Équipe-projet Inria $\pi r^2$ (Inria)
Équipe thématique Algorithmes et complexité
Équipe thématique Algèbre et calcul
Équipe thématique Automates et applications
Équipe thématique Combinatoire
Équipe-projet INRIA (La référence de gang est supprimée le 20/01/2021) GANG
Équipe thématique Modélisation et vérification
Équipe thématique Preuves et programmes
Équipe thématique Théorie et algorithmique des graphes

Jour, heure et lieu

Le mercredi à 11h, salle 3052

Le calendrier des séances (format iCal).
Pour ajouter le calendrier des séances à votre agenda favori, souscrire au calendrier en indiquant ce lien.


Voir aussi le blog du séminaire, avec des résumés de certains exposés, à l'adresse : https://semidoc.github.io/.

Si vous êtes stagiaire, doctorant extérieur à l'IRIF, ou post-doc, et que vous souhaitez recevoir les annonces du séminaire doctorants, vous pouvez vous inscrire à la liste d'annonce : https://listes.univ-paris-diderot.fr/sympa/subscribe/semidoc-irif

Séances passées

Année 2021

Séminaire des doctorants
Mercredi 2 juin 2021, 16 heures, Salle 3052
Quentin Ferro (IRIF) Distributed Recoloring using the LOCAL Model

Recoloring is a reconfiguration problem : given a graph and two proper coloring of this graph, how to recolor from one coloring to the other by a series of elementary changes ? The talk will be based on the Distributed Recoloring paper from Marthe Bonamy, Paul Ouvrard, Mikaël Rabie, Jukka Suomela, and Jara Uitto (Disc 2018) which introduced the notion of distributed recoloring as follow : the input graph represent a network of computers that need to be recolored. Each node know its input color and its target color. Nodes are allowed to exchange messages with each other synchronously and, given rounds of messages, each node have to output its recoloring schedule, indicating when the node changes its color and to which color. The recoloring schedules have to be globally consistent so that the graph remains properly colored at each point, and we require that adjacent nodes do not change their colors simultaneously. This paper gave a lot of results for different situations of coloring (different types of graph, different number of color, different number of extra color), particularly problems with 1 extra colors, and left some open questions. I will present some results we have on some of those open questions.

Séminaire des doctorants
Mercredi 26 mai 2021, 16 heures, Salle 3052
Avinandan Das (IRIF) Combinatorial Proof for Chernoff-Hoeffding Concentration Bound

In this talk, I will give a combinatorial proof of the Chernoff-Hoeffding concentration bound, which says that the sum of independent $\{0,1\}$-valued random variables is highly concentrated around the expected value. Unlike the standard proofs, this proof does not use the method of higher moments, but rather uses a simple and intuitive counting argument. In addition, this proof is constructive in the following sense: if the sum of the given random variables is not concentrated around the expectation, then we can efficiently find (with high probability) a subset of the random variables that are statistically dependent. This talk is based on the paper “Constructive Proofs of Concentration Bounds” by Russell Impagliazzo and Valentine Kabanets.

Année 2020

Séminaire des doctorants
Mercredi 2 décembre 2020, 11 heures, Online
Phd Students Welcome session!

Séminaire des doctorants
Mercredi 6 mai 2020, 11 heures, Online
Cédric Ho Thanh (IRIF) An introduction to Docker

This presentation aims to be a quick introduction to docker: its role, inner workings, ecosystem, and most importantly, how to use it. We will start with a little bit of theory, and swiftly move to a demo. Some notions about operating systems might be beneficial, but I will try to review what we need.

Séminaire des doctorants
Mercredi 22 avril 2020, 11 heures, Online
Simon Mauras (IRIF) How to aggregate top-lists

A top-list is a possibly incomplete ranking of elements: only a subset of the elements are ranked, with all unranked elements tied for last. Top-list aggregation takes as input a collection of top-lists and aggregates them into a single complete output ranking, aiming to minimize the number of upsets (pairs ranked in opposite order in the input and in the output).

This talk will start with a quick survey on rank aggregation (the special case where every input list is a complete ranking of the elements), its relation to feedback arc sets in directed graphs, NP-Hardness, and approximation algorithms. Then we will discuss how such results can be extended to the aggregation of top-lists.

Preprint available: https://arxiv.org/abs/1811.01537

Séminaire des doctorants
Mercredi 15 avril 2020, 11 heures, Online
Chaitanya Leena Subramaniam (IRIF) The plus-construction for sheaves and factorisation systems

Sheaves are a fundamental kind of algebraic structure in mathematics, and iterating the so-called plus-construction is a well known process of turning a presheaf into a sheaf.

However, the plus-construction makes sense in much more generality than sheaves, and a result (joint with M. Anel) shows that it is in fact closely related to orthogonal factorisation systems on a category. Indeed, it can be used to construct such factorisation systems.

This has many applications, including in dependent type theory, where it has a fundamental application to modalities.

The talk will be a gentle introduction to the plus-construction and its various examples.

Séminaire des doctorants
Mercredi 8 avril 2020, 11 heures, Online
Nicolas Jeannerod (IRIF) Analysing installation scenarios of Debian packages

Debian GNU/Linux is a Linux distribution composed of free and open-source software. It is heavily used all over the world as an operating system for personal computers and servers, and is the basis for many other distributions.

Deban currently includes more than 28 thousand maintainer scripts, almost all of them written in POSIX shell. These scripts are executed with root privileges at installation, update, and removal of a package, which make them critical for system maintenance. While Debian policy provides guidance for package maintainers producing the scripts, few tools exist to check the compliance of a script to it.

This presentation reports on the application of a formal verification approach based on symbolic execution to find violations of some non-trivial properties required by Debian policy in maintainer scripts. We present our methodology and give an overview of the toolchain. We focus in particular on the tree logics used to represent symbolically a file system transformation, and the use of such a logic in the symbolic engine.


Séminaire des doctorants
Mercredi 1 avril 2020, 11 heures, Online
Simona Etinski (IRIF & INRIA) Stern's Zero Knowledge Identification Scheme

In the first part of the talk, I will present the class of interactive proofs (IP) and special property of some of the interactive proofs called zero-knowledge. Public and private coin methods will also be introduced as they play a major role in most of the interactive proofs. The second part of the talk will concern Stern's identification scheme: a zero-knowledge interactive proof that enables one party to prove its identity to the other party without revealing any further information about it. Relying on the syndrome decoding problem, which is believed to be NP-complete, the scheme is considered to be post-quantum and thus a valid candidate for identification schemes to be used long-term. Nevertheless, the rather high communication complexity prevents Stern's scheme from being widely used at the moment and thus poses an issue to address. Some of the recent results and suggested future directions in addressing this issue will be presented in this talk.


