Seminars

Links' Seminars and Public Events Add to google calendar
2022
Fri 25th Feb
11:00 am
12:00 pm
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Séminaire Nico

Fri 28th Jan
11:00 am
12:00 pm
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Alexandre Vigny (visio)
Title:
Separator logic, expressive power and algorithmic applications
Abstract:
First-order logic (FO) can express many algorithmic problems on graphs,
but fails to express whether two vertices are connected. We define a
new logic (separator logic) by enriching FO with connectivity
predicates connk(x, y, z1, . . . , zk) that hold true in a graph if
there exists a path between x and y after deletion of z1, . . . , zk.
In this talk I will first present a study of the expressive power of
this new logic.
I will then present algorithmic results for this logic on graph classes
that exclude a topological minor.
These results were obtained in collaboration with Michał Pilipczuk,
Nicole Schirrmacher, Sebastian Siebertz, and Szymon Toruńczyk.

Fri 21st Jan
11:00 am
12:00 pm
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Aurélien Lemay in Seminar

2021
Fri 10th Dec
11:00 am
12:00 pm
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Séminaire Sebastien Tavenas

Title: Bornes inférieures superpolynomiales pour les circuits de profondeur constante

Abstract:
Tout polynôme multivarié P(X_1,...,X_n) peut être écrit comme une somme de
monômes, i.e., une somme de produits de variables et de constantes du corps.
La taille naturelle d'une telle expression est le nombre de monômes. Mais,
que se passe-t-il si on rajoute un nouveau niveau de complexité en
considérant les expressions de la forme : somme de produits de sommes (de
variables et de constantes) ? Maintenant, il devient moins clair comment
montrer qu'un polynôme donné n'a pas de petite expression. Dans cet exposé
nous résoudrons exactement ce problème. Plus précisément, nous prouvons que
certains polynômes explicites n'ont pas de représentations "somme de
produits de sommes'' (SPS) de taille polynomiale. Nous pouvons aussi obtenir
des résultats similaires pour les SPSP, SPSPS, etc... pour toutes les
expressions de profondeur constante.
"
Thu 25th Nov
2:00 pm
3:00 pm
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Nofar Carmeli in Links' Seminar
Fri 29th Oct
11:00 am
12:00 pm
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Séminaire Antoine Amarilli

Fri 22nd Oct
11:00 am
12:00 pm
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Mikaël Monet in Links' Seminar
Fri 15th Oct
11:00 am
12:00 pm
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Claire Soyez-Martin in Links' seminar
Fri 17th Sep
11:00 am
12:00 pm
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Séminaire Corentin Barloy
Title: Stackless Processing of Streamed Trees
Abstract:
Processing tree-structured data in the streaming model is a chal-lenge: capturing regular properties of streamed trees by means of astack is costly in memory, but falling back to finite-state automata drastically limits the computational power. We propose an intermediate stackless model based on register automata equipped with a single counter, used to maintain the current depth in the tree. We explore the power of this model to validate and query streamed trees. Our main result is an effective characterization of regular path queries (RPQs) that can be evaluated stacklessly—with and without registers. In particular, we confirm the conjectured characterization of tree languages defined by DTDs that are recognizable without registers, by Segoufin and Vianu (2002), in the special case of tree languages defined by means of an RPQ.

Link: paperman.name/data/pub.....0.pdf

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lille-Salle
Fri 10th Sep
10:00 am
11:00 am
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Séminaire de Patrick Baillot
titre: Type-based complexity analysis in a parallel process calculus

Abstract:
Some type systems have been designed to analyse statically the time
coplexity of functional languages. A natural question is whether this approach
can be extended to parallel languages. We address this problem for the
Pi-calculus, a paradigmatic calculus for parallel and concurrent computation.
In Pi-calculus, processes communicate through channels that can carry values
and channel names. We will define notions of sequential and parallel complexity
for Pi-calculus, and present a type system that provides an upper bound on the
time complexity of processes.
This is based on joint work with Alexis Ghyselen (ESOP 2021).

