Cellular Automata and Groups

• Main Authors: Ceccherini-Silberstein, Tullio (Author), Coornaert, Michel (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2010.
• Series: Springer Monographs in Mathematics,
• Subjects: Computer science.; Computer logic.; Algebra.; Dynamics.; Ergodic theory.; Computer Science.; Logics and Meanings of Programs.; Dynamical Systems and Ergodic Theory.

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:

• Cellular Automata
• Residually Finite Groups
• Surjunctive Groups
• Amenable Groups
• The Garden of Eden Theorem
• Finitely Generated Amenable Groups
• Local Embeddability and Sofic Groups
• Linear Cellular Automata
• Nets and the Tychonoff Product Theorem
• Uniform Structures
• Symmetric Groups
• Free Groups
• Inductive Limits and Projective Limits of Groups
• The Banach-Alaoglu Theorem
• The Markov-Kakutani Fixed Point Theorem
• The Hall Harem Theorem
• Complements of Functional Analysis
• Ultrafilters.