Seminars

Zoom link: univ-lille-fr.zoom.us/j/95419000064



Titre: Lower bound for arithmetic circuits via the Hankel matrix

Abstract: We study the complexity of representing polynomials by arithmetic
circuits in both the commutative and the non-commutative settings. To
analyse circuits we count their number of parse trees, which describe the
non-associative computations realised by the circuit. In the non-commutative
setting a circuit computing a polynomial of degree d has at most 2^{O(d)}
parse trees. Previous superpolynomial lower bounds were known for circuits
with up to 2^{d^{1/3-ε}} parse trees, for any ε>0. Our main result is to
reduce the gap by showing a superpolynomial lower bound for circuits with
just a small defect in the exponent for the total number of parse trees,
that is 2^{d^{1-ε}}, for any ε>0. In the commutative setting a circuit
computing a polynomial of degree d has at most 2^{O(d \\log d)} parse trees.
We show a superpolynomial lower bound for circuits with up to 2^{d^{1/3-ε}}
parse trees, for any ε>0. When d is polylogarithmic in n, we push this
further to up to 2^{d^{1-ε}} parse trees. While these two main results hold
in the associative setting, our approach goes through a precise
understanding of the more restricted setting where multiplication is not
associative, meaning that we distinguish the polynomials (xy)z and 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. Our key
technical contribution is to provide generic lower bound theorems based on
analyzing and decomposing the Hankel matrix, from which we derive the
results mentioned above. The study of the Hankel matrix also provides a
unifying approach for proving lower bounds for polynomials in the
(classical) associative setting. We demonstrate this by giving alternative
proofs of recent lower bounds as corollaries of our generic lower bound
results.

Title : One-Tape Turing Machine and Branching Program Lower Bounds for MCSP
Abstract:
eccc.weizmann.ac.il/report/2020/103/

Speaker' webpage : dimyrisiotis.github.io/

Je présenterais mon projet avec Bruno: NetworkDisk.

Abstract and Title: TBA
link to the project: TBA

Title: Managing structural and behavioral evolution in relational database: Application of Software Engineering techniques.
Abstract:

Relational databases play a central role in many information systems.
Their schemas usually contain structural and behavioral entity descriptions.
However, as any piece of software, they must continuously evolve to adapt to new
requirements of a world in constant change. From an evolution point of view,
problems are twofold: (1) relational database management systems do not allow
inconsistencies i.e., no entity can reference a non existing entity; (2) stored
procedures bodies are not described by meta-data i.e., DBMS as PostgreSQL
consider stored procedure bodies as plain text and references to entities are
unknown. As a consequence, evaluating the impact of an evolution of the database
schema is a difficult task. In this seminar, we present a semi-automatic
approach based on recommendations (sort of nested code transformations).
Recommendations are proposed to architects who select the ones fitting their
needs. Selected recommendations are then analysed and compiled to generate SQL
script respecting the constraints imposed by the RDBMS. To support
recommendations, we designed a meta-model for relational databases easing
computation of change impact. We performed an experiment to validate the
approach by reproducing a real evolution on a database. The results of our
experiment show that our approach is able to reproduce exactly a manual
modification in 75% less time.


Zoom link: univ-lille-fr.zoom.us/j/95419000064

Title: Can Earliest Query Answering on Nested Streams be achieved in Combined Linear Time?

Title: Regularizing the delay of enumeration algorithms
Zoom link: univ-lille-fr.zoom.us/j/95419000064
Abstract: Enumeration algorithms are algorithms whose goal is to output the set
of all solutions to a given problem. There exists different measures for the
quality of such algorithm, whose relevance depends on what the user wants to do
with the solutions set.

If the goal of the user is to explore some solutions or to transform the
solutions as they are outputted with a stream-like algorithm, a relevant measure
of the complexity of an enumeration algorithm is the delay between the output of
two distinct solutions. Following this line of thoughts, significant efforts
have been made by the community to design polynomial delay algorithms, that is,
algorithms whose delay between the output of two new solutions is polynomial in
the size of the input.

