Uma sequência de imagens de satélite climático é processada aplicando-se um conjunto de operações de filtros, no intuito de extrair padrões de comportamento das nuvens. Caracteres são criados a partir deste tratamento e suas transições são investigadas, explorando a possibilidade de justificar suas ocorrências através de linguagens formais e linguagens bidimensionais, definindo suas gramáticas. Com esta contagem de transições, uma análise de sua forma fractal é iniciada e um paralelo com outras contagens estabelecida, como uma forma de estruturar um modelo computacionalmente menos complexo de prever o tempo, ou o comportamento de qualquer entidade dinâmica que possa ser discretizada. Com estas investigações e experiências, foi possível diminuir a quantidade de símbolos utilizados para justificar as formas das nuvens, bem como criar classes de equivalências para representar conjuntos de símbolos que compartilham as mesmas propriedades, diminuindo ainda mais a complexidade da gramática que se espera encontrar. / A sequence of weather satellite images are processed by applying a set of filtering operations in order to extract the behavior patterns of clouds. Characters are created from this treatment and their transitions are investigated by exploring the possibility of justifying their occurrence across formal languages and two-dimensional languages, defining their grammar. With these count transitions an analysis of their fractals starts and counts a parallel with others established as a way to structure a model less computationally complex to predict the weather, or the behavior of any dynamic entity that could be discretized. With these investigations and experiments, it was possible to reduce the number of symbols used to explain the shapes of clouds and create equivalent classes to represent the symbol sets that share the same properties, further reducing the complexity of the grammar expected to be found.

L'espérance de vie a augmenté dans les dernières décennies et devrait continuer à croître dans les prochaines années. Cette augmentation entraîne de nouveaux défis concernant l'autonomie et l'indépendance des personnes âgées. Le développement d'habitats intelligents est une piste pour répondre à ces défis et permettre aux personnes de vivre plus longtemps dans un environnement sûr et confortable. Rendre un habitat intelligent consiste à y installer des capteurs, des actionneurs et un contrôleur afin de pouvoir prendre en compte le comportement de ses habitants et agir sur leur environnement, pour améliorer leur sécurité, leur santé et leur confort. La plupart de ces approches s'appuient sur la localisation en temps réel des habitants dans leur habitat. Dans cette thèse, une nouvelle approche complète permettant la localisation d'un nombre a priori inconnu d'habitants basée sur le modèle est proposée. Cette approche tire parti des paradigmes, de la théorie et des outils des Systèmes à Événements Discrets. L'utilisation des automates à états finis pour modéliser le mouvement détectable des habitants ainsi que des méthodes permettant de construire ces modèles ont été développées. A partir de ces modèles automates finis, plusieurs algorithmes permettant de localiser de manière efficace les habitants ont été définis. Enfin, plusieurs approches pour l'évaluation des performances de l'instrumentation d'un habitat intelligent pour un objectif de localisation ont été proposées. La méthode a également été totalement implémentée et mise à l'épreuve. Tout au long de cette thèse, les différentes contributions sont illustrées à l'aide de cas d'étude. / Life expectancy has continuously increased in most countries over the last decades and will probably continue to increase in the future. This leads to new challenges relative to the autonomy and the independence of elderly. The development of Smart Homes is a direction to face these challenges and to enable people to live longer in a safe and comfortable environment. Making a home smart consists in placing sensors, actuators and a controller in the house in order to take into account the behavior of their inhabitants and to act on their environment to improve their safety, health and comfort. Most of these approaches are based on the real-time indoor Location Tracking of the inhabitants. In this thesis, a whole new approach for model-based Location Tracking of an a priori unknown number of inhabitants is proposed. This approach is based on Discrete Event Systems paradigms, theory and tools. The usage of Finite Automata (FA) to model the detectable motion of the inhabitants as well as different methods to create such FA models have been developed. Based on these models, algorithms to perform efficient Location Tracking are defined. Finally, several approaches aiming at evaluating the relevance of the instrumentation of a Smart Home with the objective of Location Tracking are proposed. The approach has also been fully implemented and tested. Throughout the thesis, the different contributions are illustrated on case studies. / In den meisten Industrieländern ist die Lebenserwartung in den letzten Jahrzehnten fortlaufend gestiegen und wird höchstwahrscheinlich noch weiter steigen. Dieser Anstieg führt zu neuen Herausforderungen hinsichtlich der Autonomie und Unabhängigkeit von älteren Menschen. Die Entwicklung von intelligenten Wohnungen ist ein Weg diesen Herausforderungen zu begegnen und es den Menschen zu ermöglichen länger in einer sicheren und komfortablen Umgebung zu leben. Dazu stattet man solcheWohnungen mit Sensoren, Aktoren sowie einem Controller aus. Dies erm öglicht es, in Abhängigkeit vom Verhalten der Bewohner, dieWohnumgebung so zu beein_ussen, dass sich Sicherheit, Gesundheit und Komfort verbessern. Ansätze, die dies zum Ziel haben, basieren meistens auf Methoden, die es ermöglichen Menschen innerhalb ihrer Wohnung in Echtzeit zu lokalisieren. In dieser Dissertation wird daher ein neuer Ansatz für eine modellbasierte Lokalisierung einer a priori unbekannten Anzahl von Bewohnern vorgestellt. Dieser Ansatz fuÿt auf der Theorie, den Paradigmen und den Werkzeugen aus dem Gebiet der ereignisdiskreten Systeme. Es werden endliche Automaten eingesetzt, um die von den Sensoren erfassbaren Bewohnerbewegungen zu modellieren. Verschiedene Verfahren zur Erzeugung solcher Automaten werden gezeigt. Basierend auf diesen Modellen warden Algorithmen de_niert, mittels derer die Bewohner wirksam lokalisiert werden können. Abschlieÿend werden Methoden vorgeschlagen, die dazu dienen die Relevanz der Sensorinstrumentierung für die Lokalisierung zu bewerten. Die entwickelten Verfahren werden in der Dissertation durchgehend anhand von Fallbeispielen erläutert. Der gesamte Ansatz wurde implementiert und erprobt.

