In the LOCAL model of distributed computing, n processors are connected together through a graph. They communicate with their neighbours in a synchronised way a limited number of times (through infinite bandwith communication channels), and then produce an output. Their goal is to find a strategy solving some information processing task, e.g. to obtain a proper coloring of the graph. To answer this question, the considered physical theory of information matters: for instance, Quantum Information Theory (QIT) can in principle allow for strategies solving the task quicker.

Finding lower bounds on the maximal speed at which QIT can solve a task is tricky. To circumvent this difficulty, several proofs based on the No-Signalling (NS) Principle (which states that an event A can influence an event B only if some signal can physically be sent from A to B) were proposed and a new NS-LOCAL model of distributed computing was proposed.

I’ll re-interpret this NS-LOCAL model based on the theoretical physics formalism of light cones in circuits. I will justify that the NS-LOCAL model is the “largest reasonable model with a pre-shared resource between the nodes”. Then, I’ll introduce a weaker Causal-LOCAL model, the “largest reasonable model without pre-shared resource between the nodes”.

All this will be illustrated with easy to understand examples. I was recently told by Vaclav Rozhon: We computer scientists are very scared of the word “quantum”. Note that I’ll almost not talk about quantum theory, hence no need to be scared.

Conférence à l'IHP incluant une journée spéciale “Séminaire Flajolet” le jeudi 7.

Inscription obligatoire sur le site de la conférence: https://indico.math.cnrs.fr/event/8115/registrations/

Voir aussi: https://semflajolet.math.cnrs.fr/

Proof assistant kernels are a natural target for program certification: they are small, critical, and well-specified. Still, despite the maturity of the field of software certification, we are yet to see a certified Agda, Coq or Lean. In this talk, I will try and explain why this is not such an easy task, and present two complementary projects going in that direction. The first, MetaCoq, is a large scale project, broadly aiming at giving tools to manipulate Coq terms and derivations inside of Coq, in particular developing an important body of formalized proofs around Coq's typing. The second is a more recent endeavour, aimed at tackling the mother of all properties: normalisation.

In this presentation, I will provide an introduction to proof theory within the context of non-wellfounded proof systems. A non-wellfounded proof is generated by finitely branching logical rules, but potentially resulting in an infinitely deep proof tree. After defining the system, I will present a proof of cut-elimination for the $\mu$-MALL system, drawing from the work of Baelde et al. in 2016. Furthermore, I will discuss how we aim to extend this result with Alexis Saurin.

Primary key constraints in databases state there can be at most one tuple for every primary key in a given relation. However, these days it is common to have situations where this property cannot be maintained. Databases that violate constraints are called « inconsistent databases ». In particular, if a database violates primary key constraint, it will contain more than one tuple for the same primary key. In this setting, the notion of a repair is defined by picking exactly one tuple for each primary key (maximal consistent subset of the database). A Boolean conjunctive query q is certain for an inconsistent database D if q evaluates to true over all repairs of D. In this context, there is a dichotomy conjecture that states that for a fixed boolean conjunctive query q, testing whether q is certain for an input database D is either polynomial time or coNP-complete.

The conjecture is open in general and has been open for more than two decades. In this talk we will introduce two new algorithms that we have devised, one based on fix-point computation and the other based on bipartite matching. We will also see how these algorithms can be used to prove the dichotomy for the cases that were previously open.

These results were obtained in collaboration with Diego Figueira, Luc Segoufin and Cristina Sirangelo and combine the results that were presented at ICDT 2023 and what will be presented at PODS 2024.

the dichromatic number of a digraph is the minimum integer k such that the set of vertices of D can be partitioned into k acyclic subdigraphs. It is easy to see that the chromatic number of a graph G is the same as the dichromatic of the digraph obtained from G by replacing each edge by a digon (two anti-parallel arcs). Based on this simple observation, many theorems concerned with chromatic number of undirected graphs have been generalised to digraphs via the dichromatic number. However, no concept of clique number for digraphs was available. The purpose of this presentation is to explore such a concept and its relationship with the dichromatic number, mirroring the relationship between the clique number and chromatic number in undirected graphs. We will focus on studying the notion of chi-boundedness in particular. This is a joint work with Guillaume Aubian, Pierre Charbit and Raul Lopes.

Maintaining spectral information quickly with changing data matrix is essential in several applications. In this talk I would give an overview of what is known in this area and present a simple yet novel algorithm and analysis of maintaining an approximate maximum eigenvalue and eigenvector of a positive semi-definite matrix quickly, that undergoes decremental updates. Our algorithms also hint towards a separation between oblivious and adaptive adversaries in the dynamic setting, which has not yet been resolved.

This is based on a very recent work with Thatchaphol Sararunak.