Tesi: "Cellular automata"

1

Collins, Sean. "Interactive cellular automata". Thesis, Lancaster University, 2005. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.435877.

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2

Epperlein, Jeremias. "Topological Conjugacies Between Cellular Automata". Doctoral thesis, Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2017. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-231823.

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We study cellular automata as discrete dynamical systems and in particular investigate under which conditions two cellular automata are topologically conjugate. Based on work of McKinsey, Tarski, Pierce and Head we introduce derivative algebras to study the topological structure of sofic shifts in dimension one. This allows us to classify periodic cellular automata on sofic shifts up to topological conjugacy based on the structure of their periodic points. We also get new conjugacy invariants in the general case. Based on a construction by Hanf and Halmos, we construct a pair of non-homeomorphic subshifts whose disjoint sums with themselves are homeomorphic. From this we can construct two cellular automata on homeomorphic state spaces for which all points have minimal period two, which are, however, not topologically conjugate. We apply our methods to classify the 256 elementary cellular automata with radius one over the binary alphabet up to topological conjugacy. By means of linear algebra over the field with two elements and identities between Fibonacci-polynomials we show that every conjugacy between rule 90 and rule 150 cannot have only a finite number of local rules. Finally, we look at the sequences of finite dynamical systems obtained by restricting cellular automata to spatially periodic points. If these sequences are termwise conjugate, we call the cellular automata conjugate on all tori. We then study the invariants under this notion of isomorphism. By means of an appropriately defined entropy, we can show that surjectivity is such an invariant.

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3

Rakotomalala, Livaniaina Hary. "Network Decontamination Using Cellular Automata". Thesis, Université d'Ottawa / University of Ottawa, 2016. http://hdl.handle.net/10393/34095.

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We consider the problem of decontaminating a network where all nodes are infected by a virus. The decontamination strategy is performed using a Cellular Automata (CA) model in which each node of the network is represented by the automata cell and thus, the network host status is also mapped to the CA state (contaminated, decontaminating, decontaminated). All hosts are assumed to be initially contaminated and the status of each cell is synchronously updated according to a set of local rules, based on the state of its neighbourhood. Our goal is to find the set of local rules that will accomplish the decontamination in an optimal way. The metrics used to define optimality is the minimization of three metrics: the maximum number of decontaminating cells at each step, the required value of the immunity time of each cell and the number of steps to complete the sanitization algorithm. In our research, we explore the designing of these local decontamination rules by refining the concept of the neighbourhood radius of CA with the addition of two new dimensions: Visibility Hop and Contamination Distance. Additionally, a research tool that help us manage our study have been developed.

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4

Weimar, Jorg Richard. "Cellular automata for reactive systems". Doctoral thesis, Universite Libre de Bruxelles, 1995. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/212557.

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5

Deng, Mingyuan. "Programmable cellular automata for cryptosystems". Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp01/MQ39137.pdf.

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6

Serquera, Jaime. "Sound synthesis with cellular automata". Thesis, University of Plymouth, 2012. http://hdl.handle.net/10026.1/1189.

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This thesis reports on new music technology research which investigates the use of cellular automata (CA) for the digital synthesis of dynamic sounds. The research addresses the problem of the sound design limitations of synthesis techniques based on CA. These limitations fundamentally stem from the unpredictable and autonomous nature of these computational models. Therefore, the aim of this thesis is to develop a sound synthesis technique based on CA capable of allowing a sound design process. A critical analysis of previous research in this area will be presented in order to justify that this problem has not been previously solved. Also, it will be discussed why this problem is worthwhile to solve. In order to achieve such aim, a novel approach is proposed which considers the output of CA as digital signals and uses DSP procedures to analyse them. This approach opens a large variety of possibilities for better understanding the self-organization process of CA with a view to identifying not only mapping possibilities for making the synthesis of sounds possible, but also control possibilities which enable a sound design process. As a result of this approach, this thesis presents a technique called Histogram Mapping Synthesis (HMS), which is based on the statistical analysis of CA evolutions by histogram measurements. HMS will be studied with four different automatons, and a considerable number of control mechanisms will be presented. These will show that HMS enables a reasonable sound design process. With these control mechanisms it is possible to design and produce in a predictable and controllable manner a variety of timbres. Some of these timbres are imitations of sounds produced by acoustic means and others are novel. All the sounds obtained present dynamic features and many of them, including some of those that are novel, retain important characteristics of sounds produced by acoustic means.

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7

Powley, Edward Jack. "Global properties of cellular automata". Thesis, University of York, 2009. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.516655.

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8

Clewlow, Les. "Cellular automata and dynamical systems". Thesis, University of Warwick, 1989. http://wrap.warwick.ac.uk/4233/.

