Les présomptions interviennent pour corriger les lacunes du raisonnement juridique. Elles sont traditionnellement définies comme « des conséquences que la loi ou le magistrat tire d’un fait connu à un fait inconnu ». Les présomptions occupent un rôle important en droit de la propriété intellectuelle car la recherche de la vérité ainsi que le traitement du doute en constituent l’essence. Qu’il s’agisse d’appréhender les objets (œuvre de l’esprit, invention, marque, etc.), de désigner les acteurs (titulaires ou contrefacteurs) ou de délimiter le contenu des droits de propriété intellectuelle, l’usage des présomptions est incontournable. Cependant, les nouveaux défis (numérique, mondialisation de l’économie, communautarisation du droit, etc.) auxquels sont confrontées les créations immatérielles conduisent le législateur et le juge à galvauder les présomptions. On assiste à une inflation voire une densification de la « norme présomptive » en droit de la propriété intellectuelle : il y a une présomption pour presque tout, sur presque tout et presque partout. Cela fragilise le système de protection des créations immatérielles et, fatalement, engendre une insécurité juridique en droit de la propriété intellectuelle. L’objectif de notre thèse est d’analyser ce que recouvre réellement l’idée de présomptions en droit de la propriété intellectuelle et de délimiter concrètement leur champ d’action (première partie). Cette démarche envisage à terme de proposer une théorie générale des présomptions à partir de laquelle les présomptions applicables en propriété intellectuelle pourraient s’identifier et tirer leur légitimité (deuxième partie). Une telle approche permettra de fournir une grille de lecture plus pertinente tant aux théoriciens qu’aux praticiens de la matière pour aborder efficacement les problématiques inhérentes à ce domaine dont la complexité n’est plus à présenter. / Presumptions in intellectual property law, analysis in the light of general lawPresumptions intervene to correct shortcomings in legal reasoning. They are traditionally defined as "consequences that the law or the magistrate draws from a known fact to an unknown fact". Presumptions play an important role in intellectual property law because the search for truth and the treatment of doubt are its essence. Whether it is to apprehend the objects (intellectual work, invention, trademark, etc.), to designate the actors (owners or counterfeiters) or to delimit the content of the intellectual property rights, the use of presumptions is unavoidable. However, the new challenges (digital, globalization of the economy, communalization of the law, etc.) faced by intangible creations force the legislator and the judge to squander the presumptions. We are witnessing inflation and even densification of the "presumptive norm" in intellectual property law: there is a presumption for almost everything, on almost everything and almost everywhere. This weakens the system of protection of intangible creations and, inevitably, creates unprecedented legal uncertainty in intellectual property law. The aim of our thesis is to analyze what the idea of presumptions in intellectual property law really covers and to concretely define their field of action. This approach ultimately aims to propose a general theory of presumptions from which the presumptions applicable in intellectual property could identify and draw their legitimacy. Such an approach that will provide a reading grid more relevant to both theorists and practitioners of the subject to effectively address the issues inherent in this area whose complexity is more to present.

A proposta deste trabalho é fazer uma apreciação crítica dos laudos periciais realizados em ações judiciais de responsabilidade civil por alegado erro médico. A prova pericial deve orientar o julgador para que este possa fixar os limites da responsabilidade do médico ou profissional de saúde. O perito deve responder adequadamente as questões discutidas no processo, bem como trazer ao juiz os elementos que considerar úteis ou necessários para auxiliar a decisão judicial. Na parte teórica são estudados os campos de apuração da responsabilidade por erro médico, os pressupostos da responsabilidade civil, os tipos de prova que podem ser produzidos no processo, quais são os elementos essenciais do laudo pericial e os critérios que devem ser usados pelo perito para determinar se estão presentes os requisitos do dever de indenizar. Em seguida, utilizando-se dados obtidos em processos judiciais, são abordados os aspectos mais relevantes nas ações desta espécie, como a incidência dos tipos de dano alegados pelos autores, as especialidades médicas mais acionadas judicialmente, o tempo médio entre o ajuizamento da ação e a sentença judicial e a relevância dos laudos nas decisões judiciais observadas. Ao final, é realizada uma análise crítica dos conteúdos dos laudos, verificando se eles contêm todos os elementos recomendados e descritos na parte teórica, fazendo-se críticas sobre se eles cumpriram sua função de forma adequada e propondo instrumentos para seu aperfeiçoamento. / The aim of this work is to do a critical appreciation of the expert reports in judicial proceedings for alleged medical malpractice. The expert report should guide the judge and help to determine the limits of the physician\'s or health professional\'s responsibility. The expert must answer appropriately the questions discussed in the lawsuit, as well as bringing the elements that he or she might consider useful or necessary to aid the judicial decision. The theoretical section concerns the medical malpractice responsibility verification, the presupposed civil responsibility, the kinds of proof that can be produced in the process, what are the essential elements of the expert report, and which criteria that should be used by the expert to determine if the requirements of the duty of compensating are present. Then, using data obtained from judicial proceedings, the most important aspects in this kind of lawsuit are exposed, such as the incidence of types of damage alleged by the authors, the most prosecuted medical specialties, the average time between the beginning of the action and the judicial sentence, and the relevance of the expert reports in the observed judicial decisions. At the end, a critical analysis of the reports is accomplished, verifying if they contain all the recommended elements described in the theoretical part, criticizing the accomplishment of their function, and proposing instruments for their improvement.