Based on: link.springer.com/chap.....9-3_3
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Fri 9th Jul
 all day
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Seminar - Antonio AL SERHALI
Title: Integrating Schema-Based Cleaning into Automata Determinization

Abstract : Schema-based cleaning for automata on trees or nested words
was proposed recently to compute smaller deterministic automata for
regular path queries on data trees. The idea is to remove all rules and
states, from an automaton for the query, that are not needed to recognize
any tree recognized by a given schema automaton. Unfortunately, how-
ever, deterministic automata for nested words may still grow large for au-
tomata for XPath queries, so that the much smaller schema-cleaned ver-
sion cannot always be computed in practice. We therefore propose a new
schema-based determinization algorithm that integrates schema-based
cleaning directly. We prove that schema-based determinization always
produces the same deterministic automaton as schema-based cleaning
after standard determinization. Nevertheless, the worst-case complex-
ity is considerably lower for schema-based determinization. Experiments
confirm the relevance of this result in practice.
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Fri 4th Jun
10:00 am
12:30 pm
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Séminaire Pierre Ohlmann
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.
Fri 28th May
10:00 am
11:00 am
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Seminar Anastasia Dimou
Title: Knowledge graph generation and validation
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Fri 21st May
10:00 am
12:00 pm
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Seminar Dimitrios Myrisiotis
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/
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Fri 7th May
10:00 am
12:00 pm
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Seminar Nicole Schweikardt
Title:
Spanner Evaluation over SLP-Compressed Documents

Abstract:
We consider the problem of evaluating regular spanners over compressed documents, i.e., we wish to solve evaluation tasks directly on the compressed data, without decompression. As compressed forms of the documents we use straight-line programs (SLPs) -- a lossless compression scheme for textual data widely used in different areas of theoretical computer science and particularly well-suited for algorithmics on compressed data. In terms of data complexity, our results are as follows. For a regular spanner M and an SLP S that represents a document D, we can solve the tasks of model checking and of checking non-emptiness in time O(size(S)). Computing the set M(D) of all span-tuples extracted from D can be done in time O(size(S) size(M(D))), and enumeration of M(D) can be done with linear preprocessing O(size(S)) and a delay of O(depth(S)), where depth(S) is the depth of S's derivation tree. Note that size(S) can be exponentially smaller than the document's size |D|; and, due to known balancing results for SLPs, we can always assume that depth(S) = O(log(|D|)) independent of D's compressibility. Hence, our enumeration algorithm has a delay logarithmic in the size of the non- compressed data and a preprocessing time that is at best (i.e., in the case of highly compressible documents) also logarithmic, but at worst still linear. Therefore, in a big-data perspective, our enumeration algorithm for SLP-compressed documents may nevertheless beat the known linear preprocessing and constant delay algorithms for non-compressed documents.
[This is joint work with Markus Schmid, to be presented at PODS'21.]

Link to the paper: arxiv.org/pdf/2101.10890.pdf for the paper at least
Link to the ACM video: TBA
Fri 30th Apr
10:00 am
12:00 pm
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Présentation de NetworkDisk
Je présenterais mon projet avec Bruno: NetworkDisk.

Abstract and Title: TBA
link to the project: TBA

Fri 9th Apr
10:00 am
12:00 pm
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Seminaire Pascal Weil
titre: Problèmes algorithmiques en théorie des groupes infinis
resumé:
Malgré le titre très général, il s'agira uniquement de problèmes concernant les sous-groupes de groupes infinis, et même juste les sous-groupes de groupes libres. Les résultats et méthodes que je présenterai sont issus de près de 40 ans de littérature et sont dûs à un grand nombre d'auteurs.

Je commencerai par poser le paysage, y compris pour ceux qui ne savent plus ce qu'est le groupe libre -- où l'on verra qu'on est, du point de vue algorithmique, dans une variante de la combinatoire des mots. Je présenterai ensuite l'outil central de la plupart des algorithmes efficaces sur les sous-groupes du groupe libre : la représentation de chaque sous-groupe finiment engendré par un graphe étiqueté et enraciné (disons : d'un automate :-)…) unique et facilement calculable à partir d'un ensemble de générateurs du sous-groupe considéré, qu'on appelle le graphe de Stallings.

Le jeu consiste ensuite à traduire les problèmes algorithmiques sur les sous-groupes en problèmes algorithmiques sur les graphes de Stallings, et à résoudre ces problèmes de la façon la plus efficace possible.