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In this thesis we investigate the theoretical nature of the mathematical structures termed cellular automata. Chapter 1: Reviews the origin and history of cellular automata in order to place the current work into context. Chapter 2: Develops a cellular automata framework which contains the main aspects of cellular automata structure which have appeared in the literature. We present a scheme for specifying the cellular automata rules for this general model and present six examples of cellular automata within the model. Chapter 3: Here we develop a statistical mechanical model of cellular automata behaviour. We consider the relationship between variations within the model and their relationship to dynamical systems. We obtain results on the variance of the state changes, scaling of the cellular automata lattice, the equivalence of noise, spatial mixing of the lattice states and entropy, synchronous and asynchronous cellular automata and the equivalence of the rule probability and the time step of a discrete approximation to a dynamical system. Chapter 4: This contains an empirical comparison of cellular automata within our general framework and the statistical mechanical model. We obtain results on the transition from limit cycle to limit point behaviour as the rule probabilities are decreased. We also discuss failures of the statistical mechanical model due to failure of the assumptions behind it. Chapter 5: Here a practical application of the preceding work to population genetics is presented. We study this in the context of some established population models and show it may be most useful in the field of epidemiology. Further generalisations of the statistical mechanical and cellular automata models allow the modelling of more complex population models and mobile populations of organisms. Chapter 6: Reviews the results obtained in the context of the open questions introduced in Chapter 1. We also consider further questions this work raises and make some general comments on how these may apply to related fields.

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9

Slotta, Douglas J. "Structural Design Using Cellular Automata". Thesis, Virginia Tech, 2001. http://hdl.handle.net/10919/33368.

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Traditional parallel methods for structural design do not scale well. This thesis discusses the application of massively scalable cellular automata (CA) techniques to structural design. There are two sets of CA rules, one used to propagate stresses and strains, and one to perform design analysis. These rules can be applied serially, periodically, or concurrently, and Jacobi or Gauss-Seidel style updating can be done. These options are compared with respect to convergence, speed, and stability.
Master of Science

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10

Betel, Heather. "Properties and Behaviours of Fuzzy Cellular Automata". Thèse, Université d'Ottawa / University of Ottawa, 2012. http://hdl.handle.net/10393/22858.

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Cellular automata are systems of interconnected cells which are discrete in space, time and state. Cell states are updated synchronously according to a local rule which is dependent upon the current state of the given cell and those of its neighbours in a pre-defined neighbourhood. The local rule is common to all cells. Fuzzy cellular automata extend this notion to systems which are discrete in space and time but not state. In this thesis, we explore fuzzy cellular automata which are created from the extension of Boolean rules in disjunctive normal form to continuous functions. Motivated by recent results on the classification of these rules from empirical evidence, we set out first to show that fuzzy cellular automata can shed some light on classical cellular automata and then to prove that the observed results are mathematically correct. The main results of this thesis can be divided into two categories. We first investigate the links between fuzzy cellular automata and their Boolean counter-parts. We prove that number conservation is preserved by this transformation. We further show that Boolean additive cellular automata have a definable property in their fuzzy form which we call self-oscillation. We then give a probabilistic interpretation of fuzzy cellular automata and show that homogeneous asymptotic states are equivalent to mean field approximations of Boolean cellular automata. We then turn our attention the asymptotic behaviour of fuzzy cellular automata. In the second half of the thesis we investigate the observed behaviours of the fuzzy cellular automata derived from balanced Boolean rules. We show that the empirical results of asymptotic behaviour are correct. In fuzzy form, the balanced rules can be categorized as one of three types: weighted average rules, self-averaging rules, and local majority rules. Each type is analyzed in a variety of ways using a range of tools to explain their behaviours.

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11

Louis, Pierre-Yves. "Increasing coupling for probabilistic cellular automata". Universität Potsdam, 2005. http://opus.kobv.de/ubp/volltexte/2006/659/.

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We give a necessary and sufficient condition for the existence of an increasing coupling of N (N >= 2) synchronous dynamics on S-Zd (PCA). Increasing means the coupling preserves stochastic ordering. We first present our main construction theorem in the case where S is totally ordered; applications to attractive PCAs are given. When S is only partially ordered, we show on two examples that a coupling of more than two synchronous dynamics may not exist. We also prove an extension of our main result for a particular class of partially ordered spaces.

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12

Herr, Christiane Margerita. "From form generators to automated diagrams using cellular automata to support architectural design /". Thesis, Click to view the E-thesis via HKUTO, 2008. http://sunzi.lib.hku.hk/hkuto/record/B39848954.

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13

Louis, Pierre-Yves. "Increasing Coupling of Probabilistic Cellular Automata". Universität Potsdam, 2004. http://opus.kobv.de/ubp/volltexte/2011/5157/.

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Abstract (sommario):

We give a necessary and sufficient condition for the existence of an increasing coupling of N (N >= 2) synchronous dynamics on S-Zd (PCA). Increasing means the coupling preserves stochastic ordering. We first present our main construction theorem in the case where S is totally ordered; applications to attractive PCAs are given. When S is only partially ordered, we show on two examples that a coupling of more than two synchronous dynamics may not exist. We also prove an extension of our main result for a particular class of partially ordered spaces.

