L'IRIF est une unité mixte de recherche (UMR 8243) entre le CNRS et l'Université Paris-Diderot, qui héberge deux équipes-projets INRIA.

Les objectifs scientifiques de l'IRIF se situent au cœur de l'informatique, et plus particulièrement sur la conception, l'analyse, la preuve et la vérification d'algorithmes, de programmes et de langages de programmation. Ils s'appuient sur des recherches fondamentales développées à l'IRIF en combinatoire, graphes, logique, automates, types, sémantique et algèbre.

L'IRIF regroupe près de deux cents personnes. Six de ses membres ont été lauréats de l'European Research Council (ERC), trois sont membres de l'Institut Universitaire de France (IUF) et deux sont membres de l'Academia Europæa.

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Jean-Eric Pin

Jean-Eric Pin, CNRS senior researcher at IRIF, is awarded the Arto Salomaa prize for his outstanding contribution to the field of Automata Theory.


IRIF co-organizes the Workshop on Emergent Algorithms and Network Dynamics (Wendy) that will take place at Institut Henri-Poincaré in Paris on October 10-11, 2018. Registration is free but mandatory. More details:


The October 2, IRIF organizes the next Annual workshop of the French Working Group on Complexity and Algorithms (CoA). This year, the workshop will consist of a series of introductory and survey talks about various hot topics in algorithms, including Blockchains, Machine Learning, Sum-of-Square, etc.


The EU QuantAlgo project workshop will be held in Paris at IRIF September 25-28, 2018. This is a joint workshop with the IRIF-IQC Cooperation project between CNRS and U. Waterloo. QuantAlgo project aims to combine research on the fundamentals of quantum algorithms with the development of new applications.


IRIF organizes the 59th IEEE Symposium on Foundations of Computer Science (FOCS 2018) on October 7-9, 2018. FOCS is a leading annual conference in Theoretical Computer Science, and has served in the last 60 years as a venue for announcing the major scientific advances in the field. The list of accepted papers is now available, and the registration is now open (deadline for early rate: September 9, 2018).


IRIF organizes the 7th FILOFOCS (French-Israeli Laboratory on Foundations of Computer Science) workshop which will be held at the institut Henri Poincaré (IHP), on 3-5 October, 2018. A preliminary list of speakers in now available and registration (mandatory, but free) is now open.

Michel Habib

At the occasion of the retirement of Michel Habib and in celebration of his achievements, IRIF organizes a two-day conference “40 années d'algorithmique de graphes”, 11-12 Oct, Amphi Turing (Sophie Germain, Univ. Paris Diderot). Free mandatory registration.

lundi 24 septembre 2018, 11h10, Salle 1007
Adam Shimi (IRIT - ENSEEIHT) Characterizing Asynchronous Message-Passing Models Through Rounds

One great issue in conceiving and specifying distributed algorithms is the sheer number of models, differing in subtle and often qualitative ways: synchrony, kind of faults, number of faults… In the context of message-passing, one solution is to restrict communication to proceed by round; A great variety of models can then be captured in the Heard-Of model, with predicates on the communication graph at each round. However, this raises another issue: how to characterize a given model by such a predicate? It depends on how to implement rounds in the model. This is straightforward in synchronous models, thanks to the upper bound on communication delay. On the other hand, asynchronous models allow unbounded message delays, which makes the implementation of rounds dependent on the specific message-passing model.

I will present our formalization of this characterization for asynchronous models. Specifically, we introduce Delivered collections: the collection of all messages delivered at each round, whether late or not. Defining predicates on Delivered collections then allows us to capture message-passing models at the same level of abstraction than Heard-Of predicates. The question is then reformulated to: what Heard-Of predicates can be generated by a given Delivered predicate?

I will provide an answer by considering all possible scheduling of deliveries of messages from the Delivered collections and change of rounds for the processes. Strategies of processes then constrain those scheduling by specifying when processes can change rounds; those ensuring no process is ever blocked forever generate a Heard-Of collection per run, that is a Heard-Of predicate. Finally, we use these strategies to nd a characterizing Heard-Of predicate through a dominance relation on strategies: a dominant strategy for a Delivered predicate implements the most constrained Heard-Of predicate possible. This approach oer both the dominant Heard-Of predicates for classical asynchronous models and the existence, for every Delivered predicate, of a strategy dominating large classes of strategies. On the whole, those results confirm the power of this formalization and demonstrate the characterization of asynchronous models through rounds as a worthwhile pursuit.

This is joint work with Aurélie Hurault and Philippe Quéinnec.