O presente estudo examina a técnica da distribuição dinâmica do ônus da prova e a possibilidade de sua aplicação no direito brasileiro, incluindo a sua disciplina no Projeto do Novo Código de Processo Civil. Abordaremos as bases principiológicas da dinamização dos ônus probatórios, bem como os entendimentos doutrinários e jurisprudenciais que já sustentam a possibilidade da dinamização do ônus da prova com base no ordenamento jurídico atualmente vigente. Sustentaremos, todavia, que a adoção da técnica da dinamização do ônus da prova no ordenamento jurídico brasileiro seria cabível somente de lege ferenda, com a aprovação do Projeto do Novo CPC pelo Congresso Nacional. Por fim, no intuito de estabelecer os melhores critérios para utilização da técnica da distribuição dinâmica do ônus da prova, foram analisados os dispositivos contidos no Projeto do Novo CPC, para vislumbramos que a aplicação da técnica, deverá ser excepcional. Analisamos ainda que o magistrado brasileiro deverá aprimorar a sua função de organizador da fase instrutória do processo. Sustentaremos que a técnica da dinamização do ônus da prova é suplementar aos poderes instrutórios do juiz. Todavia, como existem limites materiais, de cunho prático, ao exercício dos poderes instrutórios do magistrado, a técnica da distribuição dinâmica do ônus da prova se mostra útil e eficaz ao sistema processual brasileiro. Assim, o juiz deverá se valer na sentença da técnica da dinamização do ônus da prova em desfavor da parte que deu causa à dificuldade ou impossibilidade de produção da prova, inviabilizando o acesso a determinado meio de prova. / The following essay examines the theory of dynamic distribution of the burden of proof and the possibility of its application in Brazilian law, including its discipline in the Project of the New Code of Civil Procedure. We will cover the principles related to the dynamic distribution of the burden of proof as well as the doctrinal and caselaw understanding that already support the possibility of the switch of the burden of proof based on the currently prevailing legal system. However, we will argue that the adoption of dynamic distribution of the burden of proof in Brazilian law would be applicable only by lege ferenda, with the approval of the New Code of Civil Procedure by the Congress. Finally, in order to establish the best criteria for use of the dynamic distribution of the burden of proof, the provisions contained in the Project of the New Code of Civil Procedure were analyzed to envision that the application of the technique should be exceptional. We will also analyze that the Brazilian judge should enhance its organizer function of proceedings phase. We will still sustain that the dynamic distribution of the burden of proof is additional in relation to the powers that the judge has in the ex officio proofs production. However, as there are material limits of the exercise of the Judges power in the ex officio proofs production, the technique of the the dynamic distribution of the burden of proof proves to be useful and effective in Brazilian legal system. Thus, the judge must take into consideration the techniques of the switch of the burden of proof, on the judgment, to the detriment of the party that gave rise to the difficulty or impossibility of evidence, preventing access to certain evidence.