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14

Bolduc, Jean-Sebastien. "Cellular-automata based nonlinear adaptive controllers". Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape10/PQDD_0002/MQ44128.pdf.

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15

Weimar, Jörg Richard. "Cellular automata models for excitable media /". This resource online, 1991. http://scholar.lib.vt.edu/theses/available/etd-03032009-040651/.

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16

Bolduc, Jean-Sébastien. "Cellular-automata based nonlinear adaptive controllers". Thesis, McGill University, 1998. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=20804.

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An analytical approach is obviously practical only when we want to study nonlinear systems of low complexity. An alternative for more complex processes that has raised a lot of interest in recent years relies on Artificial Neural Networks (ANNs).
In this work we will explore an alternative avenue to the problems of control and identification, where Cellular Automata (CAs) will be considered in place of ANNs. CAs not only share ANNs' most valuable characteristics but they also have interesting characteristics of their own, for a structurally simpler architecture. CAs applications so far have been mainly restrained to simulating natural phenomena occuring in a finite homogeneous space.
Concepts relevant to the problems of control and identification will be introduced in the first part of our work. CAs will then be introduced, with a discussion of the issues raised by their application in the context, A working prototype of a CA-based controller is introduced in the last part of the work, that confirms the interest of using CAs to address the problem of nonlinear adaptive control. (Abstract shortened by UMI.)

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17

Smith, Mark Andrew. "Cellular automata methods in mathematical physics". Thesis, Massachusetts Institute of Technology, 1994. http://hdl.handle.net/1721.1/33501.

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18

Weimar, JÃ¶rg Richard. "Cellular automata models for excitable media". Thesis, Virginia Tech, 1991. http://hdl.handle.net/10919/41365.

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A cellular automaton is developed for simulating excitable media. First, general "masks" as discrete approximations to the diffusion equation are examined, showing how to calculate the diffusion coefficient from the elements of the mask. The mask is then combined with a thresholding operation to simulate the propagation of waves (shock fronts) in excitable media, showing that (for well-chosen masks) the waves obey a linear "speedcurvature" relation with slope given by the predicted diffusion coefficient. The utility of different masks in terms of computational efficiency and adherence to a linear speed-curvature relation is assessed. Then, a cellular automaton model for wave propagation in reaction diffusion systems is constructed based on these "masks" for the diffusion component and on singular perturbation analysis for the reaction component. The cellular automaton is used to model spiral waves in the Belousov-Zhabotinskii reaction. The behavior of the spiral waves and the movement of the spiral tip are analyzed. By comparing these results to solutions of the Oregonator PDE model, the automaton is shown to be a useful and efficient replacement for the standard numerical solution of the PDE's.

Master of Science

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19

Hopman, Ryan. "Aribitrary geometry cellular automata for elastodynamics". Thesis, Atlanta, Ga. : Georgia Institute of Technology, 2009. http://hdl.handle.net/1853/29742.

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Thesis (M. S.)--Mechanical Engineering, Georgia Institute of Technology, 2010.
Committee Chair: Dr. Michael Leamy; Committee Member: Dr. Karim Sabra; Committee Member: Dr. Aldo Ferri. Part of the SMARTech Electronic Thesis and Dissertation Collection.

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20

CAPOBIANCO, Silvio. "Structure and invertibility in cellular automata". Doctoral thesis, La Sapienza, 2005. http://hdl.handle.net/11573/917108.

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21

Forrester, David M. "Fuzzy Cellular Automata in Conjunctive Normal Form". Thèse, Université d'Ottawa / University of Ottawa, 2011. http://hdl.handle.net/10393/19987.

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Cellular automata (CA) are discrete dynamical systems comprised of a lattice of finite-state cells. At each time step, each cell updates its state as a function of the previous state of itself and its neighbours. Fuzzy cellular automata (FCA) are a real-valued extension of Boolean cellular automata which "fuzzifies" Boolean logic in the transition function using real values between zero and one (inclusive). To date, FCA have only been studied in disjunctive normal form (DNF). In this thesis, we study FCA in conjunctive normal form (CNF). We classify FCA in CNF both analytically and empirically. We compare these classes to their DNF counterparts. We prove that certain FCA exhibit chaos in CNF, in contrast to the periodic behaviours of DNF FCA. We also briefly explore five different forms of fuzzy logic, and suggest further study. In support of this research, we introduce novel methods of simulating and visualizing FCA.

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22

Alvandipour, Mehrdad. "Cellular Automata, Game of Life and Chance". Thesis, Southern Illinois University at Edwardsville, 2017. http://pqdtopen.proquest.com/#viewpdf?dispub=10615332.

