Exercises in Cellular Automata and Groups

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 maindefinitions and results contained in the corresponding chapter of [CAG]. The book is suitable either for classroom or individual use.

Foreword by Rostislav I. Grigorchuk

This is the first exercise book on cellular automata over groups The presentation is detailed and self-contained Contains several exotic examples and counterexamples

Auteur
Tullio Ceccherini-Silberstein graduated from the University of Rome La Sapienza in 1990 and obtained his PhD in mathematics at the University of California at Los Angeles in 1994. Since 1997 he has been professor of Mathematical Analysis at the University of Sannio, Benevento (Italy). His main interests include harmonic and functional analysis, geometric and combinatorial group theory, ergodic theory and dynamical systems, and theoretical computer science. He is an editor of the journal Groups, Geometry, and Dynamics, published by the European Mathematical Society, and of the Bulletin of the Iranian Mathematical Society. He has published more than 90 research papers, 9 monographs, and 4 conference proceedings.

Professor Michel Coornaert taught mathematics at the University of Strasbourg from 1992 until 2021. His research interests are in geometry, topology, group theory and dynamical systems. He is the author of many Springer volumes, including Topological Dimension and Dynamical Systems (2015), Cellular Automata and Groups (2010), Symbolic Dynamics and Hyperbolic Groups (1993) and Géométrie et théorie des groupes (1990).

Texte du rabat

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

Résumé

"Exercises in cellular automata and groups provides a utilitarian and exciting introduction to the discipline, in addition to being a reservoir of guidance for fostering new evolutions. It includes numerous references to the literature and a helpful index. Readers will appreciate the worked-out exercises, which serve as a guidepost for understanding the subject matter. Note that the same exercise may be solved in different ways." (S. V. Nagaraj, Computing Reviews, February 6, 2024)

Contenu
1 Cellular Automata.- 2 Residually Finite Groups.- 3 Surjunctive Groups.- 4 Amenable Groups.- 5 The Garden of Eden Theorem.- 6 Finitely Generated Amenable Groups.- 7 Local Embeddability and Sofic Groups.- 8 Linear Cellular Automata. <p