Made available in DSpace on 2016-04-27T17:13:00Z (GMT). No. of bitstreams: 1 Alvesmar Ferreira da Silva Filho.pdf: 4341581 bytes, checksum: 7d920ecf354e0137a2bbca7e034ddc90 (MD5) Previous issue date: 2007-05-24 / Made available in DSpace on 2016-08-25T17:25:37Z (GMT). No. of bitstreams: 2 Alvesmar Ferreira da Silva Filho.pdf.jpg: 1943 bytes, checksum: cc73c4c239a4c332d642ba1e7c7a9fb2 (MD5) Alvesmar Ferreira da Silva Filho.pdf: 4341581 bytes, checksum: 7d920ecf354e0137a2bbca7e034ddc90 (MD5) Previous issue date: 2007-05-24 / Secretaria da Educação do Estado de São Paulo / The aim of this study was to involve a group of mathematics teachers from the same school in the development of a teaching sequence related to quadrilaterals and their properties. Inspired by the aims of the project AProvaMe (Argumentation and proof in school mathematics), a collaborative group was organised in the school where the teacher-researcher works, with the intention of creating a space within which teachers could engage in discussions about the theme of the research: the teaching and learning of proof. Before initiating the reunions of the group, a first version of the teaching sequence was conceived to serve as a focus for the discussions. The design of the activities of the sequence was informed by the work of Parsysz about the teaching of geometry in general and, more specifically, aspects related to justifying and proving were based in the perspectives about types of proof and their functions of Balacheff and De Villiers. With the sequence in hand, two teachers were invited to compose, together with the teacher-researcher, a collaborative group within which to work through, discuss and, where necessary, modify the proposed activities. On the basis of the initial survey of the conceptions of the teachers about prova and its teaching, it was identified that the area of the curriculum is not one woth which they are well familiar or comfortable and, in particular, both the teachers indicated that they expect their students only to understand arguments of a pragmatic and not a conceptual nature.. Given this fact, perhaps the most significant contribution of their participation in the collaborative group meetings was the oportunity to reflect upon possible teaching strategies that might help smooth the passage from pragmatic to conceptual proofs / Esse trabalho tem como objetivo envolver um grupo de professores da Matemática de uma mesma escola no desenvolvimento de uma seqüência didática sobre quadriláteros e suas propriedades. Inspirado nos objetivos do projeto AprovaME (Argumentação e Prova na Matemática Escola), resolvemos organizar um grupo colaborativo na escola onde trabalhamos, com a intenção de criar um espaço que possibilitasse a discussão sobre o tema dessa pesquisa: o ensino e aprendizagem de prova. Antes de iniciar as reuniões do grupo, concebemos uma primeira versão de uma seqüência didática para servir como base para as discussões. A elaboração das atividades da seqüência foi baseada nos trabalhos de Parsysz (2000) sobre o ensino de Geometria em geral e, mais especialmente, as partes referentes à justificativa e prova foram baseadas nas perspectivas sobre tipos de provas e suas funções de Balacheff (1988) e De Villiers (2001). Em seguida, convidamos duas professoras da Matemática para formarem, juntamente com o pesquisador/professor, um grupo colaborativo no qual realizamos, discutimos e, na medida necessária, modificamos as atividades propostas, inicialmente, na seqüência. A partir de levantamento inicial das concepções das professoras sobre provas e seu ensino, identificamos que provas não representam um tópico com qual as professoras sentiam-se muito seguras e, em particular, ambas indicaram que esperavam que seus alunos apenas entendessem provas de natureza pragmática. Assim, a contribuição mais significativa da participação delas nos encontros do grupo colaborativo foi a possibilidade de refletir sobre estratégias de ensino que pudessem facilitar a passagem de provas pragmáticas a provas conceituais

Este trabalho revisa e problematiza a usual associação entre a matemática escolar e o desenvolvimento do raciocínio lógico, introduzindo a argumentação e a prova em matemática como um elo de tal associação. Assim, desenvolve-se uma investigação tanto teórica quanto de campo, visando compreender por que, embora central na matemática acadêmica, a prova é tão pouco explorada na matemática escolar. A investigação teórica reviu diversas referências, em geral oriundas da Educação Matemática, mas também da História da Matemática, com vistas a: (1) compreender o papel de destaque da prova no contexto atual da Matemática, a partir do entrelaçamento entre a noção de demonstração e o próprio desenvolvimento dessa ciência; (2) discutir aspectos conceituais e epistemológicos da prova matemática que podem contribuir para um trabalho significativo com o tema na educação básica; e (3) compreender as razões da ausência de um trabalho significativo com a prova matemática na educação básica do Brasil nas últimas décadas. A investigação de campo complementa a investigação teórica apresentando um estudo de caso sobre conhecimentos, crenças e concepções de um pequeno grupo