On considèrera notamment les problèmes suivants -- bon, juste le début de cette longue liste.
- Le problème du mot généralisé : étant donnés k+1 éléments du groupe libre (ce sont des mots), le dernier appartient-il au sous-groupe engendré par les k premiers ?
- Le problème de l'indice : étant donné un tuple d'éléments du groupe libre, le sous-groupe qu'ils engendrent est-il d'indice fini ?
- Le problème de la base : étant donné un tuple d'éléments du groupe libre, trouver le rang, et une base du sous-groupe qu'ils engendrent.
- Le problème de l'intersection : étant donnés deux tuples d'éléments du groupe libre, calculer l'intersection des sous-groupes qu'ils engendrent (ou calculer une base de cette intersection).
- Le problème de la conjugaison : étant donnés deux tuples d'éléments du groupe libre, engendrent-ils le même sous-groupe ? deux sous-groupes conjugués ?
- Et de nombreux autres problèmes (mots clés : minimalité de Whitehead, facteur libre, malnormalité, clôture par radical, clôture au sens de la topologie pro-p, etc…)


title: Algorithmic problems in the theory of infinite groups
abstract:
In spite of the very general title, we will talk only about problems on subgroups of infinite groups, and in fact, only on subgroups of free groups . The results and methods I will present have been obtained over the past 40 years and are due to many researchers.

I will start by setting the landscape, including for those who forgot what the free group is --- and we will see that we are dealing here, from the algorithmic point of view, with a variant of combinatorics on words. I will then present the tool that is central to most efficient algorithms on subgroups of free groups: the representation of each finitely generated subgroup by a labeled rooted graph (shall we say… an automaton?) which is unique and easily computable when a tuple of generators of the subgroup under consideration is given. This graph is called the Stallings graph.

The game consists, then, in translating algorithmic problems on subgroups into algorithmic problems on Stallings graphs, and in solving these problems as efficiently as possible.

We will discuss in particular the following problems (clearly: just the beginning of this long list).
- The generalized word problem: given k+1 elements of the free group (these are words), does the last one belong to the subgroup generated by the k first ones?
- The index problem: given a tuple of elements of the free group, does the subgroup they generate have finite index?
- The basis problem: given a tuple of elements of the free group, find the rank and a basis of the subgroup they generate.
- The intersection problem: given two tuples of elements of the free group, compute the intersection of the subgroups they generate (compute a basis of this intersection).
- The conjugacy problem: given two tuples of elements of the free group, are the subgroups they generate equal? conjugated?
- And many other problems (keywords: Whitehead minimality, free factors, malnormality, closure under radicals, closure in the sense of the pro-p topology, etc…)
Fri 26th Mar
10:00 am
11:00 am
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Séminaire Anne Etien

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
Fri 19th Mar
10:00 am
12:00 pm
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Seminar Pablo Ferragin
Title: Theory and practice of learning-based compressed data structures

Presenter: Giorgio Vinciguerra

Abstract:
We revisit two fundamental and ubiquitous problems in data structure design:
predecessor search and rank/select primitives. We show that real data present a
peculiar kind of regularity based on geometric considerations. We name it
“approximate linearity”.
We thus expand the horizon of compressed data structures by presenting two
solutions for the problems above that discover, or “learn”, in a principled
algorithmic way, these approximate linearities. We provide a walkthrough of
these new theoretical achievements, also with a focus on open-source libraries
and their experimental improvements. We conclude by discussing the plethora of
research opportunities that these new learning-based approaches to data
structure design open up.

Zoom link: univ-lille-fr.zoom.us/j/95419000064
Fri 12th Mar
10:00 am
12:00 pm
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Seminar: Antonio AL SERHALI
Title: Can Earliest Query Answering on Nested Streams be achieved in Combined Linear Time?
Fri 19th Feb
10:00 am
11:00 am
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Seminar: Bernardo Subercaseau
Title: Foundations of Languages for Interpretability.

