Cellular Automata On Group Sets
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| Author | : Tullio Ceccherini-Silberstein |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 446 |
| Release | : 2010-08-24 |
| Genre | : Computers |
| ISBN | : 3642140343 |
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.
| Author | : Simon Wacker |
| Publisher | : |
| Total Pages | : |
| Release | : 2017 |
| Genre | : |
| ISBN | : |
| Author | : Tullio Ceccherini-Silberstein |
| Publisher | : Springer Nature |
| Total Pages | : 562 |
| Release | : 2024-02-16 |
| Genre | : Mathematics |
| ISBN | : 3031433289 |
This unique book provides a self-contained exposition of the theory of cellular automata on groups and explores its deep connections with recent developments in geometric and combinatorial group theory, amenability, symbolic dynamics, the algebraic theory of group rings, and other branches of mathematics and theoretical computer science. The topics treated include the Garden of Eden theorem for amenable groups, the Gromov–Weiss surjunctivity theorem, and the solution of the Kaplansky conjecture on the stable finiteness of group rings for sofic groups. Entirely self-contained and now in its second edition, the volume includes 10 appendices and more than 600 exercises, the solutions of which are presented in the companion book Exercises in Cellular Automata and Groups (2023) by the same authors. It will appeal to a large audience, including specialists and newcomers to the field.
| Author | : Tullio Ceccherini-Silberstein |
| Publisher | : Springer Nature |
| Total Pages | : 638 |
| Release | : 2023-11-01 |
| Genre | : Mathematics |
| ISBN | : 3031103912 |
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
| Author | : Samira El Yacoubi |
| Publisher | : Springer |
| Total Pages | : 482 |
| Release | : 2016-08-29 |
| Genre | : Computers |
| ISBN | : 3319443658 |
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.
| Author | : Matthew Cook |
| Publisher | : Springer |
| Total Pages | : 211 |
| Release | : 2016-06-01 |
| Genre | : Computers |
| ISBN | : 3319393006 |
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.
| Author | : Benjamin Steinberg |
| Publisher | : Walter de Gruyter GmbH & Co KG |
| Total Pages | : 589 |
| Release | : 2024-10-21 |
| Genre | : Mathematics |
| ISBN | : 3110984520 |
This reference discusses how automata and language theory can be used to understand solutions to solving equations in groups and word problems in groups. Examples presented include, how Fine scale complexity theory has entered group theory via these connections and how cellular automata, has been generalized into a group theoretic setting. Chapters written by experts in group theory and computer science explain these connections.
| Author | : Sukanta Das |
| Publisher | : Springer Nature |
| Total Pages | : 251 |
| Release | : 2022-04-27 |
| Genre | : Technology & Engineering |
| ISBN | : 9811905428 |
This book gathers selected research papers presented at the First Asian Symposium on Cellular Automata Technology (ASCAT 2022), organized online by academicians from Kolkata, India, during March 3–5, 2022. The book presents one of the most emergent areas in natural computing, cellular automaton (CA). CA is a paradigm of uniform fine-grained parallel computation which has been explored to understand complex systems by developing its model at the microscopic level. The book discusses many real-life problems in the domain of very large-scale integration (VLSI) design and test, pattern recognition and classification, cryptography, pseudo-random pattern generation, image processing, sensor networks, material science, etc., by using CA.
| Author | : Maximilien Gadouleau |
| Publisher | : Springer Nature |
| Total Pages | : 165 |
| Release | : |
| Genre | : |
| ISBN | : 3031658876 |
| Author | : Binxing Fang |
| Publisher | : Walter de Gruyter GmbH & Co KG |
| Total Pages | : 197 |
| Release | : 2019-08-05 |
| Genre | : Computers |
| ISBN | : 3110599414 |
The three volume set provides a systematic overview of theories and technique on social network analysis.Volume 2 of the set mainly focuses on the formation and interaction of group behaviors. Users’ behavior analysis, sentiment analysis, influence analysis and collective aggregation are discussed in detail as well. It is an essential reference for scientist and professionals in computer science.