While this measure is interesting, it is not always completely necessary to have
a bound on the delay and it is enough to ask for a guarantee that running the
algorithm for O(t poly(n)) will result in the output of at least t solutions. Of
course, by storing each solution seen and outputting them regularly, one can
simulate a polynomial delay but if the number of solutions is large, it may
result in a blow up in the space used by the enumerator.

In this talk, we will present a new technique that allow to transform such
algorithm into polynomial delay algorithm using polynomial space.

This is joint work with Yann Strozecki.

Title: The planar geometry of first-order string transductions (joint work with Pierre Pradic)


Abstract:
hal.archives-ouvertes......ument

We propose a new machine model recognizing star-free languages, with a geometric flavor. Our starting point is the characterization of regular languages using two-way automata (2DFA). The idea is to take seriously the visual representations found throughout the literature of the behavior of a 2DFA on a word ; by putting a total order on the set of states, one can formally define what it means for such a behavior to be planar, in a sense analogous to the planarity of combinatorial maps. Star-free languages are then exactly the languages recognized by "planar 2DFA". We also show that the corresponding planar transducer model characterizes the class of first-order transductions (a.k.a. aperiodic regular functions). If time allows, the talk will briefly discuss the connections of this work with the non-commutative lambda-calculus (cf. our recent paper Aperiodicity in a non-commutative logic, ICALP'20).

Speaker: Nofar Carmeli (nofar.carme.li/)

Zoom link: univ-lille-fr.zoom.us/j/95419000064

Title: The Complexity of Answering Unions of Conjunctive Queries.

Abstract:
We discuss the fine-grained complexity of enumerating the answers to a query over a relational database. With the ideal guarantees, linear time is required before the first answer to read the input and determine its existence, and then we need to print the answers one by one. Consequently, we wish to identify the queries that can be solved with linear preprocessing time and constant or logarithmic delay between answers. A known dichotomy classifies CQs into those that admit such enumeration and those that do not. The computationally expensive component of query answering is joining tables, which can be done efficiently if and only if the join query is acyclic. However, the join query usually does not appear in a vacuum; for example, it may be part of a larger query, or it may be applied to a database with dependencies. We inspect how the complexity changes in these settings and chart the borders of tractability within. In addition, we consider the task of enumerating query answers with a uniformly random order, and we propose to do so using an efficient random-access structure for representing the set of answers. We also prove conditional lower bounds showing that our algorithms capture all tractable queries in some cases. Among our results, we show that a union of tractable conjunctive queries may be intractable w.r.t. random access; on the other hand, a union of intractable conjunctive queries may be tractable w.r.t. enumeration.

Title: Extracting nested relational queries from implicit definitions

Abstract:
arxiv.org/pdf/2005.06503.pdf

In this talk, I will present results obtained jointly with Michael
Benedikt establishing a connection between the Nested Relational
Calculus (NRC) and sets implicitly definable using Δ₀ formulas.

Call a formula φ(I,O) an implicit definition of the relation O(x,...) in
terms of I(y,...) if O is functionally determined by I: for every I, O,
O', if both φ(I,O) and φ(I,O') hold, then we have O ≡ O'. When φ is
first-order and I and O are relations over base sorts, then Beth's
definability theorem states that there is a first-order formula
ψ(I,x,...) corresponding to O whenever φ(I,O) holds. Further, this
explicit definition ψ can be effectively be computed from a sequent
calculus proof witnessing that φ is functional. This allows for
practical use of implicit definitions in the context of database
programming, as there is a well-established link between fragments of
explicitly FO definable relations and relational calculi.

NRC is a conservative extension of relational calculi from database
theory with limited powerset types in addition to tupling and anonymous
base types. NRC expressions thus not only encompass flat relations over
primitive datatypes like SQL but also nested collections, while
remaining useful in practice.

We extend the above correspondence between first-order logic and flat
relational queries to NRC and implicit definitions using set-theoretical
Δ₀ formulas over (typed) nested collection. Our proof of the equivalence
goes through a notion of Δ₀-interpretation and a generalization of Beth
definability for multi-sorted structures. This proof is non-constructive
and thus does not yield any useful algorithm for converting implicit
definitions into NRC terms. Using an approach more closely related to
proof-theoretic interpolation, we give a constructive proof of the
result restricted to intuitionistic provability, i.e, when the input
functionality proof π of φ(I,O) is carried out in intuitionistic logic.
Further, if π is cut-free, this can be done efficiently. Whether or not
there exists a polynomial-time procedure working with classical proofs
of functionality is still an open problem.

