Cellular automata and groups
 Author/Creator
 CeccheriniSilberstein, Tullio.
 Language
 English.
 Imprint
 Heidelberg : Springer, c2010.
 Physical description
 xix, 439 p. : ill. ; 24 cm.
 Series
 Springer monographs in mathematics.
Access
Available online

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QA267.5 .C45 C43 2010

Unknown
QA267.5 .C45 C43 2010
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Contributors
 Contributor
 Coornaert, M. (Michel)
Contents/Summary
 Bibliography
 Includes bibliographical references (p. 421428) and index.
 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 BanachAlaoglu Theorem. The MarkovKakutani Fixed Point Theorem. The Hall Harem Theorem. Complements of Functional Analysis. Ultrafilters.
 (source: Nielsen Book Data)
 Publisher's Summary
 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.
(source: Nielsen Book Data)  Supplemental links

Table of contents
Publisher description
Subjects
Bibliographic information
 Publication date
 2010
 Responsibility
 Tullio CeccheriniSilberstein, Michel Coornaert.
 Series
 Springer monographs in mathematics
 ISBN
 9783642140334
 3642140335