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Cellular automata (CA) is shortly reviewed and different approaches to CAs are introduced, while the major focus is put on the Game of Life (GoL). While the GoL has deterministic rules, we suggest a method to make the game stochastic. An analysis of the new stochastic game is studied which focuses on a macroscopic characteristic of the field, the population density. The stochastic game is simulated with various different rules to compare the exact results with the analysis. The applicability of Markov chains and Markov random fields to such games is also studied briefly, while the final chapter of our work consists of a stochastic game inside a finite grid which is modeled by Markov chains. The structure of the states, the transition probabilities and other aspects of the model is both analyzed and simulated. And finally relevant directions to expand this study is suggested.

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23

Ratitch, Bohdana. "Continuous function identification with fuzzy cellular automata". Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape10/PQDD_0006/MQ44255.pdf.

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24

Testa, Joseph S. "Investigations of cellular automata-based stream ciphers /". Online version of thesis, 2008. http://hdl.handle.net/1850/7897.

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25

Waage, Aleksander Lunøe. "Discrete Tranformation of Output in Cellular Automata". Thesis, Norges teknisk-naturvitenskapelige universitet, Institutt for datateknikk og informasjonsvitenskap, 2012. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-22963.

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Cellular automata (CA) is an example of cellular computing: large numbers of simple components, no central control, and limited communication among components. A CA consists of an array of cells, each in one of a finite number of possible states. The cells are updated synchronously in discrete time steps, according to a local, identical interaction rule. CA have been studied for years due to their architectural simplicity and the wide spectrum of behaviors. It can be difficult to design CA to exhibit a specific behavior, and there is no programming paradigm for implementing parallel computations in CA. This makes CA a prime candidate for adaptive programming methods such as evolutionary algorithms (EA). EA have been successfully used to evolve CA to perform computations, such as the majority problem. In problem solving like this, CA are treated as input-output systems and evolved to visit certain states given certain initial states. The n-th state of a CA is commonly treated as its output, such that one input gives one output.In this report a way to transform the output of CA such that multiple outputs emerge is investigated. The evolution of transformed CA is also investigated. Useful applications of this include controlling multi-variable systems such as a pole balancing system.The transformation process was tested in the elementary and 3-state rule spaces. Evolution of transformed CA was successful in the elementary rule space. This suggests there is a correlation between rules of CA and their transformed output. The evolution of transformed CA was unsuccessful in the 3-state rule space. This suggests the chosen evolutionary algorithm doesn't scale with the size of the rule space.

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26

Jones, David Huw. "Design and application of convergent cellular automata". Thesis, Durham University, 2009. http://etheses.dur.ac.uk/84/.

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Systems made of many interacting elements may display unanticipated emergent properties. A system for which the desired properties are the same as those which emerge will be inherently robust. Currently available techniques for designing emergent properties are prohibitively costly for all but the simplest systems. The self-assembly of biological cells into tissues and ultimately organisms is an example of a natural dynamic distributed system of which the primary emergent behaviour is a fully operational being. The distributed process that co-ordinates this self-assembly is morphogenesis. By analysing morphogenesis with a cellular automata model we deduce a means by which this self-organisation might be achieved. This mechanism is then adapted to the design of self-organising patterns, reliable electronic systems and self-assembling systems. The limitations of the design algorithm are analysed, as is a means to overcome them. The cost of this algorithm is discussed and finally demonstrated with the design of a reliable arithmetic logic unit and a self-assembling, self-repairing and metamorphosising robot made of 12,000 cells.

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27

McIlhatton, David. "Spatial planning : cellular automata urban growth modelling". Thesis, University of Ulster, 2010. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.523107.

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28

Xu, Hao, e 許浩. "On the computational ability of cellular automata". Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2002. http://hub.hku.hk/bib/B31226942.

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29

Kim, Bokhwan. "Modelling new city growth using cellular automata". Thesis, University of Leeds, 2005. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.423002.

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30

Dow, R. A. "Algebraic methods for finite linear cellular automata". Thesis, Queen Mary, University of London, 1996. http://qmro.qmul.ac.uk/xmlui/handle/123456789/1647.

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Cellular automata are a simple class of extended dynamical systems which have been much studied in recent years. Linear cellular automata are the class of cellular automata most amenable to algebraic analytic treatments, algebraic techniques are used to study finite linear cellular automata and also finite linear cellular automata with external inputs. General results are developed for state alphabet a finite commutative ring and a notion of qualitative dynamical similarity is introduced for those systems consisting of a fixed linear cellular automata rule but with distinct time independent inputs. Sufficient conditions for qualitative dynamical similarity are obtained in the general case. Exact results are obtained for the case of state alphabet a finite field, including new results for finite linear cellular automata without inputs and a complete description of the behaviour of the corresponding system with time independent inputs. Necessary and sufficient conditions for qualitative dynamical similarity in this case are given. Results for the hitherto untreated case of state alphabet the integers modulo pk, p prime and k>1, are obtained from those for the finite field case by the technique of idempotent lifting. These two cases suffice for the treatment of the general case of st, ),t e alphabet the integers modulo any positive integer m>1, in particular a necessary and sufficient condition for qualitatively similar dynamics in the presence of time independent inputs is given for this case. The extension of the results for time independent inputs to the case of periodic and eventually periodic inputs is treated and the generalisation of the techniques developed to higher dimensional linear cellular automata is discussed.

