k-Set Agreement in Communication Networks with Omission Faults

We consider an arbitrary communication network G where at most f messages can be lost at each round, and consider the classical k-set agreement problem in this setting. We characterize exactly for which f the k-set agreement problem can be solved on G. The case with k = 1, that is the Consensus problem, has first been introduced by Santoro and Widmayer in 1989, the characterization is already known from [Coulouma/Godard/Peters, TCS, 2015]. As a first contribution, we present a detailed and complete characterization for the 2-set problem. The proof of the impossibility result uses topological methods. We introduce a new subdivision approach for these topological methods that is of independent interest. In the second part, we show how to extend to the general case with k in N. This characterization is the first complete characterization for this kind of synchronous message passing model, a model that is a subclass of the family of oblivious message adversaries

Exact and approximate agreements for message adversaries

Le sujet porte sur l'étude de la calculabilité des systèmes distribués dans la famille de modèles des adversaires de message. Plusieurs approches mathématiques sont mises en œuvre. Notamment des méthodes topologiques s'inscrivant dans les avancées récentes du domaine, mais également des méthodes géométriques, combinatoires, et des systèmes dynamiques. Dans une première partie, nous nous intéressons aux problèmes du Consensus et de l'Accord k-Ensembliste qui sont des formes d'accords exacts, c'est à dire que les valeurs décidées doivent être parmi celles qui sont proposées. En complément de FG11, nous avons caractérisé topologiquement la solvabilité du Consensus Binaire à Deux Processus dans le modèle général des adversaires de message donnant ainsi une meilleure intuition du résultat. Nous avons également caractérisé la solvabilité de l'Accord k-Ensembliste dans les adversaires d'omissions en donnant le nombre de fautes de type omissions que le système peut tolérer tout en résolvant le problème sur un graphe de communication support. En ce faisant, nous nous sommes appuyé sur une méthode topologique que nous avons étendu pour nos modèles graphiques. Enfin, avons étudié dans la deuxième partie des variantes approchées de l'Accord k-Ensembliste. Désormais, les valeurs de décisions nécessitent d'êtres proches l'une de l'autre selon des critères bien définis. Plusieurs variantes ont été étudiés, notamment une version asymptotique n'exigeant pas de terminaison explicite des processus mais requérant une certaine convergence des valeurs. Les résultats explicitent la diversité et la complexité des questions enjeu.Our subject is about computability of distributed systems in the messageadversaries family of models.For this purpose, several mathematical approaches are carried out.For instance, based on recent advances in the subject, we use well knowntopological methods to solve our problems.But we also used geometric, combinatorial and dynamical systems methods.In the first part, we are interested in the Consensus problem and the k-SetAgreement.They are what we called exact agreements, i.e. the decision values must beamong the proposed ones.As a complement to FG11, we have characterized topologically the solvability ofthe Binary Consensus problem with two process in the general model of messageadversaries.This new characterization gives a better intuition of the result.We also characterized the solvability of k-Set Agreement in omissionadversaries by giving the number of omission faults a system can tolerate inorder to solve the problem on an underlying communication graph.Doing so, we based our result on a topological method that we extended to ourgraphical models.Finally, we studied in a second part some approximate variations of the k-SetAgreement problem.In this approximate setting, the decision values are required to be close toone another, based on some precise conditions.Several variations were studied, most notably an asymptotic version thatdoesn't requires processes to explicitly terminatebut rather requires a certain type of convergence of the values.Theses results shows the diversity and intricacy of the questions that are atstake

The LIFE of CUE

Talk at CONFLANG '23, a SPLASH 2023 workshop, Cascais, PortugalIn this talk, we compare CUE and LIFE (actually a subset of these), two languages apparently far apart but which share some common roots.We elaborate on the commonalities and differences between building CUE configurations and LIFE psi-terms by relying on basic examples as well as sketches of operational semantics, considering a subset of CUE including embedded values and duplicate field declarations. Depending on the example, the mapping between CUE and LIFE can be straightforward or reveal serious discrepancies.We plan to further explore the commonalities and differences of these languages, in particular with respect to adding constraints to feature structures. It would also be worthwhile to look at some other languages based on typed feature structures to gain a better understanding of the design space. We conjecture that this understanding could lead to a theoretically-simpler configuration language, possibly extended with computational abilities