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＜電子ブック＞
Cellular Automata and Groups / by Tullio Ceccherini-Silberstein, Michel Coornaert
(Springer Monographs in Mathematics. ISSN:21969922)

版	2nd ed. 2023.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2023
本文言語	英語
大きさ	XXI, 556 p. 56 illus : online resource
著者標目	*Ceccherini-Silberstein, Tullio author Coornaert, Michel author SpringerLink (Online service)
件　名	LCSH:Algebra LCSH:Dynamical systems LCSH:Computer science FREE:Algebra FREE:Dynamical Systems FREE:Computer Science Logic and Foundations of Programming
一般注記	1 Cellular Automata -- 2 Residually Finite Groups -- 3 Surjunctive Groups -- 4 Amenable Groups -- 5 The Garden of Eden Theorem -- 6 Finitely Generated Groups -- 7 Local Embeddability and Sofic Groups -- 8 Linear Cellular Automata -- Appendix A: Nets and the Tychonoff Product Theorem -- Appendix B: Uniform Structures -- Appendix C: Symmetric Groups -- Appendix D: Free Groups -- Appendix E: Inductive Limits and Projective Limits of Groups -- Appendix G: The Markov-Kakutani Fixed Point Theorem -- Appendix I: Complements of Functional Analysis This unique book provides a self-contained exposition of the theory of cellular automata on groups and explores its deep connections with recent developments in geometric and combinatorial group theory, amenability, symbolic dynamics, the algebraic theory of group rings, and other branches of mathematics and theoretical computer science. The topics treated include the Garden of Eden theorem for amenable groups, the Gromov–Weiss surjunctivity theorem, and the solution of the Kaplansky conjecture on the stable finiteness of group rings for sofic groups. Entirely self-contained and now in its second edition, the volume includes 10 appendices and more than 600 exercises, the solutions of which are presented in the companion book Exercises in Cellular Automata and Groups (2023) by the same authors. It will appeal to a large audience, including specialists and newcomers to the field HTTP:URL=https://doi.org/10.1007/978-3-031-43328-3

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