Abstract:
The area of interpretability in Machine Learning aims for the design of algorithms that we humans can understand and trust. One of the fundamental questions of interpretability is: given a classifier M, and an input vector x, why did M classify x as M(x)? In order to approximate an answer to this "why" question, many concrete queries, metrics and scores have emerged as proxies, and their complexity has been studied over different classes of models. Many of these analyses are ad-hoc, but they tend to agree on the fact that these queries and scores are hard to compute over Neural Networks, but easy to compute over Decision Trees. It is thus natural to think of a more general approach, like a query language in which users could write an arbitrary number of different queries, and that would allow for a generalized study of the complexity of interpreting different ML models. Our work proposes foundations for such a language, tying to First Order Logic, as a way to have a clear understanding of its expressiveness and complexity. We manage to define a minimalistic structure over FO that allows expressing many natural interpretability queries over models, and we show that evaluating such queries can be done efficiently for Decision Trees, in data-complexity.

Zoom link: univ-lille-fr.zoom.us/j/95419000064
Fri 12th Feb
10:00 am
12:00 pm
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Seminar: Florent Capelli
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.
Fri 15th Jan
10:00 am
12:00 pm
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Séminaire de Kim Nguyễn
Titile: The BOLDR project
Abstract: I
n this presentation, I will give an account of the BOLDR project and
perspectives in the field of language integrated queries.

Several classes of solutions allow programming languages to express
queries: specific APIs such as JDBC, Object-Relational Mappings (ORMs)
such as Hibernate, and language-integrated query frameworks such as
Microsoft's LINQ. However, most of these solutions do not allow for
efficient cross-databases queries, and none allow the use of complex
application logic from the programming language in queries.

We study the design of a new language-integrated query
framework called BOLDR that allows the evaluation in databases of
queries written in general-purpose programming languages containing
application logic, and targeting several databases following different
data models. In this framework, application queries are translated to
an intermediate representation. Then, they are typed with a type
system extensible by databases in order to detect which database
language each subexpression should be translated to. This type system
also allows us to detect a class of errors before execution. Next,
they are rewritten in order to avoid query avalanches and make the
most out of database optimizations. Finally, queries are sent for
evaluation to the corresponding databases and the results are
converted back to the application. Our experiments show that the
techniques we implemented are applicable to real-world database
applications, successfully handling a variety of language-integrated
queries with good performances.

This talk will give an overview of what has been achieved so far (mainly
in the context of Julien Lopez' PhD Thesis) and will glimpse at preliminary
work that is being done in the context of a collaboration with Oracle Labs.
Fri 8th Jan
10:45 am
12:30 pm
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Séminaire @ Lê Thành Dũng (Tito) Nguyễn
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).


2020
Thu 17th Dec
2:00 pm
4:00 pm
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Nofar Carmeli
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.
Fri 11th Dec
10:00 am
11:30 am
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Alexandre Vigny
Title: Elimination Distance to Bounded Degree on Planar Graphs
Link to the zoominar: univ-lille-fr.zoom.us/j/95419000064
Abstract:
What does it mean for a graph to almost be planar? Or to almost have bounded
degree?
On such simple graphs classes, some difficult algorithmic problems become
tractable.
Ideally, one would like to use (or adapt) existing algorithms for graphs that
are "almost" in such a simple class.

In this talk, I will discuss the notion of elimination distance to a class C, a
notion introduced by Bulian and Dawar (2016).
The goals of the talk are:
1) Define this notion, and discuss why it is relevant by presenting some
existing results.
2) Show that we can compute the elimination distance of a given planar graph to
the class of graph of degree at most d.
I.e. answer the question: "Is this graph close to a graph of bounded degree?"

The second part is the result of a collaboration with Alexandre Lindermayer and
Sebastian Siebertz.

Fri 4th Dec
10:00 am
11:00 am
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Seminar: Pierre Pradic
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.

Fri 27th Nov
10:00 am
11:30 am
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Seminar: Charles Paperman
Title: Stackless processing of streamed trees

Abstract: In this talk, I will first present the state of the art of efficiency implementation of streaming-text algorithms on modern architecture. Then some recent results on the extraction of information on streamed of structured documents without stack overhead.

For more info: paperman.name/data/pub.....d.pdf

Fri 13th Nov
10:00 am
12:00 pm
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Seminar: Mikaël Monet
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

Permanent link to this article: https://team.inria.fr/links/seminars/