The work is concerned with the development of a multi-stage corrosion fatigue lifetime model, with emphasis on pitting as a precursor to cracking. The model is based upon the quantitative evaluation of damage during the overall corrosion fatigue process. The fatigue response of as-received API 5L X65 linepipe steel has been investigated in terms of the evolution of damage during pit development, pit-to-crack transition and crack propagation. Micro-potentiostatic polarisation was conducted to evaluate role of stress on pit development. Crack growth rate measurements were conducted on pre-pitted specimens, which were tested in air and brine, to evaluate the initiation and propagation behaviour of cracks emanating from artificial pits. Finite element analysis was undertaken to evaluate the stress and strain distribution associated with the pits. A cellular automata finite element model was also developed for predicting corrosion fatigue damage. Pit growth rate was enhanced under stress. It was considered that the strain localisation effect of the pit facilitated strain-assisted dissolution. In air, cracks initiated predominantly from the pit mouth. FEA results indicated that this was due to localisation of strain towards the pit mouth. In corrosion fatigue, cracks tended to initiate at the pit base at low stress and at the pit mouth at higher stresses. Crack initiation lifetimes were shorter in the aggressive environment compared to air and the effect of the environment on crack initiation lifetime was lower at higher stress levels. Crack initiation lifetime for double pits generally decreased with decreasing pit-to-pit separation distance. The microstructure was observed to influence crack growth behaviour in air particularly in the early stages when cracks were short. The acceleration and retardation in crack growth were attributed to the resistance of grain boundaries to crack advance. Cracks sometimes arrested at these barriers and became non-propagating. Introduction of the environment for a short period appear to eliminate the resistance of the microstructural barriers thus promoting re-propagation of the previously arrested crack. The continued crack propagation after the removal of the environment suggests that the influence of the environment is more important in the early stages of crack growth. Crack growth rates were higher in the aggressive environment than in air. The degree of environmental enhancement of crack growth was found to be greater at lower stress levels and at short crack lengths. Oxide-induced crack closure and crack coalescence were two mechanisms that also affected crack growth behaviour.2-D cellular automata finite element simulation results, with and without stress, show good agreement agreed with experiments i.e. pit depth and pit aspect ratio increase with time. Results from 3-D cellular automata simulations of pits are also consistent with experiments. Fatigue lifetimes were significantly shorter (i) in the brine environment than in air and (ii) for specimens with double pits compared to single pits of similar depth. Fatigue strength in air was found to decrease with increasing pit depth. Corrosion fatigue lifetimes predicted based upon the developed model showed good agreement with the experimental lifetimes.

<div>Topology Optimization is an optimization technique used to synthesize models without any preconceived shape. These structures are synthesized keeping in mind the minimum compliance problems. With the rapid improvement in advanced manufacturing technology and increased need for lightweight high strength designs topology optimization is being used more than ever.</div><div>There exist a number of commercially available software's that can be used for optimizing a product. These software have a robust Finite Element Solver and can produce good results. However, these software offers little to no choice to the user when it comes to selecting the type of optimization method used.</div><div>It is possible to use a programming language like MATLAB to develop algorithms that use a specific type of optimization method but the user himself will be responsible for writing the FEA algorithms too. This leads to a situation where the flexibility over the optimization method is achieved but the robust FEA of the commercial FEA tool is lost.</div><div>There have been works done in the past that links ABAQUS with MATLAB but they are primarily used as a tool for finite element post-processing. Through this thesis, the aim is to develop an interface that can be used for solving optimization problems using different methods like hard-kill as well as the material penalization (SIMP) method. By doing so it's possible to harness the potential of a commercial FEA software and gives the user the requires flexibility to write or modify the codes to have an optimization method of his or her choice. Also, by implementing this interface, it can also be potentially used to unlock the capabilities of other Dassault Systèmes software's as the firm is implementing a tighter integration between all its products using the 3DExperience platform.</div><div>This thesis as described uses this interface to implement BESO and HCA based topology optimization. Since hybrid cellular atomata is the only other method other than equivalent static load method that can be used for crashworthiness optimization this work suits well for the role when extended into a non-linear region.</div>

