Title
Cellular Automata and Groups (Springer Monographs in Mathematics),Used
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Cellular automata were introduced in the first half of the last century by John von Neumann who used them as theoretical models for selfreproducing machines. The authors present a selfcontained 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 GromovWeiss 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 selfcontained, 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.
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- Q: What are cellular automata? A: Cellular automata are mathematical models used to simulate complex systems. They consist of a grid of cells, each in a specific state, which evolve over time according to defined rules based on the states of neighboring cells.
- Q: Who is the author of 'Cellular Automata and Groups'? A: The book 'Cellular Automata and Groups' is authored by Tullio Ceccherini-Silberstein.
- Q: What topics are covered in this book? A: This book covers a variety of topics including the theory of cellular automata on groups, the Garden of Eden theorem, the Gromov-Weiss surjunctivity theorem, and the Kaplansky conjecture.
- Q: Is this book suitable for beginners? A: Yes, the book is designed to appeal to both specialists and newcomers, providing a comprehensive introduction to the theory of cellular automata.
- Q: How many pages does the book have? A: The book contains 460 pages.
- Q: What is the condition of the book? A: The book is listed as 'New' and is a used book in good condition.
- Q: What type of binding does the book have? A: The book is bound in hardcover.
- Q: When was 'Cellular Automata and Groups' published? A: The book was published on September 3, 2010.
- Q: Does the book include exercises or appendices? A: Yes, it includes more than 300 exercises and 10 appendices to help reinforce the concepts presented.
- Q: What is the significance of the book in its field? A: The book provides a comprehensive account of recent progress in the theory of cellular automata, connecting various mathematical disciplines, making it a significant contribution to the field.