A Class of Automata for the Verification of Infinite, Resource-Allocating Behaviours

Process calculi for service-oriented computing often feature generation of fresh resources. So-called nominal automata have been studied both as semantic models for such calculi, and as acceptors of languages of finite words over infinite alphabets. In this paper we investi-gate nominal automata that accept infinite words. These automata are a generalisation of deterministic Muller automata to the setting of nominal sets. We prove decidability of complement, union, intersection, emptiness and equivalence, and determinacy by ultimately periodic words. The key to obtain such results is to use finite representations of the (otherwise infinite-state) defined class of automata. The definition of such operations enables model checking of process calculi featuring infinite behaviours, and resource allocation, to be implemented using classical automata-theoretic methods

Approximate automata for omega-regular languages

Automata over infinite words, also known as ω -automata, play a key role in the verification and synthesis of reactive systems. The spectrum of ω -automata is defined by two characteristics: the acceptance condition (e.g. Büchi or parity) and the determinism (e.g., deterministic or nondeterministic) of an automaton. These characteristics play a crucial role in applications of automata theory. For example, certain acceptance conditions can be handled more efficiently than others by dedicated tools and algorithms. Furthermore, some applications, such as synthesis and probabilistic model checking, require that properties are represented as some type of deterministic ω -automata. However, properties cannot always be represented by automata with the desired acceptance condition and determinism. In this paper we study the problem of approximating linear-time properties by automata in a given class. Our approximation is based on preserving the language up to a user-defined precision given in terms of the size of the finite lasso representation of infinite executions that are preserved. We study the state complexity of different types of approximating automata, and provide constructions for the approximation within different automata classes, for example, for approximating a given automaton by one with a simpler acceptance condition

Synthèse et étude de nouveaux tensio-actifs organocatalyseurs : une voie de valorisation des lipides des algues sargasses

The aim of this thesis is to explore a valorization way of the lipids contained in sargassum seaweed, which is available in large quantities on the Caribbean coast: the development of new biosourced organocatalyst surfactants that can be used to carry out chemical reactions in aqueous media, replacing conventional organic solvents with a significant environmental impact. A chemical characterisation of sargassum was carried out on algae harvested at various sites in Guadeloupe and the Dominican Republic in 2021 and 2022. The contents of alginates, glucans, fucans, mineral matter, proteins, lipids, mannitol, polyphenols and heavy metals were determined. The results showed that algae are mainly made up of structural carbohydrates. Protein analysis have led to the determination of a nitrogen-protein conversion factor different from the reference factor usually used for brown algae. All the batches analysed were found to be contaminated with arsenic. Finally, lipid analysis have led to identified the majorty lipid in sargassum: palmitic acid, which has a 16-carbon chain. In order to synthesise organocatalyst surfactants, this majority lipid was grafted onto a MacMillan-type imidazolidinone unit obtained from phenylalaninamide. Different grafting routes were explored, starting with palmitic acid and also 10-carbon fatty acids, in order to study the impact of chain length on surfactant properties. The surface-active properties of the molecules synthesised were evaluated and for two of them, the catalytic activity was confirmed under conventional conditions, in the presence of organic solvents, on model asymmetric Friedel-Crafts alkylation reactions. Initial experiments with these molecules in aqueous media were then carried out, demonstrating their ability to carry out enantioselective reactions in an environmentally-friendly medium.L'objectif de la thèse est d'explorer une voie de valorisation des lipides contenus dans les algues sargasses disponibles en grandes quantités sur les côtes caribéennes : l'élaboration de nouveaux tensioactifs biosourcés organocatalyseurs permettant de mettre en œuvre des réactions chimiques en milieu aqueux, en substitution des solvants organiques conventionnels peu respectueux de l'environnement. Une caractérisation chimique des sargasses a été réalisée sur des algues récoltées sur différents sites en Guadeloupe et en République Dominicaine au cours des années 2021 et 2022. Les taux d'alginates, de glucanes, de fucanes, de matière minérale, de protéines, de lipides, de mannitol, de polyphénols et de métaux lourds ont été déterminés. Les résultats ont montré que les algues sont majoritairement constituées de sucres de structure. L'analyse des protéines a permis la détermination d'un facteur de conversion azote-protéine différent du facteur de référence usuellement utilisé pour les algues brunes. Tous les lots analysés se sont révélés être pollués à l'arsenic. Enfin, l'analyse des lipides a permis d'identifier le lipide majoritaire des sargasses : l'acide palmitique qui comporte une chaîne à 16 atomes de carbone. Afin de synthétiser les tensio-actifs organocatalyseurs, ce lipide majoritaire a été greffé sur un motif imidazolidinone de type MacMillan obtenu à partir de phénylalaninamide. Différentes voies de greffage ont été explorées, à partir de l'acide palmitique et également de l'acide gras à 10 carbones afin d'étudier l'impact de la longueur de chaîne sur les propriétés tensio-actives. Les propriétés tensio-actives des molécules synthétisées ont été évaluées et pour deux d'entre elles, l'activité catalytique a été confirmée dans des conditions classiques, en présence de solvants organiques, sur des réactions modèles d'alkylation de Friedel Crafts asymétriques. Des premières expérimentations avec ces molécules en milieu aqueux ont ensuite été réalisées, démontrant ainsi leur capacité à mener des réactions énantiosélectives dans un milieu respectueux de l'environnement