Séminaire des doctorants
Mercredi 25 mars 2020, 11 heures, Online
Nguyễn Lê Thành Dũng (LIPN) Aperiodicity in a non-commutative logic

We give a characterization of star-free languages in a λ-calculus with support for non-commutative affine types (in the sense of linear logic), via the algebraic characterization of the former using aperiodic monoids. Since this work is at the interface of two areas, namely automata theory and programming languages, the talk will assume very little background knowledge and recall the prerequisites for both. I will also present our main inspiration: Hillebrand and Kanellakis's little-known characterization of regular languages in the simply typed λ-calculus (LICS'96). This is a joint work with Pierre Pradic (Oxford); preprint available at https://hal.archives-ouvertes.fr/hal-02476219/document


Séminaire des doctorants
Lundi 2 mars 2020, 15 heures, Salle 3014
Pierre Cagne Les symmétries des sphères en fondations univalentes

Année 2019

Séminaire des doctorants
Mercredi 27 novembre 2019, 11 heures, Salle 3052
(Old) Phd Students Return of the PhD Seminar

Every new/old PhD student is invited to come and talk about her/his research interests.

Each talk will be 2-5 minutes long, and should be understandable by everyone.

Séminaire des doctorants
Mercredi 20 novembre 2019, 11 heures, Salle 3052
Pierre Ohlmann (IRIF) Controlling a random population

Bertrand et al. (2017) introduced a model of parameterised systems, where each agent is represented by a finite state system, and studied the following control problem: for any number of agents, does there exist a controller able to bring all agents to a target state? They showed that the problem is decidable and EXPTIME-complete in the adversarial setting, and posed as an open problem the stochastic setting, where the agent is represented by a Markov decision process. In this paper, we show that the stochastic control problem is decidable. Our solution makes significant uses of well quasi orders, of the max-flow min- cut theorem, and of the theory of regular cost functions.

Séminaire des doctorants
Mercredi 13 novembre 2019, 11 heures, Salle 3052
(New) Phd Students The PhD Seminar strikes back

Every new/old PhD student is invited to come and talk about her/his research interests.

Each talk will be 2-5 minutes long, without any slides, and should be understandable by everyone

Séminaire des doctorants
Mercredi 24 juillet 2019, 11 heures, Salle 3052
Hugo Moeneclaey (IRIF) Toward a Cubical Type Theory Univalent by Definition

Univalent foundations are based on a geometric interpretation of identity types in type theory. We will explain this interpretation, then we will give a brief introduction to Cubical Type Theory and explain why it is useful in this context. Then we will present some ideas from parametricity and sketch how we are trying to use them to build a variant of Cubical Type Theory.

Séminaire des doctorants
Mercredi 6 mars 2019, 11 heures, Salle 3014
Isaac Konan (IRIF) Partitions and Bijections

“For any positive integer n, there are as many partitions of n into distincts parts as partitions of n into odd parts”. This identity stated by Euler is quite trivial to prove by calculations, but not easy show bijectively.

I will discuss bijections for some well-known partition identities, such as Schur partition identity and q-binomial coefficient.

NB: Open talk, all you need is just how to count objects.

Séminaire des doctorants
Mercredi 27 février 2019, 11 heures, Salle 3052
Pierre Ohlmann (IRIF) Lower bounds for arithmetic circuits via the Hankel matrix

We study the complexity of representing polynomials by arithmetic circuits in both the commutative and the non-commutative settings. Our approach goes through a precise understanding of the more restricted setting where multiplication is not associative, meaning that we distinguish (xy)z from x(yz).

Our first and main conceptual result is a characterization result: we show that the size of the smallest circuit computing a given non-associative polynomial is exactly the rank of a matrix constructed from the polynomial and called the Hankel matrix. This result applies to the class of all circuits in both commutative and non-commutative settings, and can be seen as an extension of the seminal result of Nisan giving a similar characterization for non-commutative algebraic branching programs.

The study of the Hankel matrix provides a unifying approach for proving lower bounds for polynomials in the (classical) associative setting. We demonstrate this by giving alternative proofs of recent results proving superpolynomial and exponential lower bounds for different classes of circuits as corollaries of our characterization result.

Our main technical contribution is to provide generic lower bound theorems based on analyzing and decomposing the Hankel matrix. This yields significant improvements on lower bounds for circuits with many parse trees, in both (associative) commutative and non-commutative settings. In particular in the non-commutative setting we obtain a tight result showing superpolynomial lower bounds for any class of circuits which has a small defect in the exponent of the total number of parse trees.

Année 2018

Séminaire des doctorants
Mercredi 28 novembre 2018, 11 heures, Salle 3052
Cédric Ho Thanh (IRIF) Type theoretical approach to opetopes

Opetopes are shapes (akin to globules, cubes, simplices, etc.) introduced to describe laws and coherence in higher categories. Their classical definitions, however, makes them difficult to manipulate efficiently. In this presentation, I will present ongoing works aiming to describe them completely from a type-theoretic standpoint. If time permits, I will showcase a proof checker for opetopes.

Séminaire des doctorants
Mercredi 14 novembre 2018, 11 heures, Salle 3052
Thomas Colcombet (Automata team) Writing (large) LaTeX documents with the knowledge package.

Writing your PhD thesis is a huge work (took me nine months). A burden. Everyone wants it to be THE document that the next generation will read in order to learn the wonderful stuff you have developed at IRIF.

Clearly, there are some pitfalls to avoid. Sometimes a scientifically excellent thesis turns out to be barely usable, because definitions are difficult to find, hard to parse, etc… And the reviewers get mad at you (but say it gently because they are polite). It is your duty to pay attention to all these details (it is also the duty of your PhD advisor to help you in that) and make a document as user friendly as possible.

One can find many documents describing how to write good science/a good thesis on the internet (read some of them!). I will not try to cover this wide subject. My goal in this talk will be to emphasize on some presentation points, and show you how some tools can help you in your writing (this is an advertisement for the LaTeX package « knowledge »).

If you want to test, you can bring your laptop with an up-to-date distribution of LaTeX.

Séminaire des doctorants
Mercredi 31 octobre 2018, 11 heures, Salle 3052
Anupa Sunny & Zhouningxin Wang New PhD session

Explicit, Almost Optimal Epsilon-Biased Sets

by Anupa Sunny

Abstract: This talk is based on a paper by Amnon Ta-Shma on the construction of epsilon biased sets which have a support size close to the Gilbert-Varshamov bound, a notion from coding theory. We will look at the Rozenman-Wigderson construction of the epsilon-biased set in which the bias of a set is amplified by taking a walk over an expander graph. We will then look at Ta-Shma's construction which is based on a modified version of the zigzag product, namely the s-wide replacement product.

Homomorphism of signed graphs

by Zhouningxin Wang

Abstract: The signed graph is a graph whose edges are assigned with the signs + and -. A homomorphism of one graph to the other preserves the adjacencies and incidences of these two edges. We extend the concept of homomorphism for signed graphs. An intuitive example will be given to explain why we consider the homomorphism of signed graphs. We will give the minimum signed graph, namely Spal_5, to which all the signed K_4-minor-free graph admits homomorphism to. In the last part, we will show the necessary and sufficient conditions for a signed K_4-subdivision being a core.

Séminaire des doctorants
Mercredi 17 octobre 2018, 11 heures, Salle 3052
Abishek De & Simon Mauras Newcomers' session

Abishek De : Distributed Control Problem for Free Choice Systems

The distributed synthesis problem is about constructing correct distributed systems, i.e., systems that satisfy a given specification. We consider a slightly more general problem of distributed control, where the goal is to restrict the behavior of a given distributed system in order to satisfy the specification. Our systems are finite state machines that communicate via rendezvous (asynchronous automata). There are a few classes of systems for which the problem has been shown decidable. We solve it for free choice systems, systems whose entire behaviour can be expressed in a (possibly infinite) tree.