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31

Agin, Ruben. "Logic simulation on a cellular automata machine". Thesis, Massachusetts Institute of Technology, 1997. http://hdl.handle.net/1721.1/43474.

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32

Demontis, Pierfranco, Federico G. Pazzona e Giuseppe B. Suffritti. "Cellular automata modeling of diffusion under confinement". Universitätsbibliothek Leipzig, 2016. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-193309.

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33

Adams, Roxane. "Implementation of cell clustering in cellular automata". Thesis, Stellenbosch : University of Stellenbosch, 2011. http://hdl.handle.net/10019.1/6674.

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Thesis (MSc (Mathematical Sciences)) University of Stellenbosch, 2011.
ENGLISH ABSTRACT: Cellular Automata (CA) have become a popular vehicle to study complex dynamical behaviour of systems. CA can be used to model a wide variety of physical, biological, chemical and other systems. Such systems typically consist of subparts that change their state independently, based on the state of their immediate surroundings and some generally shared laws of change. When the CA approach was used to solve the LEGO construction problem, the best solution was found when using a variant of CA allowing for the clustering of cells. The LEGO construction problem concerns the optimal layout of a set of LEGO bricks. The advantages found for using the CA method with clustering in this case are the ease of implementation, the significantly smaller memory usage to previously implemented methods, and its trivial extension to construct multicoloured LEGO sculptures which were previously too complex to construct. In our research we propose to explore the definitions of clustering in CA and investigate the implementation and application of this method. We look at the ant sorting method described by Lumer and Faieta, and compare the implementation of this algorithm using regular CA as well as the clustering variation. The ant sorting model is a simple model, in which ants move randomly in space and pick up and deposit objects on the basis of local information.
AFRIKAANSE OPSOMMING: Sellulêre Outomate (SO) het ’n populêre metode geword om die komplekse dinamiese gedrag van sisteme bestudeer. SO kan gebruik word om ’n groot verskeidenheid fisiese, biologiese, chemiese en ander tipe sisteme te modelleer. Sulke sisteme bestaan tipies uit subafdelings wat, gebaseer op die status van hulle omgewing en ’n paar algemene gedeelde reëls van verandering, hulle status onafhanklik verander. Met die gebruik van die SO benadering om the LEGO konstruksieprobleem op te los, is die beste oplossing bereik deur gebruik te maak van ’n variant van SO, waar selle saamgroepeer kan word. Die LEGO konstruksieprobleem behels die optimale uitleg van ’n stel LEGO blokkies. In hierdie geval is die voordele van die SO met sel groepering die maklike implementasie, ’n beduidende kleiner geheuegebruik teenoor voorheen geïmplementeerde metodes, en die triviale uitbreiding daarvan om gekleurde LEGO beelde wat voorheen te kompleks was, te kan bou. In ons ondersoek verken ons die definisies van selgroepering in SO en ondersoek die implementasie en toepassing van die metode. Ons kyk na die miersorteringsmetode beskryf deur Lumer en Faieta, en vergelyk die implementasie van hierdie algoritme deur gewone SO asook die groeperingsvariasie te gebruik. Die miersorteringsmodel is ’n eenvoudige model waarin miere lukraak in ’n omgewing beweeg en voorwerpe optel of neersit volgens plaaslike inligting.

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34

Demontis, Pierfranco, Federico G. Pazzona e Giuseppe B. Suffritti. "Cellular automata modeling of diffusion under confinement". Diffusion fundamentals 6 (2007) 13, S. 1-2, 2007. https://ul.qucosa.de/id/qucosa%3A14187.

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35

Srivastava, Saket. "Probabilistic modeling of quantum-dot cellular automata". [Tampa, Fla.] : University of South Florida, 2007. http://purl.fcla.edu/usf/dc/et/SFE0002399.

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36

Castro, Antonio Paulo. "Dynamic water quality modeling using cellular automata". Diss., This resource online, 1996. http://scholar.lib.vt.edu/theses/available/etd-06062008-151210/.

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37

Xu, Hao. "On the computational ability of cellular automata /". Hong Kong : University of Hong Kong, 2002. http://sunzi.lib.hku.hk/hkuto/record.jsp?B25155088.

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38

Weeks, Andrew. "Neutral emergence and coarse graining cellular automata". Thesis, University of York, 2010. http://etheses.whiterose.ac.uk/2256/.