de professoras de matemática da educação básica a respeito do raciocínio lógico e da prova matemática. Essas investigações permitiram concluir que são diversas as causas do suposto abandono do trabalho com a prova matemática na educação básica, entre as quais destacamos a falta de uma discussão aprofundada sobre o tema na formação inicial de professores e a presença de práticas de ensino de matemática pautadas numa concepção tecnicista / In this dissertation, we review and problematize the usual association between school mathematics and the development of logical reasoning, introducing the proof in mathematics as a link of this association. Therefore we conducted both theoretical research and field research, in order to understand why the mathematical proof, although central to academic mathematics, is so little emphasized in school mathematics. In theoretical research, we reviewed several references, usually arising from the Mathematics Education, but also from the History of Mathematics, in order to: (1) understand the important role of proof in the current context of mathematics, from the entanglement between the notion of demonstration and even the development of this science; (2) discuss conceptual and epistemological aspects of the mathematical proof that can contribute to meaningful work with this theme in basic education; and (3) understand the reasons for the absence of meaningful work with mathematical proof in basic education in Brazil in recent decades. The field research complements the theoretical research presenting a case study on knowledge, beliefs and conceptions of a small group of mathematics teachers of basic education about logical reasoning and mathematical proof. These investigations allowed us to conclude that there are various causes for the alleged abandonment of work in mathematical proof in basic education, among which we highlight: the absence of thorough discussion of this topic school teacher education and the presence of current practice of a technical approach to math teaching

The purpose of this thesis is to determine the feasibility of using blockchain to implement proof of location. There has been an increasing demand for a way to create a validated proof of location that is economical, and easy to deploy as well as portable. There are several reasons for an increased demand in this technology including the ever-increasing number of mobile gamers that have been able to spoof their location successfully, the increasing number of on demand package shipments from companies such as Amazon, and the desire to reduce the occurrence of medical errors as well as holding hospitals accountable for their errors. Additional reasons that this technology is gaining popularity and increasing in demand is due the continually increasing number of lost baggage claims that airlines are receiving, as well as insurance companies desire to reduce the number of fraud cases that are related to high-value goods as well as increasing the probability of their recovery. Within the past year, there has been an extensive amount of research as well as work that has been completed to create an irrefutable method of location verification, which will permit a user to be able to create time-stamped documentation validating that they were at a particular location at a certain day and time. Additionally, the user is then permitted to release the information at a later date and time that is convenient for them. This research was completed using a Raspberry Pi 3B, a Raspberry Pi 3B+, two virtual Raspberry Pi’s as well as two virtual servers in which the goal was to download, and setup either Ethereum and/or Tendermint Blockchain on each piece of equipment. After completely synchronizing the blockchain it be used to store the verified location data that been time-stamped. There was a variety of issues that were encountered during the setup and installation of the blockchains on the equipment including overclocking processors, which negatively affected the computational abilities of the devices as well as causing overheating and surges in voltage as well as a variety of software and hardware incompatibilities. These issues when looked at individually appear to not have much of an impact on the results of this research but when combined together it is obvious that they reduced the results that could be obtained. In conclusion, the combination of hardware and software issues when combined with the temperature and voltage issues that were due to the overheating of the processor resulted in several insurmountable issues that could not be overcome. There are several recommendations for continuing this work including presyncing the blockchain using a computer, using a device that has more functionality and computational abilities, connecting a cooling device such as a fan or adding a heat sink, increasing the available power supply, utilizing an externally power hard drive for data storage, recreate this research with the goal in mind of determining what process or application was causing the high processor usage, or creating a distributed system that utilizes both physical and virtual equipment to reduce the amount of work on one type of device.

