behavior of the analog machine called differential analyser. We then explain the evolution that the model had in literature throughout the years and present the details about the analog characterization for the classes P and FP, which connects the GPAC model with the discrete model of Turing machines. We explain how this equivalence should be intended and what are its main consequences. Finally, we briefly discuss some of the more recent developments on the subject, mentioning how to extend the characterization for the class FEXPTIME, for each level of the Grzegorczyk hierarchy, and for polynomial space complexity classes such as FPSPACE and PSPACE.