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Emergent systems are often thought of as special, and are often linked to desirable properties like robustness, fault tolerance and adaptability. But, though not well understood, emergence is not a magical, unfathomable property. We introduce neutral emergence as a new way to explore emergent phenomena, showing that being good enough, enough of the time may actually yield more robust solutions more quickly. We then use cellular automata as a substrate to investigate emergence, and find they are capable of exhibiting emergent phenomena through coarse graining. Coarse graining shows us that emergence is a relative concept - while some models may be more useful, there is no correct emergent model - and that emergence is lossy, mapping the high level model to a subset of the low level behaviour. We develop a method of quantifying the 'goodness' of a coarse graining (and the quality of the emergent model) and use this to find emergent models - and, later, the emergent models we want - automatically.

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39

Cenek, Martin. "Information Processing in Two-Dimensional Cellular Automata". PDXScholar, 2011. https://pdxscholar.library.pdx.edu/open_access_etds/275.

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Cellular automata (CA) have been widely used as idealized models of spatially-extended dynamical systems and as models of massively parallel distributed computation devices. Despite their wide range of applications and the fact that CA are capable of universal computation (under particular constraints), the full potential of these models is unrealized to-date. This is for two reasons: (1) the absence of a programming paradigm to control these models to solve a given problem and (2) the lack of understanding of how these models compute a given task. This work addresses the notion of computation in two-dimensional cellular automata. Solutions using a decentralized parallel model of computation require information processing on a global level. CA have been used to solve the so-called density (or majority) classification task that requires a system-wide coordination of cells. To better understand and challenge the ability of CA to solve problems, I define, solve, and analyze novel tasks that require solutions with global information processing mechanisms. The ability of CA to perform parallel, collective computation is attributed to the complex pattern-forming system behavior. I further develop the computational mechanics framework to study the mechanism of collective computation in two-dimensional cellular automata. I define several approaches to automatically identify the spatiotemporal structures with information content. Finally, I demonstrate why an accurate model of information processing in two-dimensional cellular automata cannot be constructed from the space-time behavior of these structures.

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40

di, Lena Pietro <1977&gt. "Decidable and computational properties of cellular automata". Doctoral thesis, Alma Mater Studiorum - Università di Bologna, 2007. http://amsdottorato.unibo.it/371/1/dilena.pdf.

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41

di, Lena Pietro <1977&gt. "Decidable and computational properties of cellular automata". Doctoral thesis, Alma Mater Studiorum - Università di Bologna, 2007. http://amsdottorato.unibo.it/371/.

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42

BONOMI, ANDREA. "Dissipative multilayered cellular automata facing adaptive lighting". Doctoral thesis, Università degli Studi di Milano-Bicocca, 2010. http://hdl.handle.net/10281/7822.

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Cellular Automata have been primarily investigated as a theoretical model and as a method for simulation and modeling of complex system. CA are also an abstract and formal model of the cellular systems, a wide class of systems present in nature. h systems are composed of several cells acting with a certain degree of independence. The collective behavior is the result of the local interactions. The rationale of this work is to exploit this kind of self-organizing behavior present in biological systems to model, design and realize Distributed Control Systems. Adaptive Lighting is one of the paradigmatic examples of applications that cannot be always controlled in a comfortable way with a centralized control system

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MARIOT, LUCA. "Cellular Automata, Boolean Functions and Combinatorial Designs". Doctoral thesis, Università degli Studi di Milano-Bicocca, 2018. http://hdl.handle.net/10281/199011.