Les automates cellulaires sont à la fois un modèle de calcul parallèle, un système complexe et un système dynamique. Ils fonctionnent de manière synchrone et en temps discret, leur particularité est que les fonctions qu'ils définissent sont issues de l'application simultanée, en tout point de l'espace, d'une règle d'évolution locale. L'ensemble limite est un objet classique des systèmes dynamiques, c'est l'ensemble des états que le système peut atteindre arbitrairement tard. Il a été très étudié dans le cadre des automates cellulaires, et les résultats sont nombreux. Parmi ces résultats, un théorème de Rice démontré par Jarkko Kari dit que toute propriété des ensembles limites est indécidable. Dans ce mémoire, on ne s'intéresse plus à l'ensemble limite traditionnel, mais à une variante pour laquelle on utilise une mesure sur l'espace des entrées, sélectionnant ainsi les comportements susceptibles d'apparaître arbitrairement tard et souvent. Ce nouvel ensemble, que l'on nomme ensemble mu-limite, a été introduit en 2000 par Petr Kurka et Alejandro Maass. La plupart des résultats sur les ensembles limites ne se transposent pas naturellement. On étudie la famille des ensembles mu-limites d'automates cellulaires. On montre que sous certaines contraintes sur la dynamique, l'ensemble mu-limite peut être entièrement décrit. On classe ainsi les automates en fonction de ces contraintes. Dans le cas général, on montre l'existence d'automates cellulaires ayant comme ensembles mu-limites un grand nombre d'ensembles complexes. On finit par montrer un théorème de Rice pour les ensembles mu-limites d'automates cellulaires: tout propriété non triviale de ces ensembles est indécidable. / Cellular automata are simultaneously a model of parallel computation, a complex system and a dynamical system. They are synchronous and time is discrete. The functions defined by their application is the result of the synchronous application of the same local rule everywhere. The limit set is a classical tool of dynamical systems theory, it is the set of states the system can reach arbitrarily late. It has been studied often in the particular case of cellular automata and there are numerous results. Amongst them, a Rice's theorem proved by Jarkko Kari states that any non-trivial property of limit sets of cellular automata is undecidable. In this thesis, we do not consider the classical limit set, as we add a measure on the space of states of the system. Thus, we get a set which contains behaviors that appear arbitrarily far and often. This set is named mu-limit set and was introduced in 2000 by Petr Kurka and Alejandro Maass. Most of the results on limit sets cannot be directly adapted for mu-limit sets. We study the family of all mu-limit sets of cellular automata. We show that under some constraints on the dynamics, the mu-limit set can be entirely described. We then produce a classification of cellular automata according to these constraints. In the general case, we prove the existence of cellular automata whose mu-limit sets are among a large set of complex sets. We finally prove Rice's theorem for mu-limit sets: any non-trivial property is undecidable.

A teoria do caos estuda o tipo de comportamento, aparentemente aleatório, que apresentam alguns sistemas complexos sensíveis à perturbação dos seus parâmetros, como por exemplo sistemas dinâmicos, fractais, autômatos celulares, entre outros. Os autômatos celulares (ACs) são sistemas dinâmicos discretos que podem apresentar comportamentos caóticos a partir de regras simples. Os ACs tem sido empregados em diversas aplicações principalmente em simulações, mas também tem contribuído no reconhecimento de padrões, processamento de imagens e na Criptografia. A necessidade em transmitir informação de forma mais segura vem crescendo com a necessidade por novos algoritmos criptográficos. Paralelamente, os criptoanalistas vem progredindo constantemente na quebra e na procura de vulnerabilidades destes algoritmos, sendo necessaria a incursão de novas abordagens para atender estes desafios. Neste trabalho é proposto o desenvolvimento e avaliação de algoritmos criptográficos, assim como um novo método de criptoanálise, motivados pela adequação dos ACs caóticos com os princípios de confusão e difusão da Criptografia, seguindo critérios apropriados para a boa construção destes algoritmos, que são sintetizados em três partes: (i) Na proposta do algoritmo de cifra criptográfico baseado no AC caótico, foi sugerida uma estratégia de