Simon Mauras : Social choice theory, and a small survey about rank aggregation

How should we vote? This question has been adressed by philosophers and mathematicians since the XVIIIth century, but no satisfactory solution exists. The talk will start with classical results on social choice theory and move on to the aggregation of rankings seen as an optimization problem. We will discuss NP-Hardness, Hardness of approximation and Approximation algorithms for several variants of this problem.

Séminaire des doctorants
Mercredi 12 septembre 2018, 11 heures, Salle 3052
Farzad Jafarrahmani Denotational semantics of Linear Logic with least and greatest fixpoints

We develop a denotational semantics of full propositional classical linear logic extended with least and greatest fixpoints of formulae (\mu LL) in coherence spaces with totality. The presence of totality predicates, which are a denotational account of the syntactic notion of normalization, allows for dual and non-trivial denotational interpretations of the mu and nu fix point operators involving Knaster Tarski's theorem. We illustrate the construction by means of several examples such as integer numbers system, and by an embedding of Gödel's system T in \mu LL. This specific denotational semantics of muLL is clearly an instance of a more general pattern. We also encode the exponentials of linear logic using least and greatest fixpoints and then explain the difference between the new exponentials and the original ones from denotational semantics point of view. This is based on joint work by Thomas Ehrhard.

Short session

Séminaire des doctorants
Mercredi 27 juin 2018, 11 heures, Salle 3052
Victor Lanvin (Équipes Preuves, programmes, et Systèmes) Introduction to gradual typing with union and intersection types

Since the advent of types in programming languages, the two concepts of static typing and dynamic typing have been engaged in a terrible battle. Simply querying “static typing vs dynamic typing” yields more than half a million results on Stack Overflow. On the one hand, static typing provides strong safety guarantees before a program is even executed, by checking during compilation that types are not misused. On the other hand, dynamic typing is more flexible and is better suited to rapid prototyping. With both approaches having strong arguments in their favor, the battle seems endless. Yet, all hope is not lost. Gradual typing is a recent approach that aims at combining the safety guarantees of static typing with the flexibility and development speed of dynamic typing. The idea behind it is to introduce an “unknown” type, used to inform the compiler that additional type checks may need to be performed at run time in some places. Programmers can then “gradually” add type annotations to a program, and control precisely how much checking is done statically versus dynamically. Our work aims at integrating union and intersection types with gradual typing to allow for stronger safety guarantees and a finer control over dynamic types.

Note: this will (should) be a very general presentation about gradual typing and set-theoretic types consisting mostly of practical examples and without too many technical details. Don't hesitate to bring your computer, a book, or your Nintendo Switch™ if you already know the topic. :-)

Séminaire des doctorants
Mercredi 20 juin 2018, 11 heures, Salle 3052
Laurent Feuilloley (Équipes Compsys, GANG et graphes) Distributed decision

In this talk, I will introduce the domain of distributed decision, and review some of the results and insights gathered during my PhD.

The underlying model of this study is the local model. The local model is defined to answer questions of the following type: given a communication network, whose nodes are machines, and edges are communication links, is it possible that the nodes solve some task X, if they communicate only with the nodes that are close to them? A classic problem is colouring: can a node choose a colour, with only the knowledge of a small neighbourhood of the graph, such that the colours chosen by the nodes form a proper colouring of the graph? As in the centralized setting, it is interesting to study decision problems, that are yes-no questions, and to define complexity classes to classify these problems; this is distributed decision.

The complexity class we use as the equivalent of the class P in the centralized setting, is pretty small, and it is then natural to look at some form of non-determinism, to have a chance to understand more problems. In this model, non-determinism can be thought as a piece of global information that can be verified locally. The theoretical motivation is that to understand how local a problem is, one can ask how much global information is needed to solve it. The more practical motivation is that if one can design schemes with little global information then it can help to design more robust distributed algorithms such as self-stabilizing algorithms. The results I will present play with different natural notions of non-determinism, and how they influence the complexity classes defined.

I will spend time to carefully describe the model, thus no prior knowledge is needed.

Séminaire des doctorants
Mercredi 6 juin 2018, 11 heures, Salle 3052
Pierre Ohlmann & Sidi Mohammed Beillahi (Équipe automate & Équipe vérification) Unifying non-commutative arithmetic circuit lower bounds & Robustness of Programs Against Consistency Relaxation

Unifying non-commutative arithmetic circuit lower bounds (Pierre Ohlmann)

We develop an algebraic lower bound technique in the context of non-commutative arithmetic circuits. To this end, we introduce polynomials for which the multiplication is also non-associative, and focus on their circuit complexity. We show a connection with multiplicity tree automata, leading to a general algebraic characterization. We use it to derive meta-theorems for the non-commutative case, and highlight numerous consequences in terms of lower bounds.


Robustness of Programs Against Consistency Relaxation (Sidi Mohammed Beillahi)

Sequential Consistency (SC) and Serializability (Ser) are the classical consistency models for concurrent and distributed programs. They are the intuitive models for developers. Due to the costly synchronization required by the two models, most of existing memory models and distributed implementations of data structures do not use these two models. Instead, in order to reduce the latency and remove unnecessary synchronization, modern processors and databases adopt relaxed and weaker consistency models. However, this weakening of the consistency models implies new unexpected behaviors when running programs over the weaker models. We address in this work the problem of detecting unexpected behaviors of a program that were observed when weakening the consistency model. In particular, we check whether the two sets of executions traces of a program over the SC (resp, Ser) model and some weaker consistency model coincide or not. We characterize the set of executions traces that violate this equality and drive a decision procedure to detect these traces. In the case where there are no traces that violate this equality we refer to a program to be Robust.

A joint work with Ahmed Bouajjani and Constantin Enea

Séminaire des doctorants
Mercredi 23 mai 2018, 11 heures, Salle 3052
Léo Stefanesco (Algebra and calculus, proofs and programs teams) An Asynchronous Soundness Theorem for Concurrent Separation Logic

The talk will start with an introduction to (concurrent) separation logic.


Concurrent separation logic (CSL) is a specification logic for concurrent imperative programs with shared memory and locks. In this talk, we develop a concurrent and interactive account of the logic inspired by asynchronous game semantics. To every program C, we associate a pair of asynchronous transition systems [C]S and [C]L which describe the operational behavior of the Code when confronted to its Environment, both at the level of machine states (S) and of machine instructions and locks (L). We then establish that every derivation tree π of a judgment Γ ⊢ {P}C{Q} defines a winning and asynchronous strategy [π] with respect to both asynchronous semantics [C]S and [C]L. From this, we deduce an asynchronous soundness theorem for CSL, which states that the canonical map L : [C]S → [C]L from the stateful semantics [C]S to the stateless semantics [C]L satisfies a basic fibrational property. We advocate that this fibrational property provide a clean and conceptual explanation for the usual soundness theorem of CSL, including the absence of data races.

(Joint work with Paul-André Melliès)

Séminaire des doctorants
Mercredi 2 mai 2018, 11 heures, Salle 3052
Emiliano Lancini (Laboratoire d'Informatique de Paris Nord) Box-Total Dual Integrality and k-Edge-Connectivity

In the first half of the 20th century the distribution of electricity became a major issue for many european nations. From this situation arose the problem of building a connected network of minimum length. The mathematical model underlying this problem is the minimum spanning tree problem, it has been investigated by many authors and is now considered a classical problem of combinatorial optimisation.