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Lo scopo di questa tesi è studiaregli Automi Cellulari (AC) dalla prospettiva delle funzioni booleane e dei disegni combinatorici. Oltre all'intrinseco interesse teorico, questa ricerca è motivata da applicazioni alla crittografia, dato che sia le funzioni booleane che i disegni combinatorici sono utilizzati nella progettazione di generatori di numeri pseudocasuali (Pseudorandom Number Generators}, PRNG) e degli schemi di condivisione di segreti (Secret Sharing Schemes, SSS). I contributi della tesi sono stati sviluppati lungo tre linee di ricerca, di seguito descritte. La prima linea di ricerca riguarda l'utilizzo di algoritmi di ottimizzazione euristica per cercare funzioni booleane aventi buone proprietà crittografiche, da impiegare come regole locali nei PRNG basati su AC. La motivazione principale di questo studio è il miglioramento del generatore di Wolfram, che è stato dimostrato essere vulnerabile a due attacchi crittoanalitici, a causa delle cattive proprietà crittografiche della regola 30. In primo luogo, in questa linea di ricerca viene sviluppata una versione discreta di un Particle Swarm Optimizer (PSO), che esplora lo spazio delle tabelle di verità di funzioni booleane bilanciate aventi una buona combinazione di nonlinearità, ordine di resilienza e criterio di propagazione. In seguito, viene proposto un Algoritmo Genetico (Genetic Algorithm}, GA) basato su una rappresentazione differente delle funzioni booleane, in particolare il loro spettro di Walsh. La seconda linea di ricerca si occupa delle funzioni booleane vettoriali generate dalle regole globali degli AC. Il primo contributo in questa linea di ricerca considera il periodo delle preimmagini di configurazioni spazialmente periodiche sotto l'azione di un AC suriettivo, un problema che è collegato al numero di partecipanti di un SSS basato sugli AC pubblicato in letteratura. Il secondo contributo consiste nell'analisi delle proprietà crittografiche delle regole globali degli AC, con particolare riguardo al loro grado algebrico, nonlinearità e uniformità differenziale. Viene in seguito adottato un approccio euristico basato sulla Programmazione Genetica (Genetic Programming, GP) per ottimizzare le \emph{S-box} definite da AC con una buona nonlinearità e uniformità differenziale. Infine, viene considerato l'ordine di resilienza} e introdotta una nuova proprietà crittografica per le S-box generate da AC, l'immunità all'asincronia. La terza linea di ricerca riguarda i disegni combinatorici generati tramite AC. Più precisamente, viene considerato il caso dei Quadrati Latini Ortogonali} (Orthogonal Latin Squares, OLS), poiché sono equivalenti ai codici di autenticazione perfetti e agli schemi di condivisione dei segreti a soglia. Il primo contributo in questa linea di ricerca concerne la costruzione e il conteggio degli OLS generati da AC lineari, basandosi su risultati della teoria dei campi finiti. Il secondo contributo, d'altro canto, generalizza questa analisi a OLS generati da AC nonlineari, sia attraverso un metodo combinatorico per l'enumerazione esaustiva, sia tramite un approccio euristico basato su GA e GP.
The goal of this thesis is to investigate Cellular Automata (CA) from the perspective of Boolean functions and combinatorial designs. Besides the inherent theoretical interest, this research also bases its motivation in cryptography, since Boolean functions and combinatorial designs have several applications in the design of Pseudorandom Number Generators (PRNG) and Secret Sharing Schemes (SSS). The contributions presented in this thesis are developed along three main research lines, organized as follows. The first research line concerns the use of heuristic optimization algorithms for designing Boolean functions with good cryptographic properties, to be used as local rules in CA-based PRNG. The main motivation is to improve Wolfram's pseudorandom generator, which has been shown to be vulnerable to two cryptanalytic attacks due to the poor cryptographic properties of rule 30. In this research line, we first develop a discrete Particle Swarm Optimizer (PSO) which explores the space of truth tables of balanced Boolean functions having good nonlinearity, resiliency and propagation criteria. Next, we design a Genetic Algorithm (GA) which works on a different representation of Boolean functions, namely their Walsh spectrum. The second research line deals with vectorial Boolean functions generated by CA global rules. The first contribution investigates the period of preimages of spatially periodic configurations under the action of surjective CA, a problem which is related to the maximum number of players in a CA-based SSS already published in the literature. The second contribution analyzes the cryptographic properties of CA global rules, focusing on their algebraic degree, nonlinearity and differential uniformity. We then adopt a heuristic approach based on Genetic Programming (GP) to evolve S-boxes defined by CA with nonlinearity and differential uniformity. As a last contribution in this research line, we focus on the resiliency criterion and introduce a new cryptographic property for CA-based S-boxes, namely asynchrony immunity. The third research line deals with combinatorial designs generated by CA. We specifically focus on the case of Orthogonal Latin Squares (OLS), since they are equivalent to perfect authentication codes and threshold secret sharing schemes. To this end, our first contribution in this research line concerns the construction and the enumeration of OLS generated through linear CA, leveraging on results from the theory of finite fields. The second contribution, on the other hand, extends the investigation to OLS generated by nonlinear CA, using both a combinatorial approach for exhaustive enumeration and a heuristic approach based on GA and GP.

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Eon, Nathanaël. "Gauge invariance in classical and quantum cellular automata". Electronic Thesis or Diss., Aix-Marseille, 2022. http://www.theses.fr/2022AIXM0281.

