Cryptography using Automata Theory

Encryption and decryption are the two most crucial components of cryptography. Data protection is the main objective of both systems. We utilised encryption to transform plain text into ciphertext. Decryption, which works the other way around from encryption, is the process of converting encrypted text back into plain text. By using a finite state machine and the LU decomposition method, the created encryption solution ensures data secrecy for safe communication. In our suggested approach, we additionally employ lower and upper triangular matrices, which are obtained by decomposing a square matrix. During encryption, the key will be a lower triangular matrix modulated by a prime number, and during decryption, an upper triangular matrix modulated by a prime number. The tactic is beneficial. This tactic is helpful in sectors such as finance and military services where confidential material must be delivered

Difusão Anômala no Jogo da Vida

Dissertação de Mestrado apresentada ao Instituto Latino-Americano de Ciências da Vida e da Natureza da Universidade Federal da Integração Latino-Americana como parte dos requisitos para a obtenção do título de Mestre em Física Aplicada.Autômatos celulares são ferramentas computacionais versáteis, aplicadas em diversos campos multi e interdisciplinares para modelar fenômenos complexos, entre eles a difusão. Dentro deste contexto, o presente estudo dedica-se à análise da difusão no "Jogo da Vida", um modelo de autômato celular desenvolvido por John Horton Conway. Este modelo opera em uma grade de células que podem estar em um de dois estados: 'vivo' ou 'morto'. Utilizando a linguagem Python, implementamos as regras dinâmicas do Jogo da Vida em várias configurações matriciais, com o intuito de conduzir uma análise estatística sobre a distribuição espacial das células vivas e a dinâmica do seu centro de massa em ciclos sucessivos de interação. Além de avaliar métricas como assimetria e curtose, examinamos variáveis associadas ao movimento do centro de massa, como posição, velocidade e aceleração, assim como métricas derivadas, como o deslocamento quadrático médio e autocorrelações. Ao analisar dezoito configurações iniciais em uma rede expansível, identificamos diferentes regimes difusivos a partir do expoente de difusão (α), como subdifusão (02). Os resultados foram contextualizados usando o formalismo de Langevin Generalizado e comparados aos comportamentos assintóticos da função de relaxação, enriquecendo assim a compreensão do teorema de Khinchin

Reversible Computation: Extending Horizons of Computing

This open access State-of-the-Art Survey presents the main recent scientific outcomes in the area of reversible computation, focusing on those that have emerged during COST Action IC1405 "Reversible Computation - Extending Horizons of Computing", a European research network that operated from May 2015 to April 2019. Reversible computation is a new paradigm that extends the traditional forwards-only mode of computation with the ability to execute in reverse, so that computation can run backwards as easily and naturally as forwards. It aims to deliver novel computing devices and software, and to enhance existing systems by equipping them with reversibility. There are many potential applications of reversible computation, including languages and software tools for reliable and recovery-oriented distributed systems and revolutionary reversible logic gates and circuits, but they can only be realized and have lasting effect if conceptual and firm theoretical foundations are established first

Reversible Computation: Extending Horizons of Computing

This open access State-of-the-Art Survey presents the main recent scientific outcomes in the area of reversible computation, focusing on those that have emerged during COST Action IC1405 "Reversible Computation - Extending Horizons of Computing", a European research network that operated from May 2015 to April 2019. Reversible computation is a new paradigm that extends the traditional forwards-only mode of computation with the ability to execute in reverse, so that computation can run backwards as easily and naturally as forwards. It aims to deliver novel computing devices and software, and to enhance existing systems by equipping them with reversibility. There are many potential applications of reversible computation, including languages and software tools for reliable and recovery-oriented distributed systems and revolutionary reversible logic gates and circuits, but they can only be realized and have lasting effect if conceptual and firm theoretical foundations are established first