seleção de ACs em base a combinação de vários critérios como o expoente de Lyapunov, a entropia e a distância de Hamming; visando selecionar um AC apropriado para a geração de números pseudo-aleatórios usados no processo de encriptação/decriptação do algoritmo, o qual é validado por diversos testes de aleatoriedade. (ii) Foi proposto o algoritmo de hash criptográfico baseado numa abordagem híbrida dos ACs e as redes complexas, visando a construção de um algoritmo flexível e de bom desempenho. Os resultados alcançados por ambos os algoritmos criptográficos mostraram-se relevantes quando comparados com o estado da arte, com boas qualidades de segurança e um grande potencial para ser aplicados em problemas reais. (iii) Na proposta do método de criptoanálise foi sugerido traçar equivalências entre os sistemas criptográficos e os ACs caóticos visando explorar e analisar seu comportamento dinâmico, por meio da adaptação do algoritmo do expoente de Lyapunov dos ACs, cujos resultados permitiram encontrar padrões característicos nos modos de operação criptográficos. Os resultados obtidos mostraram que a abordagem dos ACs caóticos para desenvolver os algoritmos pode ser bastante útil em aplicações de Criptografia e Criptoanálise. / Chaos theory studies the apparently random behaviour from some complex systems with highly sensitive to the initial conditions, such as dynamical systems, fractals, cellular automata, among others. Cellular automata (CA) are discrete dynamical systems that may exhibit chaotic behaviour from simple rules. CA have been employed in many multidisciplinary applications, most of them in simulations systems, including pattern recognition, image processing and Cryptography. Nowadays, the development of new cryptographic algorithms is required in order to fulfil the increasing demand for secure transmission of confidential information. These algorithms are intensively analyzed, most of them broken by the cryptanalyst community. We proposed to develop two cryptographic algorithms: a block cipher and a hash function based on chaotic CA and its corresponding evaluation. We also proposed a new cryptanalysis methodology motivated by the strong relationship between the chaotic properties of CA and the cryptographic principles of confusion and diffusion, by following appropriate criteria to the proper design of these algorithms, which are summarized into three parts: (i) To proposed the block cipher proposed it was suggested a methodology to select a suitable CA to Cryptography by means of compounded measures such as the Lyapunov exponent, entropy and Hamming distance. Moreover, this selected CA is employed to generate pseudo-random numbers, which are further used in the encryption/decryption of the proposed block cipher and validated under several randomness tests. The results obtained by this cryptographic algorithm achieved similar and even higher performance when compared to others found in literature. (ii) The cryptographic hash function was developed using an hybrid approach of CA and complex networks, in order to build a flexible algorithm with acceptable performance when compared to conventional hash functions. In general, the results obtained from both cryptographic algorithms showed good security qualities and great potential to be applied in real problems. (iii) To proposed the cryptanalysis methodology it was suggested to draw parallels between cryptographic systems and CA, in order to explore and analise their dynamic behaviour. Hence, upon drawing such parallels, we have a means to adapt the Lyapunov exponent algorithm conceived in the framework of CA. Unexpectedly, the results obtained allow to discriminate among cryptographic modes of operation, which provides significant contributions to the field. Finally, we proved that the chaotic cellular automata approach can be quite useful in applications cryptography and cryptanalysis.

No estudo de sistemas complexos interessa capturar a evolução do seu comportamento emergente segundo um conjunto de regras cujas soluções descrevem o seu estado ao longo do tempo. Uma classe particular de modelos matemáticos e computacionais que permite realizar essa investigação são os autômatos celulares. O comportamento global deles é definido apenas por regras locais, o que os tornam um modelo exemplar para estudos de sistemas complexos. Estamos interessados em um tipo especial de autômato celular: os classificadores de densidade unidimensionais. Este tipo de autômato celular está relacionado com o problema da maioria que consiste em fazer convergir uma cadeia de símbolos aleatoriamente distribuídos em um reticulado, para uma cadeia homogênea com um único símbolo final (consenso global), aquele de maioria inicial. Este consenso deve ser obtido exclusivamente a partir de interações locais entre os sítios sem a instância de um controle central. Nesta pesquisa, realizamos alguns experimentos para caracterizar um autômato celular classificador de quatro estados proposto