I will focus on the effective result for the talk, and if time allows,
discuss the difficulties with extending it to classical logic. I will
not assume any background in either database or model theory.

Title: The Complexity of Counting Problems over Incomplete Databases

Abstract: In this presentation, I will talk about various counting problems that naturally
arise in the context of query evaluation over incomplete databases. Incomplete
databases are relational databases that can contain unknown values in the form
of labeled nulls. We will assume that the domains of these unknown values are
finite and, for a Boolean query $q$, we will consider the following two
problems: given as input an incomplete database $D$, (a) return the number of
completions of $D$ that satisfy $q$; or (b) return or the number of valuations
of the nulls of $D$ yielding a completion that satisfies $q$.


We will study the computational complexity of these problems when $q$ is a
self-join--free conjunctive query, and study the impact on the complexity of
the following two restrictions: (1) every null occurs at most once in $D$ (what
is called *Codd tables*); and (2) the domain of each null is the same. Roughly
speaking, we will see that counting completions is much harder than counting
valuations, and that both (1) and (2) can reduce the complexity of our
problems.

I will also talk about the approximability of these problems and prove that,
while counting valuations can efficiently be approximated, in most cases
counting completions cannot.

On our way, we will encounter the counting complexity classes #P, Span-P and
Span-L.

The presentation will be based on joint work with Marcelo Arenas and Pablo
Barcelo; see arxiv.org/abs/1912.11064

Title: Finding paths in large graphs

Abstract:
When dealing with large graphs, classical algorithms for finding paths such as Dijkstra's Algorithm are unsuitable, because they require to perform too many disk accesses. To avoid this while keeping a data structure of size quasi-linear in the size of the graph, we propose to guide the path search with a distance oracle, obtained from a topological embedding of the graph.
I will present fresh experimental research on this topic, in which we obtain graph embeddings using learning algorithms from natural language processing. On some graphs, such as the graph of publications from DBLP, our topologically-guided path search allows us to visit a small portion of the graph only, in average.
This is joint work with Charles Paperman.

Title: Containment for Probabilistic automata.

Abstract: This is an ICALP 2018 paper. We analyze when the model of probabilistic
automata has decidable properties, when restricting the ambiguity. The
notion of ambiguity is usually used in weighted automata or transducers,
but we follow a recent paper by Fijalkow, Riveros and Worrell, which
introduced this approach. We do not solve everything but our decidability
results rely unexpectedly on Schanuel's conjecture and we provide some
geometric intuition behind the hardness of the problem.

Abstract: The time complexity of 1-limited automata is investigated from a
descriptional complexity view point. Though the model recognizes
regular languages only, it may use quadratic time in the input length.
We show that, with a polynomial increase in size and preserving
determinism, each 1-limited automaton can be transformed into a
linear-time equivalent one. We also obtain polynomial transformations
into related models, including weight-reducing Hennie machines (i.e.,
one-tape Turing machines syntactically forced to operate in
linear-time), and we show exponential gaps for converse
transformations in the deterministic case.

Title: Combined Complexity of Probabilistic Query Evaluation

Abstract:
Query evaluation over probabilistic databases (probabilistic query evaluation, or PQE) is known to be intractable in many cases, even in data complexity, i.e., when the query is fixed. Although some restrictions of the queries and instances have been proposed to lower the complexity, these known tractable cases usually do not apply to combined complexity, i.e., when the query is not fixed. This talk gives an overview of my PhD research, which investigates which queries and instances ensure the tractability of PQE in combined complexity.

I will first present our work on PQE of conjunctive queries on binary signatures, which can be rephrased as a probabilistic graph homomorphism problem. We restrict the query and instance graphs to be trees and show the impact on the combined complexity of diverse features such as edge labels, branching, or connectedness. This is joint work with Antoine Amarilli and Pierre Senellart and was presented at PODS'2017.