Nowadays it is often required that telecommunication networks keep unaltered their functionality even after the failure of some of their links. This leads to a generalisation of the minimum spanning tree problem named k-edge-connected spanning subgraph problem.

In this talk we show a characterisation of a graph class in terms of integrality properties of polyhedra naturally associated to the k-edge-connected spanning subgraph problem.

The concept of total dual integrality (TDI) dates back to the works of Edmonds, Giles and Pulleyblank in the late 70's, and is strongly connected to min-max relations in combinatorial optimisation.

The system Ax>=b is TDI if, in the following equation, for each integer vector c, for which the minimum in the following equation is finite, there exists an integer optimal solution for the maximum.

min {cx: Ax>= b} = max {yb: yA = c, y >= 0}

We are interested in the stronger property of box-TDIness. A system Ax>=b is called *box-TDI* if the system Ax >= b, l ⇐ x ⇐ u is TDI for all rational vectors l and u.

We prove that, for k>=2, the k-edge-connected spanning subgraph polyhedron is a box-TDI polyhedron if and only if the graph is series-parallel. Moreover, in this case, we provide a box-TDI system with integer coefficients describing this polyhedron.

Séminaire des doctorants
Mercredi 25 avril 2018, 11 heures, Salle 3052
Raphaëlle Crubillé (Algebra and calculus, proofs and programs teams) Probabilistic Stable Functions on Discrete Cones are Power Series.

The category of probabilistic coherence spaces (PCoh_!), introduced by Danos and Ehrhard, is a fully abstract model for PCF with *discrete* probabilities, where morphisms can be seen as power series. The category Cstab_m, of measurable cones and measurable stable functions, has been introduced by Ehrhard, Pagani and Tasson as a model for PCF with *continuous* probabilities. In this talk, we will study the shape of stable functions when they are between *discrete* cones, and it will allow us to see that PCoh_! is a full subcategory of Cstab_m.

Séminaire des doctorants
Mercredi 18 avril 2018, 11 heures, Salle 3052
Paulina Cecchi & Antoine Allioux (Automata, Combinatorics teams & Algebra and calculus, proofs and programs teams) New PhD student introduction session

* Paulina Cecchi

Title: Some interactions between words combinatorics and symbolic dynamics.

Abstract: Word combinatorics has been fruitfully used to study several topological and mesure-theoretic properties of dynamical systems, through the analysis of suitably chosen symbolic dynamical systems. In this talk, we will introduce some notions of symbolic dynamics and present some examples which illustrate how word combinatorics can be used as a tool to solve questions arising from this branch of mathematics.


* Antoine Allioux

Title: The curse of Martin-Löf identity type

Abstract: The identity type of Intuitionistic Type Theory (ITT) endows types with a structure of infinity-groupoid. This higher structure follows from the fact that the Uniqueness of Identity Proof (UIP) is not derivable in ITT. Homotopy Type Theory (HoTT) takes advantage of this observation by enriching ITT with new principles which are coherent with this interpretation, namely the Univalence Axiom and the Higher Inductive Types (HITs).

HITs are a generalization of inductive types which allow, in addition to create regular inhabitants of an inductive type, to postulate identities between them as well as identities between these identities, and that ad infinitum. It is then tempting to try to present mathematical structures using these new types like one would do in mathematics using generators and relations.

However, problems quickly arise as soon as one needs a strict equality. Indeed, the identity type expresses a weak equality leading to the usual coherence problems. Trying to solve these naively, we run into the problem of having to define an infinite sequence of coherence data.

If HoTT is to be a credible foundation of mathematics, the question of formalizing structures which need a strict equality is crucial. The answer to this question rests, in part, upon our achievement to either present these structures differently in the existing theory or to enrich it so that it becomes tractable to express them.


Séminaire des doctorants
Mercredi 11 avril 2018, 11 heures, Salle 3052
Brieuc Guinard Intermittent Locomotion in Graphs

Everyone who has ever lost their keys in a busy room knows that they cannot move at full speed and hope to find them ; one must slow down enough as not to miss them. This compromise between speed of moving and success of detection is not specific to humans, of course, and in fact is commonly encountered in foraging animals, and even in cell biology. This opposition between relocation and detection can even lead to an intermittent behavior, i.e. with different phases during the search. We model such search processes by memoryless explorations on graphs, i.e. random walks, where you can decide at each step to query a node or not. The goal is to balance the time spent walking and the time spent querying.

Séminaire des doctorants
Mercredi 28 mars 2018, 11 heures, Salle 3052
Yann Hamdaoui (Proofs and Programs and Conception and Analysis of Systems teams) Translating a Concurrent Lambda Calculus into Linear Logic proof (nets)

Logical translations of intuitionnistic logic into linear logic have been studied for their sole interest. Incidentally, they provide translations of simply typed lambda calculus to linear logic: apart from its theoretical insights, the asynchronous nature of linear logic's cut-elimination make it also an interesting target of compilation, enabling distributed and/or parallel execution models. We present here translation of a richer typed calculus, featuring parallel threads and references, into a fragment of linear logic.

Séminaire des doctorants
Mercredi 21 mars 2018, 11 heures, Salle 3052
Mengchuan Zou (Theory and algorithmics of graphs team) Generalization of binary search in trees and other structures

The tree search problem is the following generalization of the binary search problem. A search strategy is required to locate an unknown target node t in a given tree T. Upon querying a node v of the tree, the strategy receives as a reply an indication of the connected component of T \ {v} containing the target t. The cost of querying each node is given by a known non-negative weight function, and the considered objective is to minimize the total query cost for a worst-case choice of the target.

We will also introduce some known facts on other structures and how tree search problem is related to other problems via equivalences.

Séminaire des doctorants
Mercredi 21 février 2018, 11 heures, Salle 3052
Zeinab Galal & Ranadeep Biswas (Algebra and computation & Modeling and verification) Species of structure: a Bridge between Differential Lambda Calculus and Combinatorics & Verifying Database Histories

*Species of structure: a Bridge between Differential Lambda Calculus and Combinatorics*

Species of structure lie at the intersection of combinatorics and denotational semantics. They were first introduced by Joyal as a unified framework for the theory of generating series in enumerative combinatorics and multiple tools were developed for the resolution of differential equations of species in this setting. Later, Fiore presented a generalized definition that both encompasses Joyal's species and constitutes a model of linear logic.

We will first introduce and connect the different viewpoints of species of structure and their series counterpart (analytic and normal functors) presented by Joyal, Girard and Hasegawa. Next, we will examine how the bicategory of generalized species of structure forms a model of differential linear logic.

As our end goal is to develop methods of resolution of differential equations for λ-terms, we will investigate the possible directions to tackle this problem.


*Verifying Database Histories*

Popular databases offer control over the isolation level to which the operations in one transaction are visible to the operations in other concurrent transactions. Lower levels allow weaker consistency. So, we have to ensure that the histories of a database are consistent with their isolation levels.

Unfortunately, these isolation levels are mostly defined as low-level operations which makes it complicated to reason about the behavior of the system running under those isolations.