em Gács, Kurdyumov e Levin (1978). Embora seja um classificador imperfeito, este autômato celular é significativamente tolerante a falhas quando o submetemos a níveis de ruídos não nulos. Os resultados corroboram com outros estudos que investigam a robustez deste tipo de autômato celular e lançam luz sobre o entendimento da origem da coordenação global de sistemas que exibem as características aqui descritas / In the study of complex systems we are interested in capturing their evolution of its emergent behavior under a set of rules whose solutions describe the state of the system over time. A particular class of mathematical and computational model to perform this kind of research is the cellular automaton (CA). Its global behavior is defined by local rules, which makes it an exemplary model to study complex systems. Here, we are interested in a particular type of CA: one-dimensional CA that classifies densities. This kind of CA is related to the problem of the majority task that consists of converging an array of symbols, initially randomly distributed, to a single symbol, the more frequent one in the initial configuration of the array (global consensus). This consensus must be obtained solely out of local interactions, without the instance of a central control. In this research, we conducted some experiments to characterize a four-state CA classifier proposed in Gács, Kurdyumov e Levin (1978). While it is an imperfect classifier, this CA is significantly fault tolerant when submitted to the levels of non-zero noise. Our results corroborate other studies that had investigated the robustness of this type of CA, and shed light on the understanding of the origin of global coordinated systems that exhibit the characteristics described here

Les incendies de forêt sont l'un des phénomènes les plus complexes auxquels sont confrontées nos sociétés. Le Liban, faisant partie du Moyen-Orient, est en train de perdre dramatiquement ses forêts vertes principalement en raison de graves incendies. Cette thèse étudie le phénomène des incendies de forêt. Elle propose des nouveaux modèles et méthodologies pour remédier à la crise des incendies de forêts, en particulier au Liban et en Méditerranée. Elle est divisée en deux parties principales: nouvelles approches de la prévision des incendies de forêt et développement d'un nouveau modèle de diffusion du feu plus fidèle du cas réel. La première partie est subdivisée en 3 chapitres. Le premier chapitre présente une étude analytique des modèles métrologiques les plus utilisés qui permettent de prédire les incendies de forêt. Dans le deuxième chapitre, nous appliquons cinq méthodes de techniques d’exploration de données: Réseaux de neurones, arbre de décision, floue logique, analyse discriminante linéaire et méthode SVM. Nous cherchons à trouver la technique la plus précise pour la prévision des incendies de forêt. Dans le troisième chapitre, nous utilisons différentes techniques d'analyse de données corrélatives (Régression, Pearson, Spearman et Kendall-tau) pour évaluer la corrélation entre l'occurrence d'incendie et les données météorologiques (température, point de rosée, température du sol, humidité, précipitation et vitesse du vent). Cela permet de trouver les paramètres les plus influents qui influencent l'occurrence de l’incendie, ce qui nous amène à développer un nouveau Indice Libanais de Risques d'Incendie (IL). L'indice proposé est ensuite validé à partir des données météorologiques pour les années 2015-2016. La deuxième partie est subdivisée en 3 chapitres. Le premier chapitre passe en revue les caractéristiques du comportement de feu et sa morphologie; il se concentre sur la validité des modèles mathématique et informatique de comportement de feu. Le deuxième chapitre montre l'importance des automates cellulaires, en expliquant les principaux types et examine certaines applications dans différents domaines. Dans le troisième chapitre, nous utilisons des automates cellulaires pour élaborer un nouveau modèle de comportement pour prédire la propagation de l’incendie, sur des bases elliptiques, dans des paysages homogènes et hétérogènes. La méthodologie proposée intègre les paramètres de la vitesse du vent, du carburant et de la topographie. Notre modèle développé est ensuite utilisé pour simuler les incendies de forêt qui ont balayé la forêt du village d'Aandqet, au nord du Liban. Les résultats de simulation obtenus sont comparés avec les résultats rapportés de l'incident réel et avec des simulations qu'on a iv effectuées sur le modèle de Karafyllidis et le modèle de Karafyllidis modifié par Gazmeh. Ces comparaisons ont prouvé l'ambiguë du modèle proposé. Dans cette thèse, la crise des feux de forêt a été étudiée et de nouveaux modèles ont été développés dans les deux phases: pré-feu et post-feu. Ces modèles peuvent être utilisés comme outils préventifs efficaces dans la gestion des incendies de forêt . / Wildland fires are one of the most complex phenomena facing our