Cellular Automata And Groups
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Cellular Automata And Groups
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Author : Tullio Ceccherini-Silberstein
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-08-24
Cellular Automata And Groups written by Tullio Ceccherini-Silberstein and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-08-24 with Computers categories.
Cellular automata were introduced in the first half of the last century by John von Neumann who used them as theoretical models for self-reproducing machines. The authors present a self-contained exposition of the theory of cellular automata on groups and explore its deep connections with recent developments in geometric group theory, symbolic dynamics, and other branches of mathematics and theoretical computer science. The topics treated include in particular the Garden of Eden theorem for amenable groups, and the Gromov-Weiss surjunctivity theorem as well as the solution of the Kaplansky conjecture on the stable finiteness of group rings for sofic groups. The volume is entirely self-contained, with 10 appendices and more than 300 exercises, and appeals to a large audience including specialists as well as newcomers in the field. It provides a comprehensive account of recent progress in the theory of cellular automata based on the interplay between amenability, geometric and combinatorial group theory, symbolic dynamics and the algebraic theory of group rings which are treated here for the first time in book form.
Exercises In Cellular Automata And Groups
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Author : Tullio Ceccherini-Silberstein
language : en
Publisher: Springer Nature
Release Date : 2023-11-01
Exercises In Cellular Automata And Groups written by Tullio Ceccherini-Silberstein and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-11-01 with Mathematics categories.
This book complements the authors’ monograph Cellular Automata and Groups [CAG] (Springer Monographs in Mathematics). It consists of more than 600 fully solved exercises in symbolic dynamics and geometric group theory with connections to geometry and topology, ring and module theory, automata theory and theoretical computer science. Each solution is detailed and entirely self-contained, in the sense that it only requires a standard undergraduate-level background in abstract algebra and general topology, together with results established in [CAG] and in previous exercises. It includes a wealth of gradually worked out examples and counterexamples presented here for the first time in textbook form. Additional comments provide some historical and bibliographical information, including an account of related recent developments and suggestions for further reading. The eight-chapter division from [CAG] is maintained. Each chapter begins with a summary of the main definitions and results contained in the corresponding chapter of [CAG]. The book is suitable either for classroom or individual use. Foreword by Rostislav I. Grigorchuk
Additive Cellular Automata
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Author : Parimal Pal Chaudhuri
language : en
Publisher: John Wiley & Sons
Release Date : 1997-07-11
Additive Cellular Automata written by Parimal Pal Chaudhuri and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-07-11 with Technology & Engineering categories.
This book presents an extensive survey and report of related research on important developments in cellular automata (CA) theory. The authors introduce you to this theory in a comprehensive manner that will help you understand the basics of CA and be prepared for further research. They illustrate the matrix algebraic tools that characterize group CA and help develop its applications in the field of VLSI testing. The text examines schemes based on easily testable FSM, bit-error correcting code, byte error correcting code, and characterization of 2D cellular automata. In addition, it looks into CA-based universal pattern generation, data encryption, and synthesis of easily testable combinational logic. The book covers new characterizations of group CA behavior, CA-based tools for fault diagnosis, and a wide variety of applications to solve real-life problems.
Cellular Automata And Discrete Complex Systems
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Author : Matthew Cook
language : en
Publisher: Springer
Release Date : 2016-06-01
Cellular Automata And Discrete Complex Systems written by Matthew Cook and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-06-01 with Computers categories.
This volume constitutes the thoroughly refereed proceedings of the 22nd IFIP WG 1.5International Workshop on Cellular Automata and Discrete ComplexSystems, AUTOMATA 2016, held in Zurich, Switzerland, in June 2016. This volume contains 3 invited talks in full-paper length and 12 regularpapers, which were carefully reviewed and selected from a total of 23submissions. The papers feature research on all fundamental aspects of cellular automata and related discrete complex systems and deal with the following topics: dynamical, topological, ergodic and algebraic aspects; algorithmic and complexity issues; emergent properties; formal language processing; symbolic dynamics; models of parallelism and distributed systems; timing schemes; phenomenological descriptions; scientific modeling; and practical applications.
Cellular Automata And Discrete Complex Systems
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Author : Hector Zenil
language : en
Publisher: Springer Nature
Release Date : 2020-10-21
Cellular Automata And Discrete Complex Systems written by Hector Zenil and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-21 with Computers categories.
This volume constitutes the refereed post-conference proceedings of the 26th IFIP WG 1.5 International Workshop on Cellular Automata and Discrete Complex Systems, AUTOMATA 2020, held in Stockholm, Sweden, in August 2020. The workshop was held virtually. The 11 full papers presented in this book were carefully reviewed and selected from a total of 21 submissions. The topics of the conference include dynamical, topological, ergodic and algebraic aspects of CA and DCS, algorithmic and complexity issues, emergent properties, formal languages, symbolic dynamics, tilings, models of parallelism and distributed systems, timing schemes, synchronous versus asynchronous models, phenomenological descriptions, scientific modeling, and practical applications.
Cellular Automata And Discrete Complex Systems
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Author : Alonso Castillo-Ramirez
language : en
Publisher: Springer
Release Date : 2019-06-19
Cellular Automata And Discrete Complex Systems written by Alonso Castillo-Ramirez and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-06-19 with Computers categories.