In this talk, we will present some popular isolation levels and consistency criteria for databases. We will introduce a framework, in which it becomes easier to formally reason about the behavior of a system. Then we will explore the complexities of deciding some consistency criteria using that framework.

Séminaire des doctorants
Mercredi 14 février 2018, 11 heures, Salle 3052
Narcisse Nya Kamtchoum (LIP6) Modèles analytiques pour les performances des réseaux cellulaires

Afin d'augmenter le débit et accroître la couverture réseau, les réseaux mobiles ne cessent d'évoluer rapidement vers des technologies caractérisées par des interfaces radio plus sophistiquées. Par exemple, alors que le déploiement des réseaux 4G ne faisait que commencer, les premières mises à jour des solutions LTE-A étaient déjà planifiées par les opérateurs et Actuellement, les technologies 5G font l'objet de recherches actives dans le monde entier. Ces changements rapides sont motivés par l'explosion du trafic mobile, tel que prédit par de nombreuses études et observé dans les réseaux actuels.

Cependant, les opérateurs ont du mal à s'adapter à la proportion toujours grandissante d'utilisateurs mobiles et à leur offrir une qualité d'expérience (QoE) satisfaisante. Dans ce contexte, il est importante pour les opérateurs et les équipementiers de disposer d'outils simples et efficaces pour mieux comprendre le comportement de leurs réseaux et évaluer la qualité des services offerts aux utilisateurs. Notre objectif est de proposer des modèles analytiques pour l'évaluation des performances des réseaux cellulaires en tenant compte de la mobilité des utilisateurs. Tout en permettant de résoudre des problèmes d'évaluation de performance les plus complexes, ces modèles se doivent d'être simple afin de faciliter leur utilisation.

Le séminaire sera donné en français.

Séminaire des doctorants
Mercredi 7 février 2018, 11 heures, Salle 3052
Nicolas Jeannerod (Team Analysis and conception of systems) Unix filesystems and First-Order Theory of an Algebra of Feature Trees with Updates

In the CoLiS project (for Correctness of Linux Scripts), our mid-term goal is to automatically verify certain properties on installation packages that may include shell scripts. In order to do that, we want to write a symbolic execution tool that would compute abstract specification for each installation script in term of filesystem transformations.

We investigate a logic of an algebra of trees with an update operation, which expresses that a tree is obtained from an input tree by replacing a particular direct subtree while leaving the rest intact. This operation improves on the expressivity of existing logics of tree algebras in our case of feature trees. These allow for an unbounded number of children of a node in a tree.

We show an efficient way of testing the satisfiability of existential clauses in this algebra that can lead to an efficient implementation of our symbolic execution engine. We also show the decidability of the first-order theory of this algebra via a weak quantifier elimination procedure which is allowed to swap existential quantifiers for universal quantifiers.

Séminaire des doctorants
Mercredi 31 janvier 2018, 11 heures, Salle 3052
Thomas Williams (Gallium, INRIA) Refactoring ML programs using ornaments

Ornaments are a way to describe changes in datatype definitions that preserve their recursive structure, reorganizing, adding, or dropping some pieces of data. The relation between two types given by an ornament can be used to define a lifting relation between functions operating on a bare definition and functions operating on the ornamented structures. Thus, ornaments provide a way to specify the desired behaviour of a program refactored to work on an ornamented datatype.

In this talk, I will explain how ornaments can be used to automatically lift a function. I will present a prototype implementation of lifting along ornaments for a subset of OCaml and describe some families of use cases. I will introduce a principled approach to obtaining a lifting from the base code, as abstraction followed by specialization. I will explain how this approach allows us to prove the correctness of the lifting.

Séminaire des doctorants
Mercredi 24 janvier 2018, 11 heures, Salle 3052
Alessandro Luongo & Ny Aina Andriambolamalala (Algorithms and complexity team & Combinatorics team) Recent updates in quantum machine learning & Election de leader dans un réseau radio simple saut avec detection de collision

*Recent updates in quantum machine learning*

In this talk we are going through some recent algorithms in the field of quantum machine learning. Most of the techniques use tools from quantum algorithmics such as counting, optimizing, estimating distances and singular values which will be introduced here. Using these primitives it's possible to build more complex operations of a matrix algebra. I'll also describe a classical machine learning algoritm in the process of being translated in a fully fledged quantum algorithm. This is the first biologically plausible quantum algorithm with an exponential speedup w.r.t the dimension of the space and the number of datapoints. This quantum algorithm has been simulated and used to classify handwritten digits with high accuracy.

*Election de leader dans un réseau radio simple saut avec detection de collision*

Les résultats de Dan Willard (1986) montrent un algorithme randomizé d'élection de leader en temps moyen $O(\log\log{n})$.

Depuis, la question de savoir s'il existe un algorithme convergeant en temps log-logarithmique mais avec très forte probabilité est ouverte.

Nous répondons affirmativement à cette question. Nous montrons aussi comment utiliser nos résultats pour élaborer des protocoles d'élection dans divers modèles de systèmes distribués.

These are two newcomers talk, 30 minutes each. The first will be in English, the second in French.

Année 2017

Séminaire des doctorants
Mercredi 20 décembre 2017, 11 heures, Salle 3052
Leo Stefanesco (Équipes “Preuves et Programmes” et “Algèbre et Calcul”) “A concise introduction to logical relations” followed by “A Logical Relation for Monadic Encapsulation of State”

1st part (E for Everyone): A concise introduction to logical relations

Logical relations are a powerful technique to prove properties about programs. In particular, for proving that two programs are contextually equivalent.

In this talk, we will see that, in System F (aka the polymorphic lambda calculus), the only program of type ∀ a, a → a is the identity.

I will also sketch how to extend logical relations to realistic languages such as ML.

2nd part (POPL talk rehearsal):

A Logical Relation for Monadic Encapsulation of State

We present a logical relations model of a higher-order functional programming language with impredicative polymorphism, recursive types, and a Haskell-style ST monad type with runST. We use our logical relations model to show that runST provides proper encapsulation of state, by showing that effectful computations encapsulated by runST are heap independent. Furthermore, we show that contextual refinements and equivalences that are expected to hold for pure computations do indeed hold in the presence of runST. This is the first time such relational results have been proven for a language with monadic encapsulation of state. We have formalized all the technical development and results in Coq.

Séminaire des doctorants
Mercredi 13 décembre 2017, 11 heures, Salle 3052
Simon Halfon (ENS Cachan) Well Quasi-Orders and Extreme Stratospheric-Complexity-Classes of Death — Beaux pré-ordres et classes de complexité stratosphériques de la mort

It is widely known how to prove the termination of an algorithm using well-founded orderings. It is however usually believed that no complexity upper bound can be derived from these termination proof, often seen as non-constructive. In this talk, I will present some ideas to infer upper bounds from such termination proofs. I will try to give you a taste of the complicated combinatorics behind, that results in surprisingly high complexities. Oxygen bottles and pressure suits required, we are going beyond Elementary.

No special knowledge is required to follow the talk.