Uma sequência de imagens de satélite climático é processada aplicando-se um conjunto de operações de filtros, no intuito de extrair padrões de comportamento das nuvens. Caracteres são criados a partir deste tratamento e suas transições são investigadas, explorando a possibilidade de justificar suas ocorrências através de linguagens formais e linguagens bidimensionais, definindo suas gramáticas. Com esta contagem de transições, uma análise de sua forma fractal é iniciada e um paralelo com outras contagens estabelecida, como uma forma de estruturar um modelo computacionalmente menos complexo de prever o tempo, ou o comportamento de qualquer entidade dinâmica que possa ser discretizada. Com estas investigações e experiências, foi possível diminuir a quantidade de símbolos utilizados para justificar as formas das nuvens, bem como criar classes de equivalências para representar conjuntos de símbolos que compartilham as mesmas propriedades, diminuindo ainda mais a complexidade da gramática que se espera encontrar. / A sequence of weather satellite images are processed by applying a set of filtering operations in order to extract the behavior patterns of clouds. Characters are created from this treatment and their transitions are investigated by exploring the possibility of justifying their occurrence across formal languages and two-dimensional languages, defining their grammar. With these count transitions an analysis of their fractals starts and counts a parallel with others established as a way to structure a model less computationally complex to predict the weather, or the behavior of any dynamic entity that could be discretized. With these investigations and experiments, it was possible to reduce the number of symbols used to explain the shapes of clouds and create equivalent classes to represent the symbol sets that share the same properties, further reducing the complexity of the grammar expected to be found.