Submitted by Cássia Santos (cassia.bcufg@gmail.com) on 2014-09-19T13:14:21Z No. of bitstreams: 2 Dissertacao Hermogenes Hebert Pereira Oliveira.pdf: 452221 bytes, checksum: b2469cc663d70c03f4dcf9dbea202fb2 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2014-09-19T13:19:45Z (GMT) No. of bitstreams: 2 Dissertacao Hermogenes Hebert Pereira Oliveira.pdf: 452221 bytes, checksum: b2469cc663d70c03f4dcf9dbea202fb2 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Made available in DSpace on 2014-09-19T13:19:45Z (GMT). No. of bitstreams: 2 Dissertacao Hermogenes Hebert Pereira Oliveira.pdf: 452221 bytes, checksum: b2469cc663d70c03f4dcf9dbea202fb2 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Previous issue date: 2014-02-14 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / Proof-theoretic Semantics provides a new approach to the semantics of logical constants. It has compelling philosophical motivations which are rooted deeply in the philosophy of language and the philosophy of mathematics. We investigate this new approach of logical semantics and its perspective on logical validity in the light of its own philosophical aspirations, especially as represented by the work of Dummett (1991). Among our findings, we single out the validity of Peirce’s rule with respect to a justification procedure based on the introduction rules for the propositional logical constants. This is an undesirable outcome since Peirce’s rule is not considered to be constructively acceptable. On the other hand, we also establish the invalidity of the same inference rule with respect to a justification procedure based on the elimination rules for the propositional logical constants. We comment on the implications of this scenario to Dummett’s philosophical programme and to proof-theoretic semantics in general. / As semânticas construtivas oferecem uma nova abordagem semântica para as constantes lógicas. Essas semânticas gozam de fortes motivações filosóficas advindas da filosofia da linguagem e da filosofia da matemática. Nós investigamos essa nova abordagem semântica da lógica e sua concepção de validade lógica sob a luz de suas próprias aspirações filosóficas, em especial aquelas representadas pelo trabalho de Dummett (1991). Dentre nossos resultados, destacamos a validade da Regra de Peirce em relação ao procedimento justificatório baseado nas regras de introdução para as constantes lógicas proposicionais. Essa é uma situação indesejável, pois a Regra de Peirce não é considerada aceitável de um ponto de vista construtivo. Por outro lado, verificamos que o procedimento justificatório baseado nas regras de eliminação atesta a invalidade dessa mesma regra. Tecemos alguns comentários a respeito das consequências desse cenário para o projeto filosófico de Dummett e para as semânticas construtivas em geral.

Les propriétés que l’on souhaite exprimer sur les applications système d’information ne peuvent se restreindre aux propriétés statiques, dites propriétés d’invariance, qui portent sur des états du système pris au même moment. En effet, certaines propriétés, dites propriétés dynamiques, peuvent faire référence à l’état passé ou futur du système. Les travaux existants sur la vérification de telles propriétés utilisent généralement le model checking dont l’efficacité pour le domaine des systèmes d’information est plutôt réduite à cause de l’explosion combinatoire de l’espace des états. Aussi, les techniques, fondées sur la preuve, requièrent des connaissances assez avancées en termes de raisonnement mathématique et sont donc difficiles à mettre en œuvre d’autant plus que ces dernières ne sont pas outillées. Pour palier ces limites, nous proposons dans cette thèse des méthodes de vérification de propriétés dynamiques basées sur la preuve en utilisant la méthode formelle B. Nous nous intéressons principalement aux propriétés d’atteignabilité et de précédence pour lesquelles nous avons défini des méthodes de génération d’obligations de preuve permettant de les prouver. Une propriété d’atteignabilité permet d’exprimer qu’il existe au moins une exécution du système qui permet d’atteindre un état cible à partir d’un état initial donné. Par contre, la propriété de précédence permet de s’assurer qu’un état donné du système est toujours précédé par un autre état. Afin de rendre ces différentes approches opérationnelles, nous avons développé un outil support qui permet de décharger l’utilisateur de la tâche de génération d’obligations de preuve qui peut être longue et fastidieuse / The properties that we would like to express on data-intensive applications cannot be limited to static properties, called invariance properties, which depend on states taken at the same time. Indeed, some properties, called dynamic properties, may refer to the past or the future states of the system. Existing work on the verification of such properties typically use model checking whose effectiveness for data-intensive applications is rather limited due to the combinatorial explosion of the state space. In addition, the techniques, based on the proof, require fairly advanced knowledge and mathematical reasoning especially that they are not always supported by tools. To overcome these limitations, we propose in this thesis proof-based verification approaches that use the B formal method. We are mainly interested in reachability and precedence properties for which we defined formal rules to generate proof obligations that permit to discharge them. A reachability property expresses that there is at least one execution scenario that permits to reach a target state from a given initial state while a precedence property ensures that a given system state is always preceded by another state. To make these different approaches workable, we have developed a support tool that permits to discharge the users from tedious and error-prone tasks