Nous savons tous qu’il est très pratique pour prouver la terminaison d’un algorithme d’utiliser des ordres bien fondés. Cependant, il est commun de penser que cette technique ne donne aucune information sur la complexité de l’algorithme, car la preuve est non constructive. Dans cet exposé, je présenterai quelques idées pour extraire une borne supérieur de complexité d’une telle preuve de terminaison. J’essaierai de vous donner une idée de la combinatoire compliquée que cela engendre, et qui résulte en des complexité très élevée. Bouteilles d’oxygène et combinaisons pressurisées obligatoire, on s’envole au delà de l’Élémentaire.

Aucune connaissance spécifique n'est nécessaire pour suivre l'exposé.

Séminaire des doctorants
Mercredi 6 décembre 2017, 11 heures, Salle 3052
Axel Osmond & Yassine Hamoudi ([1] “Algebra and calculus” and “Proofs and programs” teams, [2] Algorithms and complexity team) New PhD student introduction session. [1] From pointless topology to formal topology [2] ACC0 and multiparty communication: fighting the log n barrier.

[1] While point-set topology is highly practical as a framework to do spatial reasoning, one can rise some ontological and logical suspicions about naive notion of points as they constitute idealized objects with somewhat inaccessible aspects in a constructive and finite point of view. Locales and Frames theories are two deeply entangled realms aimed at rebuilding topology on latticial and categorical foundations, in which usual notions of points, opens, subspaces, separability, compacity… can be reexpressed as first order algebraic properties in latticial context, or both generalized and made constructive.

Formal topology goes further into this last direction, using systems of axioms about coverings as a deductive systems which leads to a type-theoretic flavored, predicative and constructive topology, endowed with multiple and finer notions of points, separability… and suited for intuitionistic reasoning.

[2] The Number On the Forehead model is a multiparty communication game between k players that collaboratively want to evaluate a given function F : X1 x … x Xk → Y on some input (x1, …, xk) by broadcasting bits according to a predetermined protocol. The input is distributed between the players in such a way that each player i sees all of it except xi (as if xi is written on the forehead of player i).

A central open question in this model, called the log n barrier, is to find a function which is hard to compute when the number of players is polylog(n) or more (where the xi's have size poly(n)). This has an important application in circuit complexity, as it could help to separate ACC0 from other complexity classes.

In this talk, we will recall first the connection between ACC0 and communication complexity, and then describe a new efficient communication protocol that prevents some important functions from breaking the log n barrier.

Séminaire des doctorants
Mercredi 22 novembre 2017, 11 heures, Salle 3052
Jules Chouquet (Proofs and Programs team) Linear logic proof nets and Taylor expansion.

I will first introduce linear logic proof nets, for the multiplicative and exponential fragment (MELL), and I will especially insist on the computational meaning of the exponential boxes: these are constructions containing the possibility of duplication and deletion of entire parts of the structures (all the non linear part of the calculus).

Once these notions are introduced, I will explain how it is possible to express this computational paradigm in a linear setting through a syntactical Taylor expansion. The idea is to understand exponential boxes in a differential variant of linear logic, and to represent it with linear combination.

If we have time, I will try to give an idea of some algebraic issues concerning this construction, and a method to show for example, that the normal form of the Taylor expansion of a MELL always converges.

NB: Taylor expansion is here analogical to the lambda calculus (with its differential version too) one, if someone heard about it, it can give a first intuition.

Séminaire des doctorants
Mercredi 15 novembre 2017, 11 heures, Salle 3052
Chaitanya Leena Subramaniam (“Algebra and calculus” and “proofs and programs” teams) Homotopy type theory and the fibred structure of dependent types

This is another session of the PhD introduction series.

Chaitanya will do a 30 minutes talk. Given that the talk will not last as long as usual, we will also take advantage of the opportunity to discuss the organization of the seminar.


The talk will not be about my particular research problem. It will seek instead to give a gentle pictorial introduction to the inherent structure of dependent types and how this structure determines what dependent types and dependently-typed programs (or proofs) *mean*.

The focus will be on why this structure naturally leads to homotopy type theory and univalence. As a bonus, and if time permits, there will be some remarks on univalence and extensionality.

Séminaire des doctorants
Mercredi 8 novembre 2017, 11 heures, Salle 3052
Francesco Antonio Genco (Technische Universität Wien) Typing Parallelism and Communication through Hypersequents

We present a Curry–Howard correspondence for Gödel logic based on a simple natural deduction reformulating the hypersequent calculus for this logic. The resulting system extends simply typed λ-calculus by a symmetric higher-order communication mechanism between parallel processes. The normalization proof employs reductions that implement forms of code mobility. We consider this result from a broader perspective and, following A. Avron's 1991 thesis on the connection between hypersequents and parallelism, we discuss the generalisation of the employed techniques for other intermediate logics.

Séminaire des doctorants
Mercredi 25 octobre 2017, 11 heures, Salle 3052
Cédric Ho Thanh & Isaac Konan (Algebra and calculus team / Combinatorics team) New PhD student introduction session

This special session will introduce two new PhD students who will each be giving a short talk.

Isaac Konan, Bijective proof and generalization of Siladic's theorem

In a recent paper, Dousse introduced a refinement of Siladic̀’s theorem on partitions, by using the method of weighted words, where the different parts could take 2 colours. The proof of that refined theorem used some recursive equations with q-series. In this presentation, I will give the big lines of a bijective proof of the Dousse’s theorem, moreover which could be extended on a coloring with more than 2 colours.

Cédric Ho Thanh, Opétopes, Réécriture, et Koszulité

Ma thèse consiste en 3 mots que je vais tenter d'expliquer.

Séminaire des doctorants
Mercredi 11 octobre 2017, 11 heures, Salle 3052
Hadrien Batmalle (Équipe Preuves et Programmes) From Cohen's Forcing to Classical Realisability: A New Approach

English abstract below

Du forcing à la réalisabilité classique: une nouvelle approche

La réalisabilité classique permet d'interpréter des théories mathématiques classiques, comme la théorie des ensembles ZF, dans divers modèles de calculs (lambda-calcul avec continuations, domaines…). L'intérêt est double: côté informatique, il s'agit d'extraire des interprétations calculatoires de preuves classiques; côté mathématique, on obtient de nouveaux modèles de ces théories classiques (les deux aspects étant intimement liés). Une grande partie de la recherche en réalisabilité classique étudie la structure de ces modèles, qui apparaissent comme une généralisation du forcing de Cohen. Nous nous intéresserons ici à une nouvelle méthode pour exporter des propriétés des modèles de forcing aux modèles de réalisabilité, qui permet de construire des interprétations de deux théories contradictoires dans un même modèle de calcul, ce qui ouvre la voie à une analyse fine des conséquences calculatoires de la présence ou non de tel ou tel axiome.

From Cohen's Forcing to Classical Realisability: A New Approach

Classical realisability is a framework for interpreting classical theories in mathematics, such as the ZF set theory, in various models of computation (lambda-calculus with continuations, domains…). The goal is twofold: from the computer scientist's point of view, this is a method for extracting computational interpretations out of classical proofs; from the mathematician's, this is a trove of new models for these classical theories (both sides being tightly interwoven). A good deal of the research in this area is focussing on the structure of these models, arising as a generalisation of Cohen's forcing. In this talk we'll present some consequences of a new method for exporting properties of Cohen's forcing models into properties of classical realisability models. In particular we obtain interpretations of two incompatible theories in the same model of computation, which clears the path to studying the computational consequences of the presence, or lack thereof, of some axiom.

