Cellular Automata And Groups
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Cellular Automata and Groups
Author: Tullio Ceccherini-Silberstein
language: en
Publisher: Springer Science & Business Media
Release Date: 2010-08-24
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
Author: Tullio Ceccherini-Silberstein
language: en
Publisher: Springer Nature
Release Date: 2023-11-01
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
Cellular Automata and Discrete Complex Systems
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.