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Catalogue Information
Field name	Details
Dewey Class	515.39
Dewey Class	515.48
Title	Cellular Automata and Groups ([Ebook]) / by Tullio Ceccherini-Silberstein, Michel Coornaert.
Author	Ceccherini-Silberstein, Tullio
Added Personal Name	Coornaert, Michel
Other name(s)	SpringerLink (Online service)
Publication	Berlin, Heidelberg : Springer , 2010.
Physical Details	XX, 440 pages : online resource.
Series	Springer monographs in mathematics 1439-7382
ISBN	9783642140341
Summary Note	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 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 Gromov-Weiss 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 self-contained, 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.:
Contents note	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.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
Internet Site	http://dx.doi.org/10.1007/978-3-642-14034-1
Links to Related Works	Subject References: Differentiable dynamical systems . Dynamical systems and ergodic theory . Mathematics . Authors: author . Ceccherini-Silberstein, Tullio . Coornaert, Michel . Corporate Authors: SpringerLink (Online service) . Series: Springer monographs in mathematics . Classification: 515.39 . 515.48 . 515.39 (DDC 23) .

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Cellular Automata and Groups

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