This volume constitutes the refereed proceedings of the 25th IFIP WG 1.5 International Workshop on Cellular Automata and Discrete Complex Systems, AUTOMATA 2019, held in Guadalajara, Mexico, in June 2019.The 7 regular papers presented in this book were carefully reviewed and selected from a total of 10 submissions. The topics of the conference include deal with dynamical, topological, ergodic and algebraic aspects of CA and DCS, algorithmic and complexity issues, emergent properties, formal languages, symbolic dynamics, tilings, models of parallelism and distributed systems, timing schemes, synchronous versus asynchronous models, phenomenological descriptions, scientic modeling, and practical applications.
Cellular Automata
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Author : Samira El Yacoubi
language : en
Publisher: Springer
Release Date : 2016-08-29
Cellular Automata written by Samira El Yacoubi and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-08-29 with Computers categories.
This book constitutes the proceedings of the 12th International Conference on Cellular Automata for Research and Industry, ACRI 2016, held in Fez, Morocco, in September 2014. The 45 full papers and 4 invited talks presented in this volume were carefully reviewed and selected from 59 submissions. This volume contains invited contributions and accepted papers from the main track and from the three organized workshops. The first part is organized according to three topics: (1) Cellular Automata Theory and Implementation (2) Cellular Automata Dynamics and Synchronization, (3) Asynchronous Cellular Automata and Asynchronous Discrete Models - ACA. The second part of the volume contains three topics: (4) Modelling and Sim-ulation with Cellular Automata (5) Crowds, Traffic and Cellular Automata –CT&CA (6) Agent-Based Simulation and Cellular Automata – ABS&CA.
Cellular Automata Analysis And Applications
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Author : Karl-Peter Hadeler
language : en
Publisher: Springer
Release Date : 2017-05-27
Cellular Automata Analysis And Applications written by Karl-Peter Hadeler and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-05-27 with Mathematics categories.
This book provides an overview of the main approaches used to analyze the dynamics of cellular automata. Cellular automata are an indispensable tool in mathematical modeling. In contrast to classical modeling approaches like partial differential equations, cellular automata are relatively easy to simulate but difficult to analyze. In this book we present a review of approaches and theories that allow the reader to understand the behavior of cellular automata beyond simulations. The first part consists of an introduction to cellular automata on Cayley graphs, and their characterization via the fundamental Cutis-Hedlund-Lyndon theorems in the context of various topological concepts (Cantor, Besicovitch and Weyl topology). The second part focuses on classification results: What classification follows from topological concepts (Hurley classification), Lyapunov stability (Gilman classification), and the theory of formal languages and grammars (Kůrka classification)? These classifications suggest that cellular automata be clustered, similar to the classification of partial differential equations into hyperbolic, parabolic and elliptic equations. This part of the book culminates in the question of whether the properties of cellular automata are decidable. Surjectivity and injectivity are examined, and the seminal Garden of Eden theorems are discussed. In turn, the third part focuses on the analysis of cellular automata that inherit distinct properties, often based on mathematical modeling of biological, physical or chemical systems. Linearity is a concept that allows us to define self-similar limit sets. Models for particle motion show how to bridge the gap between cellular automata and partial differential equations (HPP model and ultradiscrete limit). Pattern formation is related to linear cellular automata, to the Bar-Yam model for the Turing pattern, and Greenberg-Hastings automata for excitable media. In addition, models for sand piles, the dynamics of infectious d
Cellular Automata And Discrete Complex Systems
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Author : Alberto Dennunzio
language : en
Publisher: Springer
Release Date : 2017-05-24
Cellular Automata And Discrete Complex Systems written by Alberto Dennunzio and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-05-24 with Computers categories.
This volume constitutes the thoroughly refereed proceedings of the 23rd IFIP WG 1.5 International Workshop on Cellular Automata and Discrete Complex Systems, AUTOMATA 2017, held in Milan, Italy, in June 2017. The 14 full papers presented together with one full-length invited paper and 2 invited talk abstracts were carefully reviewed and selected from a total of 28 submissions. The papers feature research on correlated models of automata. The topics include aspects and features of such models: dynamics; topological, ergodic, and algebraic aspects; algorithmic and complexity issues; emergent properties; formal languages; symbolic dynamics; tilings; models of parallelism and distributed systems; timing schemes; synchronous versus asynchronous models; phenomenological descriptions; scientific modelling; practical applications.
The Cellular Automaton Interpretation Of Quantum Mechanics
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Author : Gerard 't Hooft
language : en
Publisher: Springer
Release Date : 2016-09-02
The Cellular Automaton Interpretation Of Quantum Mechanics written by Gerard 't Hooft and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-09-02 with Science categories.
This book presents the deterministic view of quantum mechanics developed by Nobel Laureate Gerard 't Hooft. Dissatisfied with the uncomfortable gaps in the way conventional quantum mechanics meshes with the classical world, 't Hooft has revived the old hidden variable ideas, but now in a much more systematic way than usual. In this, quantum mechanics is viewed as a tool rather than a theory. The author gives examples of models that are classical in essence, but can be analysed by the use of quantum techniques, and argues that even the Standard Model, together with gravitational interactions, might be viewed as a quantum mechanical approach to analysing a system that could be classical at its core. He shows how this approach, even though it is based on hidden variables, can be plausibly reconciled with Bell's theorem, and how the usual objections voiced against the idea of ‘superdeterminism' can be overcome, at least in principle. This framework elegantly explains - and automatically cures - the problems of the wave function collapse and the measurement problem. Even the existence of an “arrow of time" can perhaps be explained in a more elegant way than usual. As well as reviewing the author’s earlier work in the field, the book also contains many new observations and calculations. It provides stimulating reading for all physicists working on the foundations of quantum theory.