Seminars

Speaker: Sarah Winter — sarahwinter.net/

Title: A Regular and Complete Notion of Delay for Streaming String Transducers

Abstract:
The notion of delay between finite transducers is a core element of numerous fundamental results of transducer theory. The goal of this work is to provide a similar notion for more complex abstract machines: we introduce a new notion of delay tailored to measure the similarity between streaming string transducers (SST).

We show that our notion is regular: we design a finite automaton that can check whether the delay between any two SSTs executions is smaller than some given bound. As a consequence, our notion enjoys good decidability properties: in particular, while equivalence between non-deterministic SSTs is undecidable, we show that equivalence up to fixed delay is decidable. Moreover, we show that our notion has good completeness properties: we prove that two SSTs are equivalent if and only if they are equivalent up to some (computable) bounded delay.

Together with the regularity of our delay notion, it provides an alternative proof that SSTs equivalence is decidable. Finally, the definition of our delay notion is machine-independent, as it only depends on the origin semantics of SSTs. As a corollary, the completeness result also holds for equivalent machine models such as deterministic two-way transducers, or MSO transducers.

This is joint work with Emmanuel Filiot, Ismaël Jecker, and Christof Löding.

Speaker: Rémi Morvan — www.morvan.xyz/

Titre: Approximation and Semantic Tree-width of Conjunctive Regular Path Queries

Abstract:
We show that the problem of whether a query is equivalent to a query of tree-width k is decidable, for the class of Unions of Conjunctive Regular Path Queries with two-way navigation (UC2RPQs). A previous result by Barceló, Romero, and Vardi has shown decidability for the case k=1, and here we show that decidability in fact holds for any arbitrary k>1. The algorithm is in 2ExpSpace, but we show that the complexity drops to the second level of the polynomial hierarchy for a restricted but practically relevant case of queries obtained by only allowing simple regular expressions.
We also investigate the related problem of approximating a UC2RPQ by queries of small tree-width. We exhibit an algorithm which, for any fixed number k, builds the maximal under-approximation of tree-width k of a UC2RPQ. The maximal under-approximation of tree-width k of a query q is a query q' of tree-width k which is contained in q in a maximal and unique way, that is, such that for every query q'' of tree-width k, if q'' is contained in q then q'' is also contained in q'. Joint work with Diego Figueira.

Speaker: Pierre Pradic — perso.ens-lyon.fr/pierre.pradic/

Title: Synthesizing Nested Relational Queries from Implicit Specifications

Abstract:
Derived datasets can be defined implicitly or explicitly. An implicit
definition (of dataset O in terms of datasets I⃗ ) is a logical specification
involving the source data I⃗ and the interface data O. It is a valid definition
of O in terms of I⃗ , if any two models of the specification agreeing on I⃗
agree on O. In contrast, an explicit definition is a query that produces O from
I⃗ . Variants of Beth's theorem state that one can convert implicit definitions
to explicit ones. Further, this conversion can be done effectively given a
proof witnessing implicit definability in a suitable proof system. In this
talk, I will discuss an analogous effective implicit-to-explicit result for
nested relations: implicit definitions, given in the natural logic for nested
relations, can be effectively converted to explicit definitions in the nested
relational calculus NRC.

I will first spend some time explaining what NRC is and what logic we use to
describe implicit definitions of nested queries. Then I will present the
results obtained in our papers, attempt to give some intuitions on the proof of
the main theorem and say a few words on in particular the proof-theoretic
techniques and concerns that come up (namely, cut-elimination and focussing)
and how this can impact the complexity of extracting explicit definitions from
proofs of implicit definability. Then if time allows I will discuss a more
general model-theoretic result that we first used to give a non-constructive
proof of our theorem, and some ideas that we have towards making it
constructive and bounding the complexity of extracting explicit definitions.

This is Joint work with Michael Benedikt and Christoph Wenhard. The main
results I will be discussing were written up in
arxiv.org/abs/2005.06503 and arxiv.org/abs/2209.08299.

Speaker : Luis Galárraga — luisgalarraga.de/about/

Title: Computing How-Provenance for SPARQL Queries via Query Rewriting

Abstract:
Over the past few years, we have witnessed the emergence of large knowledge graphs built by extracting and combining information from multiple sources. This has propelled many advances in query processing over knowledge graphs, however the aspect of providing provenance explanations for query results has so far been mostly neglected. In this talk I will present SPARQLprov, a method based on query rewriting, to compute how-provenance polynomials for SPARQL queries over knowledge graphs. Contrary to existing works, SPARQLprov is system-agnostic and can be applied to standard and already deployed SPARQL engines without the need of customized extensions. To do so, we rely on spm-semirings to compute polynomial annotations that respect the property of commutation with homomorphisms on monotonic and non-monotonic SPARQL queries without aggregate functions. An evaluation on real and synthetic data shows that SPARQLprov over standard engines competes with state-of-the-art solutions for how-provenance computation, while covering a larger fragment of the query language.

Title:The Regular Languages of First-Order Logic with One Alternation
Abstract: The regular languages with a neutral letter expressible in first-order logic with one alternation are characterized. Specifically, it is shown that if an arbitrary Σ2 formula defines a regular language with a neutral letter, then there is an equivalent Σ2 formula that only uses the order predicate. This shows that the so-called Central Conjecture of Straubing holds for Σ2 over languages with a neutral letter, the first progress on the Conjecture in more than 20 years. To show the characterization, lower bounds against polynomial-size depth-3 Boolean circuits with constant top fan-in are developed. The heart of the combinatorial argument resides in studying how positions within a language are determined from one another, a technique of independent interest.

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.

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

Title: Knowledge graph generation and validation

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

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…)

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

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

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.

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.

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

Title: ShEx Learning from Typed Graphs

Abstract: In knowledge graphs, schemas are becoming a new asset to describe the organization of data. The new world-leading format Shex is becoming a de-facto standard in the industry that allows defining flexible and powerful schemas.

In this context, the inference of schemas can become a solution to provide shex expressions that describe already existing data. Typically, the inference starts from untyped graphs. However, these tasks appears to be more complex than expected in general, and is possible only for subclasses of Shex.

The inference of schemas from typed graph gives a baseline for those algorithms. Its comprehension allows to understand better the underlying difficulties of the task. It presents already unexpected difficulties.

We present an algorithm that infers Shex-defined schemas from fully typed graphs. We also present some encountered difficulties, as well as the limitations of the approach.

Introduction to argumentation theory

Title: General Dynamic Yannakakis: Conjunctive Queries with Theta Joins Under Updates
Abstract:
The ability to efficiently analyze changing data is a key requirement
of many real-time analytics applications like Stream Processing,
Complex Event Recognition, Business Intelligence, and Machine
Learning.

Traditional approaches to this problem are based either on the
materialization of subresults (to avoid their recomputation) or on the
recomputation of subresults (to avoid the space overhead of
materialization). Both techniques have recently been shown suboptimal:
instead of fully materializing results and subresults, one can
maintain a data structure that supports efficient maintenance under
updates and can quickly enumerate the full query output, as well as
the changes produced under single updates.

In our work we are concerned with designing a practical family of
algorithms for dynamic query evaluation based on this idea, and for
queries featuring both equi-joins and inequality joins, as well as
certain forms of aggregation. Our main insight is that, for acyclic
conjunctive queries, such algorithms can naturally be obtained by
modifying Yannakakis' seminal algorithm for processing acyclic joins
in the static setting.

In this talk I present the main ideas behind this modfication,
offset it against the traditional ways of doing incremental view
maintenance, and discuss recent extensions such as dealing with
general theta-joins.