This dissertation is devoted to groups generated by bounded automata and geometric objects related to these groups (limit spaces, Schreier graphs, etc.). It is shown that groups generated by bounded automata are contracting. We introduce the notion of a post-critical set of a finite automaton and prove that the limit space of a contracting self-similar group generated by a finite automaton is post-critically finite (finitely-ramified) if and only if the automaton is bounded. We show that the Schreier graphs on levels of automaton groups can be constructed by an iterative procedure of inflation of graphs. This was used to associate a piecewise linear map of the form fK(v) = minA∈KAv, where K is a finite set of nonnegative matrices, with every bounded automaton. We give an effective criterium for the existence of a strictly positive eigenvector of fK. The existence of nonnegative generalized eigenvectors of fK is proved and used to give an algorithmic way for finding the exponents λmax and λmin of the maximal and minimal growth of the components of f(n) K (v). We prove that the growth exponent of diameters of the Schreier graphs is equal to λmax and the orbital contracting coefficient of the group is equal to 1/λmin . We prove that the simple random walks on orbital Schreier graphs are recurrent. A number of examples are presented to illustrate the developed methods with special attention to iterated monodromy groups of quadratic polynomials. We present the first example of a group whose coefficients λmin and λmax have different values.

This dissertation is devoted to groups generated by bounded automata and geometric objects related to these groups (limit spaces, Schreier graphs, etc.). It is shown that groups generated by bounded automata are contracting. We introduce the notion of a post-critical set of a finite automaton and prove that the limit space of a contracting self-similar group generated by a finite automaton is post-critically finite (finitely-ramified) if and only if the automaton is bounded. We show that the Schreier graphs on levels of automaton groups can be constructed by an iterative procedure of inflation of graphs. This was used to associate a piecewise linear map of the form fK(v) = minA[set]KAv, where K is a finite set of nonnegative matrices, with every bounded automaton. We give an effective criterium for the existence of a strictly positive eigenvector of fK. The existence of nonnegative generalized eigenvectors of fK is proved and used to give an algorithmic way for finding the exponents λmax and λmin of the maximal and minimal growth of the components of fK(n)(v). We prove that the growth exponent of diameters of the Schreier graphs is equal to λmax and the orbital contracting coefficient of the group is equal to 1/λmin . We prove that the simple random walks on orbital Schreier graphs are recurrent. A number of examples are presented to illustrate the developed methods with special attention to iterated monodromy groups of quadratic polynomials. We present the first example of a group whose coefficients λmin and λmax have different values.

There are numerous connections between the theory of formal languages and that of symbolic dynamics. In each, the transition from one dimension to two dimensionsis accompanied by much difficulty due in large part to the emptiness problem, which is related to the presence (or lack thereof) of periodic points and is known to be undecidable. Here, we focus on two-dimensional languages that have the property that all blocks allowed by the language can be extended to a configuration of the plane satisfying the structure of the language; for such languages the emptiness problem is not an issue. We first show that dot systems may be associated with two-dimensional languages having this property, so that we might employ these languages as varied examples. We next define a new type of finite automaton and with it, a tool for recognizing two-dimensional "strings" of data. It is then shown that these automata correctly represent the sofic shift spaces that result from the application of block maps to shifts of finite type. Thereafter, these automataare utilized to investigate properties of transitivity in the two-dimensional languages that they represent. More specifically, new definitions for different types of two-dimensional transitivity are adapted from topological dynamics and then illustrated through the use of dot systems. The appearance of periodic points in the languages represented by these automata is also explored, with a main result being that the existence of a periodic pointis guaranteed under certain conditions. Finally, issues of equivalence are introduced in the two-dimensional setting with regards to formal languages (syntactic monoids) and symbolic dynamics (the follower sets of a graph representing a sofic shift space).