Second, we will explore the combined complexity of evaluating queries on treelike databases, i.e., databases whose treewidth is bounded by a constant. We introduce a class of queries (named 'CFG-Datalog') which generalizes many known query languages that are tractable in this context. Specifically, we show that the (non-probabilistic) evaluation of CFG-Datalog on treelike databases can be solved with complexity linear in the product of the instance size and of the query size. In the process, we introduce a new representation of the provenance of a query on a database, based on cyclic Boolean circuits. This is joint work with Antoine Amarilli, Pierre Bourhis, and Pierre Senellart, and was presented at ICDT'2017.

Last, we will move to the field of knowledge compilation and present our work that connects various notions of width for Boolean circuits. We show that circuits of bounded treewidth can be efficiently compiled into structured deterministic decomposable normal forms (d-SDNNFs), which in particular allows efficient probability computation. We show the implications of this result for PQE of CFG-Datalog on treelike databases. We also prove general lower bounds on knowledge compilation formalisms, which imply lower bounds for provenance computation. This is joint work with Antoine Amarilli and Pierre Senellart and was presented at ICDT'2018.

This talk connects two classical areas of theoretical computer science: descriptive complexity and distributed computing. The former is a branch of computational complexity theory that characterizes complexity classes in terms of equivalent logical formalisms. The latter studies algorithms that run in networks of interconnected processors.

Although an active field of research since the late 1970s, distributed computing is still lacking the analogue of a complexity theory. One reason for this may be the large number of distinct models of distributed computation, which make it rather difficult to develop a unified formal framework. In my talk, I will outline how the descriptive approach, i.e., connections to logic, could be helpful in this regard.

Paul présentera le papier de Sylvain, Aurélien et Paul, soumis à LICS 2018, sur le sujet des transducteurs d'arbres d'ordre supérieur.

In this talk I present a logic, called LT, to express properties of transductions, i.e. binary relations from input to output (finite) words. I argue that LT is a suitable candidate as a specification language for verification of non reactive systems, extending the successful approach of verifying synchronous systems via Mealy Machines and MSO.

In LT, the input/output dependencies are modelled via an origin function which associates to any position of the output word, the input position from which it originates. LT is well-suited to express relations (which are not necessarily functional), and can express all regular functional transductions, i.e. transductions definable for instance by deterministic two-way transducers.
Despite its high expressive power, LT has decidable satisfiability problems. The main contribution is a synthesis result: it is always possible to synthesis a regular function which satisfies the specification.

Finally, I explicit a correspondence between transductions and data words. As a side-result, we obtain a new decidable logic for data words.

Cypher is a query-language for property-graphs. It was originally designed and implemented as part of the Neo4j graph database, and it is currently used by several commercial database products and researchers. The semantics of Cypher queries is currently described using natural language and, as a result, it is often not well defined. This work is part of a project to define a full denotational semantics of Cypher queries. The talk will first present the main features of Cypher through examples, including the core mecanism: graph pattern-matching, and then will describe the formal semantics in its current state.

Cours extérieur de Gérard Berry du Collège de France

Le centre Inria Lille - Nord Europe reçoit Gérard Berry, du Collège de France pour son cours sur la photographie numérique. Ce cours se prolongera par un séminaire de Stéphane Huot, responsable de l'équipe Mjolnir. Cette manifestation sera suivie d'un cocktail au cours duquel Isabelle Herlin, directrice du centre de recherche Inria Lille - Nord Europe présentera ses voeux.

Date : 31/01/2018
Lieu : Lilliad, Campus Université Lille - sciences et technologies - 2 avenue Jean Perrin, Villeneuve d'Ascq

Programme

15h30 : Accueil

15h45 : Introduction par Isabelle Herlin

16h - 17h30 : Cours de Gérard Berry, "La photographie numérique, un parfait exemple de la puissance de l'informatique"

17h30 - 18h30 : Séminaire de Stéphane Huot, "Interaction humain-machine : passé composé et futur simple... ou l'inverse"

18h30 - 18h45 : Questions aux deux orateurs

19h - 20h30 : Cocktail

Cours de Gérard Berry

Bio express : Gérard Berry est informaticien, professeur au Collège de France où il est titulaire de la chaire d'Algorithmes, machines et langages.