Soutenances de thèses
mardi 25 septembre 2018, 14h00, Salle 3052, Bâtiment Sophie Germain
Yann Hamdaoui (IRIF) Concurrency, References and Linear Logic

The topic of this thesis is the study of the encoding of references and concurrency in Linear Logic. Our perspective is to demonstrate the capability of Linear Logic to encode side-effects to make it a viable, formalized and well studied compilation target for functional languages in the future. The key notion we develop is that of routing areas: a family of proof nets which correspond to a fragment of differential linear logic and which implements communication primitives. We develop routing areas as a parametrizable device and study their theory. We then illustrate their expressivity by translating a concurrent λ-calculus featuring concurrency, references and replication to a fragment of differential nets. To this purpose, we introduce a language akin to Amadio’s concurrent λ-calculus, but with explicit substitutions for both variables and references. We endow this language with a type and effect system and we prove termination of well-typed terms by a mix of reducibility and a new interactive technique. This intermediate language allows us to prove a simulation and an adequacy theorem for the translation.

Combinatoire énumérative et analytique
jeudi 27 septembre 2018, 11h45, Salle 1007
François Bergeron (Université du Québec à Montréal) Positivité, fonctions symétriques, et énumération

La théorie des fonctions symétriques est une source particulièrement fertile d'identités combinatoires importantes. Pour ce faire, il faut bien entendu des expressions positives (avec coefficients entiers). Après avoir illustré les mécanismes qui permettent d'obtenir de belles identités combinatoires à partir des fonctions symétriques, nous allons montrer qu'il y a à la fois une rareté de ces phénomènes, et d'autre part une forte invariance de la positivité pour toutes les opérations importantes du contexte. On mentionnera au passage des liens avec une version algébrique du problème P vs NP.

Soutenances de thèses
jeudi 27 septembre 2018, 15h30, Salle 470E, Bâtiment Halle aux Farines
Pablo Rotondo (IRIF) Probabilistic studies in Number Theory and Word Combinatorics: instances of dynamical analysis

Dynamical Analysis incorporates tools from dynamical systems, namely the Transfer Operator, into the framework of Analytic Combinatorics, permitting the analysis of numerous algorithms and objects naturally associated with an underlying dynamical system. This dissertation presents, in the integrated framework of Dynamical Analysis, the probabilistic analysis of seemingly distinct problems in a unified way: the probabilistic study of the recurrence function of Sturmian words, and the probabilistic study of the Continued Logarithm algorithm.

Sturmian words are a fundamental family of words in Word Combinatorics. They are in a precise sense the simplest infinite words that are not eventually periodic. Sturmian words have been well studied over the years, notably by Morse and Hedlund (1940) who demonstrated that they present a notable number theoretical characterization as discrete codings of lines with irrational slope, relating them naturally to dynamical systems, in particular the Euclidean dynamical system. These words have never been studied from a probabilistic perspective. Here, we quantify the recurrence properties of a “random” Sturmian word, which are dictated by the so-called “recurrence function”; we perform a complete asymptotic probabilistic study of this function, quantifying its mean and describing its distribution under two different probabilistic models, which present different virtues: one is a naturaly choice from an algorithmic point of view (but is innovative from the point of view of dynamical analysis), while the other allows a natural quantification of the worst-case growth of the recurrence function. We discuss the relation between these two distinct models and their respective techniques, explaining also how the two seemingly different techniques employed could be linked through the use of the Mellin transform. In this dissertation we also discuss our ongoing work regarding two special families of Sturmian words: those associated with a quadratic irrational slope, and those with a rational slope (not properly Sturmian). Our work seems to show the possibility of a unified study.

The Continued Logarithm Algorithm, introduced by Gosper in Hakmem (1978) as a mutation of classical continued fractions, computes the greatest common divisor of two natural numbers by performing division-like steps involving only binary shifts and substractions. Its worst-case performance was studied recently by Shallit (2016), who showed a precise upper-bound for the number of steps and gave a family of inputs attaining this bound. In this dissertation we employ dynamical analysis to study the average running time of the algorithm, giving precise mathematical constants for the asymptotics, as well as other parameters of interest. The underlying dynamical system is akin to the Euclidean one, and was first studied by Chan (around 2005) from an ergodic, but the presence of powers of 2 in the quotients ingrains into the central parameters a dyadic flavour that cannot be grasped solely by studying this system. We thus introduce a dyadic component and deal with a two-component system. With this new mixed system at hand, we then provide a complete average-case analysis of the algorithm by Dynamical Analysis.

Catégories supérieures, polygraphes et homotopie
vendredi 28 septembre 2018, 14h00, Salle 1007
Juan Pablo Vigneaux (IMJ-PRG) Une introduction à la topologie de l'information