Enumerative and Analytic Combinatorics for Propositional Logic and Concurrency Theory: Towards a quantification of the model expressiveness

This habilitation thesis presents combinatorial and algorithmic studies in the context of Boolean logic and concurrency theory. It seems there is no direct relationship between these two domains. Nevertheless, there are similarities in the nature of the studies. Indeed, the original idea consists in studying the semantics of the models, that links, in logic as well as in language theory, the syntactic structures (usually abstract syntax trees) and their interpretation. Moreover, my approaches of the problems are unified by the nature of the questions I am interested and by the techniques I use: analytic combinatorics.
How can we interpret and what information can we extract of a large structure? More specifically, my goal consists in interpreting the syntactic and semantic structures as combinatorial classes in order to obtain quantitative and algorithmic information.
In this thesis, we will concentrate more on combinatorial models than on their applications. I want to highlight the evolutions of the models, explaining the contributions of each characteristic in the results. I presents several cases,where a more complex model does not fundamentally modify its guantitative behavior. These iterative studies, built on more and and more complex bricks, allow to understand the combinatorics underlying the more evolved models and the reasons why an approach or an algorithm cannot finally be adapted

Defence : 09/22/2017 - 13h30 - Site Jussieu 15-16/101

Jury members :

M. Michael DRMOTA- Professeur & Technische Universität Wien (Vienne)-Rapporteur
M. Arnaud DURAND- Professeur & Université Denis Diderot (Paris)-Rapporteur
M. Conrado MARTINEZ -Professeur & Universitat Politècnica de Catalunya (Barcelone)-Rapporteur

Mme Béatrice BERARD-Professeur & Université Pierre et Marie Curie (Paris)- Examinateur
M. Olivier BODINI- Professeur & Université Paris-Nord (Paris)- Examinateur
M. Alain DENISE -Professeur & Université Paris-Sud (Paris)- Examinateur
M. Jean MAIRESSE - Directeur de Recherche CNRS & Université Pierre et Marie Curie (Paris)- Examinateur
M. Cyril NICAUD- Professeur & Université Paris-Est, Marne-la-Vallée (Paris)- Examinateur
Mme Michèle SORIA-Professeur & Université Pierre et Marie Curie (Paris)- Examinateur

1 PhD graduated 2021