Mathematical modelling of diffusion processes at the nanoscale

In this thesis we study diffusion processes of nanoparticle evolution and develop appropriate models with the aim of being able to optimise their functions according to the needs of industry. Two distinct diffusion processes are studied in detail throughout this thesis: phase change and atomic interdiffusion. To do this we employ various mathematical techniques. The list includes asymptotic analysis, the Heat Balance Integral Method (HBIM), the opTimal HBIM (TIM), similarity variables, separation of variables and numerical methods. In Chapters 3, 4 and 5 we focus on the phase change problem, also termed the Stefan problem. In Chapter 3 we explore the application of the HBIM to Stefan problems in spherical and cylindrical coordinates. Working with a reduced one-phase model, we use the standard version of this method and one designed to minimise the error. Furthermore, we define coordinate transformations with the aim of improving their accuracy. We compare the results obtained against numerical and perturbation solutions. It is shown that, whilst the results for the cylindrical problem are not excellent, for the spherical case it is possible to obtain highly accurate approximate solutions. In Chapter 4 we present a model for the melting of a spherical nanoparticle that differs from previous ones. This model includes the size dependence of the latent heat and a cooling condition at the boundary. The latent heat variation is modelled by a new relation, which matches experimental data better than previous models. A novel form of Stefan condition is used to determine the position of the melt front. Other features that the model includes are melting point depression and density change in the different phases. For large Stefan numbers we compare the perturbation solution with a numerical one and show that the agreement between them is excellent. Results show faster melting times than previous theoretical models, primarily due to latent heat variation. Chapter 5 links the previous two chapters; we use the optimal exponents found in Chapter 3 in the approximate solution for a simplified one-phase reduction of the model presented in Chapter 4. We study different outer boundary conditions, and then compare the solution given by the TIM with numerical and perturbation solutions for the same problem. Results indicate that the TIM is more accurate than the first order perturbation for all cases studied. In Chapters 6 and 7 we shift our focus to binary diffusion in solids. In Chapter 6 we detail the mechanisms that drive substitutional binary diffusion via vacancy exchange, and derive appropriate governing equations. Our focus is on the one-dimensional case with insulated boundary conditions. We are able to make analytical progress by reducing the expressions for the concentration-dependent diffusion coefficients for different limiting cases related to the ratio of diffusion rates between species. After carrying out an asymptotic analysis of the problem, and obtaining analytical solutions, we compare them against a numerical solution. We find that these reductions are in excellent agreement in the limiting cases. Moreover, they are valid, within 10%, to the general solution. In Chapter 7 we develop a cellular automata (CA) model to study the problem presented in the previous chapter. Using a very simple state of change rule we are able to define an asynchronous CA model that shows excellent agreement when compared to the solution of the continuum model derived in Chapter 6. This is proven further by taking the continuum limit of the CA model presented and showing that the governing equations are the same as the ones rigorously derived before, for one of the limiting cases. This provides us with a new, simple method to study and model binary diffusion in solids. Further, since the computational expense of the CA model increases with the number of cells, this approach is best suited to small materials samples such as nanoparticles.En aquesta tesi estudiem processos de difusió relacionats amb l'evolució de nanopartícules i desenvolupem models amb l'objectiu de ser capaços d'optimitzar les seves funcions d?acord amb les necessitats de la indústria. Estudiarem en detall dos models distingits al llarg d'aquesta tesi: el canvi de fase i la interdifusió atòmica. Per fer-ho, utilitzarem diverses tècniques matemàtiques tals com anàlisi asimptòtica, el Heat Balance Integral Method (HBIM), el opTimal HBIM (TIM), variables de similitud, separació de variables i mètodes numèrics. Als Capítols 3, 4 i 5 ens centrem en el problema de canvi de fase (o problema de Stefan). Al Capítol 3 explorem l'aplicació del HBIM als problemes de Stefan en coordenades esfèriques i cilíndriques. Treballant amb un model reduït d'una fase, utilitzem la versió estàndard d'aquest mètode i una versió dissenyada per minimitzar l'error. A més a més, definim transformacions de coordenades amb l'objectiu de millorar la precisió. Comparem els resultats obtinguts amb solucions numèriques i de pertorbació. Els resultats pel problema cilíndric no són excel·lents; pel cas esfèric és possible obtenir solucions aproximades altament precises. Al Capítol 4 presentem un model diferent als anteriors per descriure la fusió d'una nanopartícula esfèrica. Aquest model inclou una definició de calor latent que depèn de la mida de la nanopartícula i una condició de refredament de Newton a la frontera. Modelem la variació de la calor latent amb una nova relació que coincideix amb dades experimentals millor que models anteriors. Utilitzem una nova condició de Stefan per determinar la posició de la interfície. Altres característiques que inclou el model són la depressió del punt de fusió i canvi de la densitat en les diferents fases. Per nombres de Stefan grans comparem la solució de pertorbació amb una solució numèrica i mostrem que l?acord entre elles és excel·lent. Els resultats mostren temps de fusió més ràpids que en models teòrics previs, principalment degut a la variació de calor latent. Al Capítol 5 enllacem els dos capítols anteriors; utilitzem els exponents òptims que hem trobat al Capítol 3 per la solució aproximada al model reduït i d'una fase del Capítol 4. Estudiem dues condicions de frontera i comparem la solució del mètode TIM amb la solució numèrica i de pertorbació del mateix problema. Els resultats indiquen que el TIM és més precís que la pertorbació de primer ordre per tots els casos estudiats. Als Capítols 6 i 7 ens centrem en la difusió binària en sòlids. Al Capítol 6 detallem els mecanismes que controlen la difusió binària mitjançant intercanvi de vacants, i posteriorment derivem les equacions governants. Ens centrem en el cas unidimensional amb condicions de frontera d'aïllament. Obtenim avenços analítics reduint les expressions dels coeficients de difusió (que depenen de la concentració) per casos límits relacionats amb la ràtio dels índexs de difusió de les dues espècies. Després d'obtenir solucions analítiques mitjançant una anàlisi asimptòtica del problema les comparem amb la solució numèrica. Les reduccions que hem fet al problema concorden de manera excel·lent en els casos límit. A més a més, són vàlides amb un marge d'error del 10% a la solució general del problema. Al Capítol 7 desenvolupem un model autòmat cel·lular (CA, en anglès) per estudiar el problema presentat al capítol anterior. Utilitzant una norma de canvi d'estat simple som capaços de definir un model CA asíncron que mostra un acord excel·lent quan el comparem amb la solució del model continu derivat en el Capítol 6. Prenent el límit continu del model CA observem que les equacions governants que obtenim són les mateixes que les prèviament derivades de manera rigorosa. Obtenim així un mètode nou i simple per estudiar difusió binària en sòlids. A més a més, com que el cost computacional del model CA incrementa amb el nombre de cel·les, aquest enfocament va millor per estudiar mostres de material a la nanoescala.Postprint (published version