Résumé

L’appareil photo numérique est un excellent exemple de l’évolution actuelle des systèmes cyberphysiques, c’est-à-dire des systèmes couplant intimement mécanique, physique, électronique et logiciel. C’est aussi un exemple merveilleux et accessible à tous de la puissance des méthodes de l’informatique par rapport à celles de la physique et de la mécanique seules. Le cours présentera la panoplie des algorithmes embarqués dans les appareils photos modernes et dans les logiciels de postproduction, puis discutera l’impact majeur qu’ils ont sur la conception des appareils et des objectifs, totalement bouleversée en ce moment, et celui qu’ils ont sur les photographes professionnels ou amateurs.

La photographie argentique, fort ancienne, n’a que lentement progressé au cours du XXe siècle : amélioration lente des pellicules et papiers, introduction de l’exposition automatique calculée analogiquement à partir de cellules photo-électriques, visée télémétrique ou reflex, tout cela a demandé des dizaines d’années. Au contraire, à partir de la commercialisation du premier appareil numérique en 1990, la photographie numérique a évolué extrêmement vite. En 2003, on trouvait déjà des appareils semi-professionnels corrects et, dès 2009, des appareils reflex de haute qualité à un prix abordable. Maintenant, il existe toute une panoplie d’appareils de tailles variées, tous capables de fournir des images de grande qualité. Même les téléphones sont devenus de très bons appareils photos et caméras vidéo, principalement grâce aux algorithmes qu’ils mettent en œuvre. Comme ils savent faire bien d’autres choses, par exemple envoyer immédiatement les images sur Internet, ils sont en train de remplacer les anciens petits appareils compacts et de servir d’équipement unique pour les photographes occasionnels et pour tous dans les pays où la photo argentique était d’un coût inabordable pour les habitants. La logique de la photo numérique est ainsi devenue très différente de celle de l’argentique, ce qui n’empêche cependant pas que cette dernière garde toujours les faveurs de certains artistes.

Qu’est-ce qui a permis cette révolution et pourquoi est-elle allée aussi vite ? Il y a trois raisons principales : la conception par les physiciens et la fabrication industrielle en grand volume de capteurs de haute qualité ; l’augmentation considérable de la puissance et la diminution de la dépense énergétique des ordinateurs embarqués, grâce à la fameuse loi de Moore ; enfin, et surtout, l’amélioration continue des algorithmes de la photographie, qui jouent en fait un rôle plus important que celui des capteurs. Dans les quinze dernières années, nous avons gagné au moins 4 degrés de sensibilité, dont les trois quarts grâce aux algorithmes. Même des appareils aux capteurs relativement petits savent faire des photos de très haute qualité à 3200 ISO, ce qui était complètement impossible avec l’argentique.

Le cours détaillera d’abord la suite des transformations algorithmiques subtiles qui permettent le développement des images des données numériques du capteur, aboutissant à l’image finale en gérant au mieux la lumière, la netteté et le bruit. Ensuite, il étudiera les algorithmes dédiés à la correction automatique des divers défauts optiques des objectifs ; il montrera que la puissance de ces algorithmes fait que ces objectifs ne seront plus conçus comme auparavant : leur conception intègre désormais totalement physique et algorithmique, fournissant des optiques de meilleure qualité, moins encombrantes, plus légères et moins chères. Il insistera sur l’importance que prennent les nouveaux traitements fondés sur la fusion de prises de vue successives pour l’amélioration de la qualité selon divers objectifs (lumière, bruit, profondeur de champ, etc.), en particulier pour les téléphones. Il montrera pourquoi fonder les nouveaux appareils directement sur les algorithmes modifie de plus en plus le cœur de leur conception, ce qui fait que bien d’autres nouveautés surprenantes pourront apparaître. Des évolutions similaires bouleversent d’ailleurs tout autant les imageries médicale et astronomique.