Séminaire des doctorants
Mercredi 27 septembre 2017, 11 heures, Salle 3052
Baptiste Louf & Victor Lanvin (Combinatorics and PPS teams) New PhD student introduction session

This special session will introduce two new PhD students who will each be giving a short talk. Here are the titles and abstracts of the talks:

Combinatorial maps : algebraic and bijective enumeration

Combinatorial maps (which are embeddings of graphs on surfaces) are well studied objects in combinatorics, which have applications in other domains, such as quantum gravity. The goal is to enumerate them (sometimes exactly, sometimes asymptotically). For this purpose, one can resort to (among other things) bijective or algebraic methods. The algebraic method is often more powerful and yields results more easily, however bijections give a more in-depth understanding of the models. Often, formulas are found via powerful methods, then people try to re-prove them bijectively. In this talk, I present what I’m focusing on, on the bijective side (Carell-Chappy formula) and on the algebraic side (KP equations). If time permits, I will explain a simple bijection I discovered during my Master’s internship.

Gradual Set-Theoretic Types

A static type system can be an extremely powerful tool for a programmer, providing early error detection, and offering strong compile-time guarantees on the behavior of a program. However, compared to dynamic typing, static typing often comes at the expense of development speed and flexibility, as statically- typed code might be more difficult to adapt to changing requirements. Gradual typing is a recent and promising approach that tries to get the best of both worlds, by allowing the programmer to finely tune the distribution of dynamic and static checking over a program. However, this “gradualization” is sometimes too coarse, and an expression is often either fully dynamic or fully static. We argue that adding full-fledged union and intersection types (a.k.a. set-theoretic types) to a gradual type system solves this issue by making the transition between dynamic typing and static typing smoother.

Séminaire des doctorants
Mercredi 28 juin 2017, 11 heures, Salle 3052
Tommaso Petrucciani (PPS team) Semantic subtyping: an introduction

Many type systems for programming languages include a notion of subtyping. Subtyping is often defined syntactically by a formal system, but this gets increasingly complex when union, intersection, and negation types are introduced.

In the semantic subtyping approach, instead, types are interpreted as sets and subtyping is defined in terms of set containment. Then, an algorithm is derived from the definition. While the algorithm is complex, the interpretation of types serves as a fairly simple specification. This approach also ensures that union and intersection on types behave as the corresponding operations on sets.

I will give an introduction to this approach and show how to define subtyping semantically for types including arrows, union, intersection, and negation, following [Frisch et al., 2008]. Then, we will look at ongoing work on adapting this approach (originally studied for call-by-value languages) to lazy semantics.

[Frisch et al., 2008] A. Frisch, G. Castagna, and V. Benzaken, Semantic subtyping, JACM, 2008.

Séminaire des doctorants
Mercredi 14 juin 2017, 11 heures, Salle 3052
Timo Zijlstra & Emmanuel Arrighi Quantum algorithms and Learning With Errors- based Cryptography & Distance Labels and Tree Skeletons

Quantum algorithms and Learning With Errors- based Cryptography:

Post quantum cryptography is meant to replace today's standards like RSA and Elliptic Curve Cryptography (ECC), since these standards are threathened by quantum algorithms. The most researched post-quantum candidates are based on lattice problems, and in particular the Learning with Errors (LWE) problem. It is assumed that there exists no quantum algorithm that solves this problem efficiently. However, in a particular setting and under some strong hypothesis, it is very easy to solve LWE using a generalization of the Bernstein-Vazirani quantum algorithm. We will take a look at possible quantum cryptanalysis on LWE-based cryptographic applications.

Distance Labels and Tree Skeletons:

To answer distance queries on a fix known graph, it is interesting to do precalculation in order to reduce query time. A methode is to use Hub Labeling. Hub Labeling works well on road transport network. We will take a look at this methode and introduce the notion of Skeleton Dimension which give an insight on why it works well on road network.

Séminaire des doctorants
Mercredi 31 mai 2017, 11 heures, Salle 3052
Clément Jacq (PPS team) A playful introduction to game semantics (category-light)

(English abstract below)

Une introduction ludique à la sémantique des jeux (allégée en catégories)

La sémantique des jeux est une branche de la théorie des modèles dont l'objectif est d'interpréter des formules de certaines logiques sous forme de jeux à deux joueurs. Son objectif initial était de lier les notions de vérité et de validité à des concepts de théorie des jeux tels que l'existence de stratégies gagnantes…

Après quelques exemples historiques, nous nous intéresserons dans cet exposé de manière informelle à un cas plus récent ou la sémantique des jeux modélise désormais des langages de programmation.

En guise de conclusion, nous évoquerons l'aspect formel avec la notion de structure catégorielle.

A playful introduction to game semantics (category-light)

Game semantics is a branch of model theory that aims at interpreting formulas of a given logic as two-player games. Initially, it was developed to link the notions of truth and validity to game-theoretic notions such as the existence of winning strategies.

After an historical example, we will look informally at a more recent case of game semantics where the games are used to model programming languages.

At the end, we'll mention the formal part with the notion of categorical model.

Séminaire des doctorants
Mercredi 17 mai 2017, 11 heures, Salle 3052
Pierre Vial (PPS team) An Introduction to Intersection Type Systems, and a New Answer to Klop's Problem

Although the following abstract is (mostly) in French, the talk will be in English if there are non-French speakers in the room.

L'exposé aura deux buts:

1) Présenter les systèmes de types-intersection (ITS, intersection type systems), en particulier, les ITS à intersection non-idempotente. Je commencerai par des rappels basiques en lambda-calcul. On verra en quoi la représentation des lambda-termes par des arbres (bien qu'élémentaire) permet de comprendre la façon dont les ITS sont conçus et vérifient naturellement des propriétés que les systèmes de types simples ne peuvent (raisonnablement) pas avoir. Par exemple, dans un ITS, un terme est normalisable (i.e. il termine) ssi il est typable. Par opposition, dans un système de types simples, on aura seulement l'implication “Si le terme t est typable, alors il est normalisable” (*Propriété de Terminaison*). La notion de normalisation (i.e. terminaison) admet de nombreuses variantes: on en verra deux, la réduction de tête (HN, Head Normalization) et la réduction faible (WN, Weak Normalization). On verra aussi que les ITS ont des conséquences en lambda-calcul qui sont *externes* à la théorie des types.

Etant donné un système de type Sys (que Sys soit un ITS ou un système de types simples, d'ordre supérieur ou non), la propriété de terminaison (typable dans Sys ⇒ normalisable) est souvent difficile à établir (on doit généralement recourir à un argument dit de réalisabilité, attribué à Tait). Cependant, je présenterai le système R, introduit par Gardner et de de Carvalho, dans lequel l'opérateur d'intersection peut être vu comme non-idempotent et la terminaison repose sur un argument très simple que nous verrons ensemble.