societies. Lebanon, a part of Middle East, is losing its green forests dramatically mainly due to severe fires. This dissertation studies the phenomenon of forest fires. It proposes new models and methodologies to tackle the crisis of forest fires particularly in Lebanon and Mediterranean. It is divided into two main parts: New Approaches in Forest Fire Prediction and Forest Fire modeling. The first part is sub-divided into 3 chapters. First chapter presents an analytical study of the most widely used metrological models that can predict forest fires. In the second chapter we apply five data mining techniques methods: Neural Networks, Decision Tree, Fuzzy Logic, Linear Discriminate Analysis and Support Vector Machine. We aim to find the most accurate technique in forecasting forest fires. In the third chapter, we use different correlative data analysis techniques (Regression, Pearson, Spearman and Kendall-tau) to evaluate the correlation between fire occurrence and meteorological data (Temperature, Dew point, Soil temperature, Humidity, Precipitation and Wind speed). This allows to find the most influential parameters that affect the occurrence of fire, which lead us to develop a new Lebanese fire danger Index (LI). The proposed index is then validated using meteorological data for the years 2015-2016. The second part is sub-divided into 3 chapters. The first chapter reviews the fire behavior characteristics and its morphology; and focuses on the validity of mathematical and computer fire behavior models. The second chapter manifests the importance of cellular automata, explains the main types of cellular automata and reviews some applications in various domains. In the third chapter, we use cellular automata to develop a new behavior model for predicting the spread of fire, on elliptical basis, in both homogeneous and heterogeneous landscapes .The proposed methodology incorporates the parameters of wind speed, fuel and topography. The developed model is then used to simulate the wildfire that swept through the forest of Aandqet village, North Lebanon. Obtained simulation results are compared with reported results of the real incident and with simulations done on Karafyllidis model and Gazmeh-Modified Karafyllidis model. These comparisons have proven the outperformance of the proposed model. In this dissertation, the crisis of forest fires has been studied and new models have been developed in both phases: pre-fire and post-fire. These models can be used as efficient preventive tools in forest fire management.

Apresentamos dois autômatos celulares com regras de interação locais que permitem descrever a dinâmica de população de um sistema predador-presa. Os modelos são definidos sobre uma rede regular quadrada e se diferenciam pelo caráter isotrópico ou anisotrópico da interação entre os sítios. A cada sítio é associada uma variável estocástica, que pode assumir três estados - vazio, presa ou predador. A dinâmica de competição entre espécies animais que nos interessa é a mesma descrita pelo modelo de Lotka-Volterra no qual as populações de presas e predadores oscilam temporalmente. Nosso objetivo é a análise dessas oscilações, como se comportam com o aumento da rede e se permanecem estáveis. Para a obtenção das séries temporais realizamos simulações de Monte Carlo. Para o autômato definido sobre o espaço isotrópico, também realizamos análise de campo médio dinâmico. Os resultados indicam que a oscilação é um efeito local (não sobrevive em sistemas infinitos), e é mais significativo devido à migração das espécies pelos subsistemas. O estudo da anisotropia revela alguns padrões espaciais organizados e que as oscilações são menos intensas do que no caso isotrópico e como consequência a fase ativa é mais abrangente. / We present two cellular automata with local interaction rules which allow us to describe the dynamical population of a predator-prey system. The models are defined on a regular square lattice and are distinguished by the isotropic or anisotropic character of the interaction between sites. To each site a stochastic variable is associated, which can assume three states- void, prey or predator. The competition dynamics between animal species which interest us is the same described by the Lotka-Volterra model in which the populations of preys and predators oscillate in time. Our aim is the analysis of these oscillations, how they behave with an increasing lattice and if they remain stable. In order to obtain temporal series we perform Monte Carlo simulations. For the automaton defined on isotropic space, dynamical mean field analysis was also performed. Results indicate that the oscillation is a local effect ( vanishing in infinite systems), and is more significant due to migration of species through the subsystems. The study of anisotropy reveals some organized spatial patterns and that oscillations are less intense than in the isotropic case and as a consequence the active phase is more comprehensive.