Enfin, le cours soulignera l’importance des nouveaux algorithmes destinés à l’amélioration de l’ergonomie de la prise de vue, qui rendent la vie technique du photographe bien plus facile sur quasiment tous les aspects : interaction humain-machine bien conçue, stabilisation du capteur et de l’objectif pour supprimer le flou de bougé, gestion sophistiquée de la lumière et de la mise au point, nombreuses aides à la prise de vue dans le viseur devenant électronique, liaison directe avec les ordinateurs et téléphones.
Séminaire de Stéphane Huot

Résumé

Bien avant l'avènement des ordinateurs personnels, de l'internet et des smartphones , l'Interaction Homme-Machine (IHM) était déjà une préoccupation au cœur de certaines des visions qui ont contribué à forger l'informatique moderne, qu'elle soit personnelle ou professionnelle. Pour autant, la conception et l'étude des interactions est encore souvent considérée comme secondaire dans la conception des systèmes, la priorité étant souvent mise sur le développement des fonctionnalités plutôt que sur les moyens pour les utiliser.

Cette situation s'est progressivement améliorée, avec notamment l'avènement des dispositifs tactiles (smartphones et tablettes) ou de divertissement (consoles de jeux) pour lesquels l'argument de simplicité d'utilisation a détrôné celui de la puissance intrinsèque. Cela a bien évidemment permis de populariser et démocratiser l'accès à la technologie. Mais une conséquence est, selon nous, un relatif appauvrissement des possibilités offertes par ces technologies paradoxalement plus puissantes que jamais. En masquant la complexité plutôt qu'en aidant à la maîtriser, en entretenant le mythe qu'avec ces dispositifs il est aisé pour chacun de faire beaucoup sans efforts, la tendance est à sacrifier le potentiel de l'outil informatique et la performance des utilisateurs pour la rapidité de prise en main, sans permettre un usage plus avancé, plus performant, et peut-être plus gratifiant pour l'utilisateur.

Cet équilibre entre simplicité d'usage et puissance de l'outil est un compromis difficile à trouver, et c'est selon nous un des défis et une difficulté majeure de l'IHM : observer et comprendre les phénomènes sensorimoteurs et psychomoteurs, cognitifs, sociaux et technologiques mis en œuvre lors de l'interaction entre des personnes et des systèmes afin d'améliorer cette interaction et d'en guider la conception pour encapaciter les utilisateurs. Le but étant finalement de leur permettre de réaliser ce qu'il leur serait impossible de faire sans cet outil, même si cela requiert de leur part des efforts certains d'apprentissage.
Dans ce séminaire, nous commencerons par présenter ce qu'est l'Interaction Homme-Machine en tant que domaine de recherche avec ses objectifs, ses méthodes et ses pratiques.

Ensuite, au travers d'une brève histoire de l'informatique sous le prisme de l'interaction, nous évoquerons quelques innovations d'aujourd'hui qui découlent des visions de pionniers du domaine, en considérant notamment ce compromis simplicité / puissance de l'outil. Nous verrons aussi avec des exemples et contre-exemples issus de nos environnements numériques actuels, ainsi qu'avec des travaux de recherche récents, que ces visions portent encore de nombreux défis présents et futurs de l'IHM. En particulier, nous conclurons en discutant de la nécessité d'adopter une approche centrée utilisateur et interaction à l'heure des grands défis scientifiques, technologiques et sociétaux du numérique tels que la conception des systèmes autonomes ou le traitement et l'exploitation automatique des données.

Mots-clés : Machines et langages Algorithme Interaction Homme machine (IHM).

Cet exposé se veut une introduction à la transformation de
programmes datalog. En particulier, je présenterai la transformation
appelée "supplementary magic set rewriting" qui permet d'obtenir des
programmes datalog dont l'évaluation semi-naïve se comporte de façon
similaire à l'évaluation des programmes originaux par résolution SLD. Je
montrerai l'algorithme et des exécutions de programmes sur des exemples
issus de problèmes d'analyses grammaticales.

A hyperstream is a sequence of streams with references to others. We study the complexity of computing certain answers for queries defined by automata and evaluated on hyperstreams of words. We show that the problem is PSPACE-complete for deterministic query automata, but that it can be solved in PTime for linear hyperstreams even with factorization.

This talk will survey old and recent results about word transductions, i.e. functions mapping (finite) words to words. Connections between automata models (transducers), logic and algebra will be presented. Starting with rational functions, defined by (one-way) finite transducers, and the canonical model of bimachines introduced by Reutenauer and Schützenberger, the talk will also target the more expressive class of functions defined by two-way transducers and their equivalent MSO-based formalism.