Computação evolucionária para indução de regras de autômatos celulares multidimensionais

A cellular automata is a discrete dynamic system that evolves thought interactions of rules and can be applied to solve several complex problems. The task to find the transition rule to solve a problem can be generalized as a problem of rule induction for cellular automata. Several approaches, based on evolutionary computation techniques, have been proposed to solve this problem. However, there is no generic methodology capable of being applied to a large range of problems. The main contribution of this work is a generic methodology for rule induction for cellular automata. This research was done in four steps to achieve this objective. In the first step we evaluated the performance of some dynamic behavior forecasting parameters calculated as function of a transition rule. The obtained results indicated that those parameters can be used in a careful way. This is due to the possibility of obtaining valid, but insatisfactory solutions. We stress the importance of considering reference parameters, which for the majority of real problems, are not available. In the second research step we proposed a new method to forecast the dynamic behavior. This method considers the transition rule and the initial configuration of the cellular automata. We used the qualitative dynamic behavior patterns described by Wolfram as reference to the forecast. This method was efficient for null behavior rules. Since the process of dynamic simulation can have a high computational cost, we developed a third methodology: an architecture based on the concept of hardware/software co-design to accelerate the processing time. This architecture implements the evolution of cellular automata using reconfigurable logic and was able to decrease hundreds of times the processing time. In the fourth step we developed a new parallel architecture based on the master-slave paradigm. In this paradigm, the master process implements the evolutionary algorithm and a set of slaves processes divide the task of validating the obtained rules. The system runs in a cluster with 120 processing cores connected by a local area network. The co-evolutionary strategy based on an insular model allowed the search for high quality solutions. The generic system implemented over a parallel environment was able to solve the problems proposed. A task distribution analyses among several processors emphasized the benefits of parallel processing. The experiments also indicated a set of reference parameters that can be used to configure the system. The contributions of this work were theoretical and methodological. The former refers to the evaluations done and the different methods for dynamic behavior forecasting parameters. The latter is about the development of two architectures for processing.Um autômato celular é um sistema dinâmico discreto que evolui pela iteração de regras. Os valores das variáveis do sistema mudam em função de seus valores correntes. Os autômatos celulares podem ser aplicados na resolução de diversos problemas. A tarefa de encontrar uma regra de transição que solucione um determinado problema pode ser generalizada como um problema de indução de regras para autômatos celulares. Várias abordagens baseadas em técnicas de computação evolucionária vêm sendo empregadas neste problema. No entanto, estas restringem-se a aplicações específicas. A principal contribuição deste trabalho é a proposição de uma metodologia genérica para indução de regras de autômatos celulares. Para alcançar este objetivo a pesquisa foi segmentada em quatro etapas. Na primeira etapa avaliou-se o desempenho de alguns parâmetros de previsão de comportamento calculados em função de regras de transição. Os resultados obtidos nesta etapa indicaram que os parâmetros de previsão de comportamento dinâmico devem ser utilizados de forma criteriosa. Este cuidado reside na possibilidade de se obter soluções válidas, porém, não satisfatórias. Ressalta-se também a necessidade da existência de parâmetros de referência que para a maioria dos problemas reais, não está disponível. Na segunda etapa apresentou-se um novo método para a previsão do comportamento dinâmico. Este método considera a regra de transição e a configuração inicial do autômato celular. Para a previsão utilizou-se como referência os padrões de comportamento dinâmico qualitativos descritos por Wolfram. O método mostrou-se eficiente para regras de comportamento nulo. Como o processo de simulação da dinâmica de um sistema pode ter um custo computacional elevado, desenvolveu-se uma terceira metodologia. Nesta metodologia implementou-se uma arquitetura baseada no conceito de hardware/software co-design com a finalidade de contornar problemas referentes a tempo de processamento. Esta arquitetura realiza a evolução de autômatos celulares utilizando lógica reconfigurável. A arquitetura diminuiu o tempo de processamento por centenas de vezes, mas algumas restrições do modelo, como número limitado de células lógicas e reprogramações do hardware inviabilizaram seu uso. Considerando-se as restrições impostas pela arquitetura implementada, iniciou-se a quarta etapa da pesquisa onde foi desenvolvida uma nova arquitetura paralela fundamentada no paradigma mestre-escravo. Neste paradigma um processo mestre implementa o algoritmo evolucionário e um conjunto de processos escravos dividem a tarefa de validação das regras obtidas. O sistema é executado em um cluster composto por 120 núcleos de processamento que se interligam por meio de uma rede ethernet. A estratégia co-evolucionária baseada em um modelo insular permitiu a busca por soluções que apresentam um melhor valor para função de fitness. O sistema genérico implementado sobre um ambiente paralelo foi capaz de solucionar os problemas abordados. Uma análise de distribuição de tarefas entre vários processadores enfatizou os benefícios do processamento paralelo. Os experimentos também indicaram um conjunto de parâmetros evolucionários de referência que podem ser utilizados para configurar o sistema. As contribuições deste trabalho foram tanto teóricas, com as avaliações realizadas sobre os parâmetros e os diferentes métodos de previsão de comportamento dinâmico, quanto metodológicas, pois desenvolveu-se a proposta de duas arquiteturas de processamento distintas