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L'invariance de jauge est un concept fondamental en physique, servant de fondement mathématique à la dérivation des interactions fondamentales. Dans cette thèse, la notion d'invariance de jauge est formalisée dans le cadre des automates cellulaires (AC).Cette formalisation offre un chemin simple et direct vers les concepts essentiels de la symétrie de jauge. Usuellement, une symétrie de jauge est tout d'abord motivée par l'existence d'une symétrie globale. La théorie est ensuite étendue de sorte que cette symétrie devienne locale. Les AC permettent de formaliser ce processus d'extension de jauge. Nous montrons dans cette thèse l'équivalence entre l'existence d'une symétrie globale et l'existence d'une extension de jauge dite "relative". L'universalité des AC invariants de jauge est ensuite démontrée.Dans le cadre des automates cellulaires quantiques, nous utilisons ici l'invariance de jauge pour parvenir à une formulation en espace-temps discret de l'électrodynamique quantique (EDQ) en trois dimensions d'espace. Elle prend la forme d'un circuit quantique, se répétant à l'infini dans l'espace et le temps, paramétré par un pas de discrétisation relativiste \Delta_t=\Delta_x. Cette construction suit la logique qui amène à la définition du Lagrangien pour l'EDQ. C'est-à-dire qu'elle démarre par une marche quantique de Dirac, dont la convergence vers des fermions relativistes libres est connue. Puis cette marche est étendue au cas multi-particules à travers un automate cellulaire quantique de sorte que les relations d'anti-commutation des fermions et l'invariance de jauge soient respectées. Finalement, une dynamique électromagnétique est donnée au champ de jauge
Gauge invariance is a fundamental concept in Physics, known to provide mathematical justification for the fundamental forces. In this thesis, gauge invariance is brought to the realm of classical and quantum cellular automata (CA). In a classical setting, it provides a simple yet rigorous route straight to the core concepts of gauge theories. Usually, gauge theories are built from a theory featuring a global symmetry, which is then extended to make the symmetry a local one (a.k.a. gauge-invariant). CA allows for this gauge extension process to be made formal. We show the equivalence between the pre-existence of a global symmetry and the ability to perform a "relative" gauge extension. Moreover, gauge invariant cellular automata are shown to be universal. In the framework of quantum cellular automata (QCA), we use gauge invariance to construct a discrete spacetime formulation of 3+1 quantum electrodynamics (QED). It takes the form of a quantum circuit, infinitely repeating across space and time, parameterized by the relativistic discretization step \Delta_t=\Delta_x. The construction replays the logic that leads to the QED Lagrangian. Namely, it starts from the Dirac quantum walk, well-known to converge towards free relativistic fermions. It then extends the quantum walk into a multi-particle sector quantum cellular automata in a way which respects the fermionic anti-commutation relations and the discrete gauge invariance symmetry. Lastly the gauge field is given its own electromagnetic dynamics

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Weston, James. "Cellular Automata Based Binary Arithmetic Implemented Within A Fault Tolerant Cellular Architecture". Thesis, University of Kent, 2008. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.499644.

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Fransson, Linnea. "Monomial Cellular Automata : A number theoretical study on two-dimensional cellular automata in the von Neumann neighbourhood over commutative semigroups". Thesis, Linnéuniversitetet, Institutionen för matematik (MA), 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-51865.

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In this report, we present some of the results achieved by investigating two-dimensional monomial cellular automata modulo m, where m is a non-zero positive integer. Throughout the experiments, we work with the von Neumann neighbourhood and apply the same local rule based on modular multiplication. The purpose of the study is to examine the behaviour of these cellular automata in three different environments, (i.e. the infinite plane, the finite plane and the torus), by means of elementary number theory. We notice how the distance between each pair of cells with state 0 influences the evolution of the automaton and the convergence of its configurations. Similar impact is perceived when the cells attain the values of Euler's- $\phi$ function or of integers with common divisors with m, when m > 2. Alongside with the states of the cells, the evolution of the automaton, as well as the convergence of its configurations, are also decided by the values attributed to m, whether it is a prime, a prime power or a multiple of primes and/or prime powers.

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甄冠僑 e Koon-kiu Yan. "Phase transition of certain iterative cellular automation models". Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1999. http://hub.hku.hk/bib/B42575382.

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Yan, Koon-kiu. "Phase transition of certain iterative cellular automation models". Click to view the E-thesis via HKUTO, 1999. http://sunzi.lib.hku.hk/hkuto/record/B42575382.

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Dridi, Sara. "Recent advances in regional controllability of cellular automata". Doctoral thesis, Perpignan, 2019. http://hdl.handle.net/2158/1181181.

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The issue addressed in this thesis concerns the controllability of a class of dis- crete spatio-temporal systems named cellular automata (CA). The purpose of this study is to highlight new ways to prove the controllability of complex systems. More specifically, this thesis focuses on regional controllability which consists in restricting the study to a subregion of the domain where the system will have to achieve a given objective through targeted actions. The case of Boolean CA have been particularly examined throughout this thesis. The first part is devoted to the study of the prob- lem of the regional controllability of deterministic CAs when the actions are exerted on the boundaries of the controlled region. A first approach that we used relies on Markov chains and controllability is characterized by establishing a matrix similar to their transition matrix using the definitions of a regular and ergodic chain. This study has been extended to the case of probabilistic CAs that are widely used to model many real phenomena. The same problem has been apprehended using tools of graph theory. We propose necessary and sufficient conditions for the regional controllability of deterministic CAs using the notions of Hamiltonian circuit and strongly connected component. The control that ensures regional controllability is defined through a preimage algo- rithm. The second part is devoted to the problem of the boundary regional controllability of Boolean CAs, which consists of acting on the boundary of the domain in order to reach a desired goal in a target region. We first consider linear CAs for which we give a characterization result using the Kalman condition. We propose an algorithm to determine the control that allows to force the appearance of a desired configuration in the study area. The case of nonlinear CAs was also considered using a preimage search algorithm.

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Li, Gang. "Anisotropic wet etch simulation using vector cellular automata". Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1999. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp01/MQ39675.pdf.

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Tesi sul tema "Cellular automata"

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