Life expectancy has continuously increased in most countries over the last decades and will probably continue to increase in the future. This leads to new challenges relative to the autonomy and the independence of elderly. The development of Smart Homes is a direction to face these challenges and to enable people to live longer in a safe and comfortable environment. Making a home smart consists in placing sensors, actuators and a controller in the house in order to take into account the behavior of their inhabitants and to act on their environment to improve their safety, health and comfort. Most of these approaches are based on the real-time indoor Location Tracking of the inhabitants. In this thesis, a whole new approach for model-based Location Tracking of an a priori unknown number of inhabitants is proposed. This approach is based on Discrete Event Systems paradigms, theory and tools. The usage of Finite Automata (FA) to model the detectable motion of the inhabitants as well as different methods to create such FA models have been developed. Based on these models, algorithms to perform efficient Location Tracking are defined. Finally, several approaches aiming at evaluating the relevance of the instrumentation of a Smart Home with the objective of Location Tracking are proposed. The approach has also been fully implemented and tested. Throughout the thesis, the different contributions are illustrated on case studies.

Finite automata appear in almost every branch of computer science, for example in model checking, in natural language processing and in database theory. In many applications where finite automata occur, it is highly desirable to deal with automata that are as small as possible, in order to save memory as well as excecution time. Deterministic finite automata (DFAs) can be minimized efficiently, i.e., a DFA can be converted to an equivalent DFA that has a minimal number of states. This is not the case for non-deterministic finite automata (NFAs). To minimize an NFA we need to compute the corresponding DFA using subset construction and minimize the resulting automaton. However, subset construction may lead to an exponential blow-up in the size of the automaton and therefore even if the minimal DFA may be small, it might not be feasible to compute it in practice since we need to perform the expensive subset construction. To aviod subset construction we can reduce the size of an NFA using heuristic methods. This can be done by identifying and collapsing states that are equal with respect to some suitable equivalence relation that preserves the language of the automaton. The choice of an equivalence relation is a trade-off between the desired amount of reduction and the computation time since the coarser a relation is, the more expensive it is to compute. This way we obtain a reduction method for NFAs that is useful in practice. In this thesis we address the problem of reducing the size of non-deterministic automata. We consider two different computation models: finite tree automata and finite automata. Finite automata can be seen as a special case of finite tree automata and all of the previously mentioned results concerning finite automata are applicable to tree automata as well. For non-deterministic bottom-up tree automata, we present a broad spectrum of different relations that can be used to reduce their size. The relations differ in their computational complexity and reduction capabilities. We also provide efficient algorithms to compute the relations where we translate the problem of computing a given relation on a tree automaton to the problem of computing the relation on a finite automaton. For finite automata, we have extended and re-formulated two algorithms for computing bisimulation and simulation on transition systems to operate on finite automata with alphabets. In particular, we consider a model of automata where the labels are encoded symbolically and we provide an algorithm for computing bisimulation on this partial symbolic encoding.

Most of the cryptosystems currently used are based on number theoretic problems. We focus on cryptosystems based on finite automata (FA) which are lightweight in nature and have relatively small key sizes. The security of these systems relies on the difficulties in inverting non-linear finite automata and factoring matrix polynomials. In symmetric or single key encryption, the secret key consists of two finite automata and their inverses. By applying the inverses of the automata to the cipher text, the plain text can be effectively calculated. In case of asymmetric or public key encryption, the public key consists of another automaton, which is the combination of the two finite automata while the private key consists of the inverse of the two individual automata. It is hard to invert the combined automaton without the knowledge of the private key automata. We propose a third variant which is based on a 128-bit key and uses a DES-based key generation algorithm. We implement and test all three cryptosystems - the standard single key and public key cryptosystems as well as our novel DES-based FA cryptosystem. We also extensively test the finite automata cryptosystems on a standard desktop machine as well as the Nokia N900 smartphone. All statistical tests carried out on the ciphertext are satisfactory. / Graduate

Finite automata are an important mathematical abstraction, and in formal verification, they are used for a concise representation of regular languages. Operations often used on finite automata in this setting are testing their universality and language inclusion. \mbox{A naive} approach to implement these operations leads to an explicit determinization of the automata, which can be costly and undesirable. There is, however, a more advanced method for performing those operations, called the Antichains algorithm, which avoids such an explicit determinization. This work shows how finite automata operations can be effectively implemented in Haskell and compares several approaches of their implementation. The obtained results are compared with VATA, an imperative implementation of a finite automata library.