Situational Awareness Enhancement for Connected and Automated Vehicle Systems

Recent developments in the area of Connected and Automated Vehicles (CAVs) have boosted the interest in Intelligent Transportation Systems (ITSs). While ITS is intended to resolve and mitigate serious traffic issues such as passenger and pedestrian fatalities, accidents, and traffic congestion; these goals are only achievable by vehicles that are fully aware of their situation and surroundings in real-time. Therefore, connected and automated vehicle systems heavily rely on communication technologies to create a real-time map of their surrounding environment and extend their range of situational awareness. In this dissertation, we propose novel approaches to enhance situational awareness, its applications, and effective sharing of information among vehicles.;The communication technology for CAVs is known as vehicle-to-everything (V2x) communication, in which vehicle-to-vehicle (V2V) and vehicle-to-infrastructure (V2I) have been targeted for the first round of deployment based on dedicated short-range communication (DSRC) devices for vehicles and road-side transportation infrastructures. Wireless communication among these entities creates self-organizing networks, known as Vehicular Ad-hoc Networks (VANETs). Due to the mobile, rapidly changing, and intrinsically error-prone nature of VANETs, traditional network architectures are generally unsatisfactory to address VANETs fundamental performance requirements. Therefore, we first investigate imperfections of the vehicular communication channel and propose a new modeling scheme for large-scale and small-scale components of the communication channel in dense vehicular networks. Subsequently, we introduce an innovative method for a joint modeling of the situational awareness and networking components of CAVs in a single framework. Based on these two models, we propose a novel network-aware broadcast protocol for fast broadcasting of information over multiple hops to extend the range of situational awareness. Afterward, motivated by the most common and injury-prone pedestrian crash scenarios, we extend our work by proposing an end-to-end Vehicle-to-Pedestrian (V2P) framework to provide situational awareness and hazard detection for vulnerable road users. Finally, as humans are the most spontaneous and influential entity for transportation systems, we design a learning-based driver behavior model and integrate it into our situational awareness component. Consequently, higher accuracy of situational awareness and overall system performance are achieved by exchange of more useful information