Made available in DSpace on 2017-07-21T19:25:54Z (GMT). No. of bitstreams: 1 Fernando da Silva Borges.pdf: 3003505 bytes, checksum: c77a390868c21644a0396314c4bf4e0e (MD5) Previous issue date: 2016-11-22 / Fundação Araucária de Apoio ao Desenvolvimento Científico e Tecnológico do Paraná / In this thesis, we use mathematical models to study the dynamic range of neural networks. The dynamic range is the difference between maximum and minimum levels of sensation produced by known stimuli. Using cellular automata to model neuronal dynamics and different network topologies with different types of synapses, we investigate for which conditions the dynamic range is enhanced. In a network where local connections represent the electrical synapses and nonlocal connections the chemical synapses, we analyze the dynamic range in function of the number of nonlocal connections and time delay between these connections. We find that the dynamic range is enhanced for neural networks with low time delay when the number of nonlocal connections increases. Furthermore, we propose a neural network model separated into two layers, where one layer corresponds to inhibitory and the other to excitatory neurons. We randomly distribute electrical and chemical synapses in the network in order to analyse the effects on the dynamic range. In our proposed model, the chemical synapses, that are directed, can be excitatory or inhibitory, while the electrical synapses are bidirectional. Through the mean-field approximation, we analytically calculate the dynamic range as a function of the model parameters. The values that we find are very close to the results obtained from simulations. We verify that electrical synapses have a complementary effect on the enhancement of the dynamic range. Finally, we found that electrical synapses on excitatory layer are responsible for this complementary effect, while the electrical synapses in inhibitory layer promote a small increase in the dynamic range value. / Nesta tese usamos modelos matemáticos para estudar a faixa dinâmica de redes neuronais. A faixa dinâmica é a diferença entre a resposta máxima e mínima produzida por um determinado estímulo. Utilizando autômatos celulares para modelar a dinamica neuronal e diversas topologias de redes com diferentes tipos de sinapses, investigamos para quais configurações a faixa dinamica ´e maximizada. Em uma rede onde conexões locais representam sinapses elétricas e conexões não locais as sinapses químicas, analisamos o que ocorre com a faixa dinamica quando varia-se a quantidade de conexões não locais ou um tempo de atraso entre essas conexões é considerado. Neste caso, verificamos que a faixa dinamica é maior para redes neuronais com valores baixos de atraso e aumenta com o acréscimo de conexões não locais. Além disso, propomos um modelo de rede de neurônios dispostos em duas camadas, uma excitatória e outra inibitótira, com sinapses química e elétricas distribuidas aleatoriamente. Neste modelo, as sinapses quimicas são direcionadas e podem ser excitatorias ou inibitórias, enquanto as sinapses elétricas são bidirecionais e apresentam apenas carater excitatorio. Fazendo aproximações de campo médio, calculamos analiticamente a faixa dinamica em função dos parametros do modelo. Os valores encontrados estão muito próximos dos obtidos por simulações e mostram que a faixa dinãmica é maximizada em pontos que dependem complementarmente das sinapses quimicas e elétricas. Finalmente, verificamos que as sinapses eletricas na camada excitatória sao responsaveis por esse efeito complementar, enquanto as sinapses elétricas na camada inibitoria promovem um pequeno acrescimo no valor da faixa dinamica.

Dans le contexte du calcul géométrique abstrait, les machines à signaux ont été développées comme le pendant continu des automates cellulaires capturant les notions de particules, de signaux et de collisions. Une question importante est la génération automatique d’un automate cellulaire reproduisant la dynamique d’une machine à signaux donnée. D’une part, il existe des conversions ad hoc. D’autre part, ce n’est pas toujours possible car certaines machines à signaux présentent des comportements « continus ». Par conséquent, la discrétisation automatique de telles structures est souvent complexe et pas toujours possible. Cette thèse propose trois manières différentes de discrétiser automatiquement les machines à signaux en automates cellulaires, avec ou sans approximation possible. La première s’intéresse à une sous-catégorie de machines à signaux, qui présente des propriétés permettant d’assurer une discrétisation automatique exacte pour toute machine de ce type. La deuxième est utilisable sur toutes les machines mais ne peut assurer ni l’exactitude ni la correction du résultat. La troisième s’appuie sur une nouvelle expression de la dynamique d’une machine à signaux pour proposer une discrétisation. Cette expression porte le nom de modularité et est décrite avant d’être utilisée pour discrétiser. / In the context of abstract geometrical computation, signal machines have been developed as a continuous counter part of cellular automata capturing the notions of particles, signals and collisions. An important issue is the automatic generation of a cellular automaton mimicking the dynamics of a given signal machine. On the one hand, ad hoc conversions exist.On the other hand, it is not always possible since some signal machines exhibit “purely continuous” behaviors. Therefore, automatically discretizing such structures is often complicated and not always possible. This thesis proposes different ways to automatically discretize signal machines into cellular automata, both with and without handling the possiblity of approximation.The first is concerned with a subcategory of signal machines, which has properties ensuring an exact automatic discretization for any machine of this type. The second is usable on all machines but cannot guarantee the exactness and correction of the result. The third is based on a new expression of the dynamics of a signal machine to propose a discretization.This dynamical expression takes the name of modularity and is described before being used to discretize.

Thesis (B.S.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1982. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND ENGINEERING / Bibliography: leaf 22. / by Inwhan Choi. / B.S.