Cellular Automata and Groups

• Main Authors: Ceccherini-Silberstein, Tullio. (Author), Coornaert, Michel. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2010.
• Series: Springer Monographs in Mathematics,
• Subjects: Mathematics.; Differentiable dynamical systems.; Dynamical Systems and Ergodic Theory.
• Online Access: https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-3-642-14034-1

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 dev...

Table of Contents:

• Preface
• 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
• Appendices: A.Nets and the Tychonoff product theorem
• B.Uniform structures
• C.Symmetric groups
• D.Free groups
• E.Inductive limits and projective limits of groups
• F.The Banach-Alaoglu theorem
• G.The Markov-Kakutani fixed point theorem
• H.The Hall harem Theorem
• I.Complements of functional analysis
• J.Ultrafilters
• Open problems
• References
• List of symbols
• Index.