La réalisabilité classique de Jean-Louis Krivine associe à chaque modèle de calcul et chaque modèle de la théorie des ensembles un nouveau modèle de la théorie des ensembles, appelé modèle de réalisabilité, d'une façon similaire au forcing. Chaque modèle de réalisabilité est muni d’une algèbre de Boole caractéristique $\gimel 2$ (gimel 2), dont la structure donne des informations sur les propriétés du modèle de réalisabilité. En particulier, les modèles de forcing correspondent au cas où $\gimel 2$ est l'algèbre de Boole à deux éléments.Ce travail présente de nouveaux outils pour manipuler les modèles de réalisabilité et donne de nouveaux résultats obtenus en les exploitant. L'un d'entre eux est qu'au premier ordre, la théorie des algèbres de Boole à au moins deux éléments est complète pour $\gimel 2$, au sens où $\gimel 2$ eut être rendue élémentairement équivalente à n'importe quelle algèbre de Boole. Deux autres résultats montrent que $\gimel 2$ peut être utilisée pour étudier les modèles dénotationnels de langage de programmation (chacun part d'un modèle dénotationnel et classifie ses degrés de parallélisme à l'aide de $\gimel 2$). Un autre résultat montre que la technique de Jean-Louis Krivine pour réaliser l'axiome des choix dépendants à partir de l'instruction quote peut se généraliser à des formes plus fortes de choix. Enfin, un dernier résultat, obtenu en collaboration avec Laura Fontanella, accompagne le précédent en adaptant la condition d'antichaîne dénombrable du forcing au cadre de la réalisabilité, ce qui semble semble ouvrir une piste prometteuse pour réaliser l'axiome du choix. / Jean-Louis Krivine's classical realizability defines, from any given model of computation and any given model of set theory, a new model of set theory called the realizability model, in a similar way to forcing. Each realizability model is equipped with a characteristic Boolean algebra $\gimel 2$ (gimel 2), whose structure encodes important information about the properties of the realizability model. For instance, forcing models are precisely the realizability models in which $\gimel 2$ is the Boolean algebra with to elements.This document defines new tools for studying realizability models and exploits them to derive new results. One such result is that, as far as first-order logic is concerned, the theory of Boolean algebras with at least two elements is complete for $\gimel 2$, meaning that for each Boolean algebra B (with at least two elements), there exists a realizability model in which $\gimel 2$ is elementarily equivalent to B. Next, two results show that $\gimel 2$ can be used as a tool to study denotational models of programming languages (each one of them takes a particular denotational model and classifies its degrees of parallelism using $\gimel 2$). Moving to set theory, another results generalizes Jean-Louis Krivine's technique of realizing the axiom of dependant choices using the instruction quote to higher forms of choice. Finally, a last result, which is joint work with Laura Fontanella, complements the previous one by adapting the countable antichain condition from forcing to classical realizability, which seems to open a new, promising approach to the problem of realizing the full axiom of choice.

L’intérêt porté aux algorithmes probabilistes est, entre autres,dû à leur simplicité. Cependant, leur analyse peut devenir très complexeet ce particulièrement dans le domaine du distribué. Nous mettons en évidencedes algorithmes, optimaux en terme de complexité en bits résolvantles problèmes du MIS et du couplage maximal dans les anneaux, qui suiventle même schéma. Nous élaborons une méthode qui unifie les résultatsde bornes inférieures pour la complexité en bits pour les problèmes duMIS, du couplage maximal et de la coloration. La complexité de ces analysespouvant facilement mener à l’erreur et l’existence de nombreux modèlesdépendant d’hypothèses implicites nous ont motivés à modéliserde façon formelle les algorithmes distribués probabilistes correspondant ànotre modèle (par passage de messages, anonyme et synchrone), en vuede prouver formellement des propriétés relatives à leur analyse. Pour cela,nous développons une bibliothèque, RDA, basée sur l’assistant de preuveCoq. / Probabilistic algorithms are simple to formulate. However, theiranalysis can become very complex, especially in the field of distributedcomputing. We present algorithms - optimal in terms of bit complexityand solving the problems of MIS and maximal matching in rings - that followthe same scheme.We develop a method that unifies the bit complexitylower bound results to solve MIS, maximal matching and coloration problems.The complexity of these analyses, which can easily lead to errors,together with the existence of many models depending on implicit assumptionsmotivated us to formally model the probabilistic distributed algorithmscorresponding to our model (message passing, anonymous andsynchronous). Our aim is to formally prove the properties related to theiranalysis. For this purpose, we develop a library, called RDA, based on theCoq proof assistant.