2) Présenter un article (accepté récemment à LICS) traitant de lambda-calcul et de réduction infinitaires et dont voici l'abstract:

Infinitary Intersection Types as Sequences: a New Answer to Klop’s Problem

We provide a type-theoretical characterization of weakly-normalizing terms in an infinitary lambda-calculus. We adapt for this purpose the standard quantitative (with non-idempotent intersections) type assignment system of the lambda-calculus to our infinite calculus. Our work provides a positive answer to a semi-open question known as Klop’s Problem, namely, finding out if there is a type system characterizing the set of hereditary head-normalizing (HHN) lambda-terms. Tatsuta showed in 2007 that HHN could not be characterized by a finite type system. We prove that an infinitary type system endowed with a validity condition called approximability can achieve it. As it turns out, approximability cannot be expressed when intersection is represented by means of multisets. Multisets are then replaced coinductively by sequences of types indexed by integers, thus defining a type system called System S.

Séminaire des doctorants
Mercredi 3 mai 2017, 11 heures, Salle 3052
Alexandre Nolin (Algorithms and complexity Group) Quantum, a look through nonlocality

In this talk I will try to give an introduction to the mathematical framework of quantum computing, completely disconnected of the underlying theory of quantum physics. After an exposition of a circuit model for quantum computing, we will split those circuits into two parts (the infamous Alice and Bob) and talk about the behaviours of those bipartite systems, more specifically somewhat counter-intuitive phenomenons like entanglement and nonlocality. Finally, we will see how those phenomenons are relevant in the study of communication complexity, and discuss recent results.

Séminaire des doctorants
Mercredi 19 avril 2017, 11 heures, Salle 3052
Pierre Cagne (PPS team) Lawvere’s hyperdoctrines and notions of equality

This talk will present hyperdoctrines, a widget invented by Lawvere in the late 70’s to give a categorical account of type theories. It has the advantage to dissociate every construction/rules of a type theory: structural rules, logical rules, quantifier rules, equality rules, etc. As a welcomed side effect, it questions the legitimacy of such rules. In particular, we will take some time to study the equality and the relevance of its usual definition, and try to give a feeling of Lawvere’s seminal thoughts on HoTT. If time permits, we shall discuss the insight of such an approach about a (for now non well established) “directed type theory”, by which is roughly meant a type theory in which paths between terms are not necessarily reversible.

Séminaire des doctorants
Mercredi 5 avril 2017, 11 heures, Salle 3052
Guillaume Lagarde (Automata and applications Group) On the stability of the Lempel-Ziv compression algorithm

LZ78 is a very simple lossless data compression algorithm published by Abraham Lempel and Jacob Ziv in 1978. It is fair enough to expect a certain stability from a data compression algorithm against small perturbation on the input. In this direction, Jack Lutz among with others asked the following question, so-called “the one-bit catastrophe”: given an infinite word w, can the compression ratio of w be different from 1w? In this presentation, I will give some results in this fashion; in particular I would like to give the intuition of the fact that a catastrophe can indeed occur in LZ78. Joint work with Sylvain Perifel.

The presentation will just use basic combinatorics.

Séminaire des doctorants
Mercredi 22 mars 2017, 11 heures, Salle 3052
Gabriel Radanne (PPS team) GADTs gone mild

Generalized Algebraic Data Types, often also called “Poor man's dependent types”, are an extension of regular sum and product types that is available in OCaml and Haskell.

Since their adoption in “mainstream” languages, GADTs have been known for allowing to elegantly write toy typed interpreter at the cost of horrible type error messages and numerous headaches. Or, as Yaron Misky said, “I assumed that it was the kind of nonsense you get when you let compiler writers design your programming language.”.

In this talk, I will present GADTs, what they are, and what useful things we can do with them. This will take us on quite a journey, with some traces of C, a pinch of memory layout, a cameo from pushdown automata and a healthy amount of Prolog. The only requirements will be a passing familiarity with OCaml and the caffeinated beverage of your choice.

Séminaire des doctorants
Mercredi 8 mars 2017, 11 heures, Salle 3052
Pablo Eduardo Rotondo (Automata and applications Group) Continued Fractions and the Recurrence of Sturmian Words

In this talk I will present various aspects of Continued Fractions, motivating and explaining their relation to the factors of the so-called Sturmian Words. We conclude by a probabilistic study of the recurrence function of Sturmian Words, which is common work with Brigitte Vallée (CNRS, Univ. Caen).

Séminaire des doctorants
Mercredi 22 février 2017, 11 heures, Salle 3052
Lucas Boczkowski (Algorithms and complexity Group) Minimizing Message Size in Stochastic Communication Patterns: Fast Self-Stabilizing Protocols with 3 bits

The talk is based on a paper whose abstract is the following:

This paper considers the basic PULL model of communication, in which in each round, each agent extracts information from few randomly chosen agents. We seek to identify the smallest amount of information revealed in each interaction (message size) that nevertheless allows for efficient and robust computations of fundamental information dissemination tasks. We focus on the Majority Bit Dissemination problem that considers a population of n agents, with a designated subset of source agents. Each source agent holds an input bit and each agent holds an output bit. The goal is to let all agents converge their output bits on the most frequent input bit of the sources (the majority bit). Note that the particular case of a single source agent corresponds to the classical problem of Broadcast (also termed Rumor Spreading). We concentrate on the severe fault-tolerant context of self-stabilization, in which a correct configuration must be reached eventually, despite all agents starting the execution with arbitrary initial states. In particular, the specification of who is a source and what is its initial input bit may be set by an adversary.

We first design a general compiler which can essentially transform any self-stabilizing algorithm with a certain property (called “the bitwise-independence property”) that uses l-bits messages to one that uses only (log l)-bits messages, while paying only a small penalty in the running time. By applying this compiler recursively we then obtain a self-stabilizing Clock Synchronization protocol, in which agents synchronize their clocks modulo some given integer T, within O(log n log T) rounds w.h.p., and using messages that contain 3 bits only. We then employ the new Clock Synchronization tool to obtain a self-stabilizing majority broadcast protocol which converges in O(log n) time, w.h.p., on every initial configuration, provided that the ratio of sources supporting the minority opinion is bounded away from half. Moreover, this protocol also uses only 3 bits per interaction.

Based on joint work with A. Korman and E. Natale.

Séminaire des doctorants
Mercredi 25 janvier 2017, 11 heures, Salle 3052
Thibaut Girka (PPS team) Oracle-based Differential Operational Semantics (or Explaining program differences with programs)

We present a formal framework to characterize differences between deterministic programs in terms of their small-step semantics. This language-agnostic framework defines the notion of /difference languages/ in which /oracles/—programs that relate small-step executions of pairs of programs written in a same language—can be written, reasonned about and composed.

We illustrate this framework by instantiating it on a toy imperative language and by presenting several /difference languages/ ranging from trivial equivalence-preserving syntactic transformations to characterized semantic differences. Through those examples, we will present the basis of our framework, show how to use it to relate syntactic changes with their effect on semantics, how one can abstract away from the small-step semantics presentation, and discuss the composability of oracles.

Séminaire des doctorants
Mercredi 11 janvier 2017, 11 heures, Salle 3052
Fabian Reiter (Automata and applications Group) Asynchronous Distributed Automata

The goal of this talk is to raise interest in the connections between distributed computing and formal logic. I will illustrate this relatively unexplored area of research by presenting an equivalence result between two very specific systems. The distributed computing side will be represented by a network of identical finite-state machines that communicate in an asynchronous manner, while the formal logic side will be represented by a small fragment of least fixpoint logic (more specifically, a fragment of the modal mu-calculus).