國立虎尾科技大學 |

Cellular automata and groups

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Cellular automata and groups/ by Tullio Ceccherini-Silberstein, Michel Coornaert.
Author:	Ceccherini-Silberstein, Tullio.
other author:	Coornaert, M.
Published:	Cham :Springer International Publishing : : 2023.,
Description:	xxi, 556 p. :ill., digital ; : 24 cm.;
Contained By:	Springer Nature eBook
Subject:	Cellular automata. -
Online resource:	https://doi.org/10.1007/978-3-031-43328-3
ISBN:	9783031433283

Cellular automata and groups
Ceccherini-Silberstein, Tullio.

Cellular automata and groups[electronic resource] /by Tullio Ceccherini-Silberstein, Michel Coornaert. - Second edition. - Cham :Springer International Publishing :2023. - xxi, 556 p. :ill., digital ;24 cm. - Springer monographs in mathematics,2196-9922. - Springer monographs in mathematics..

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.

ISBN: 9783031433283

Standard No.: 10.1007/978-3-031-43328-3doiSubjects--Topical Terms:

574251
Cellular automata.

LC Class. No.: QA267.5.C45

Dewey Class. No.: 511.3

Cellular automata and groups
LDR:02517nam a2200349 a 4500 001 1120761
003 DE-He213
005 20240113005357.0
006 m d
007 cr nn 008maaau
008 240612s2023 sz s 0 eng d
020 $a 9783031433283 $q (electronic bk.)
020 $a 9783031433276 $q (paper)
024 7 $a 10.1007/978-3-031-43328-3 $2 doi
035 $a 978-3-031-43328-3
040 $a GP $c GP
041 0 $a eng
050 4 $a QA267.5.C45
072 7 $a PBF $2 bicssc
072 7 $a MAT002000 $2 bisacsh
072 7 $a PBF $2 thema
082 0 4 $a 511.3 $2 23
090 $a QA267.5.C45 $b C387 2023
100 1 $a Ceccherini-Silberstein, Tullio. $e author. $3 1326452
245 1 0 $a Cellular automata and groups $h [electronic resource] / $c by Tullio Ceccherini-Silberstein, Michel Coornaert.
250 $a Second edition.
260 $a Cham : $c 2023. $b Springer International Publishing : $b Imprint: Springer,
300 $a xxi, 556 p. : $b ill., digital ; $c 24 cm.
490 1 $a Springer monographs in mathematics, $x 2196-9922
505 0 $a 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.
520 $a 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.
650 0 $a Cellular automata. $3 574251
650 0 $a Group theory. $3 527791
650 0 $a Algebra. $2 gtt $3 579870
650 2 4 $a Dynamical Systems. $3 1366074
650 2 4 $a Computer Science Logic and Foundations of Programming. $3 1365757
700 1 $a Coornaert, M. $3 1431769
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
830 0 $a Springer monographs in mathematics. $3 882184
856 4 0 $u https://doi.org/10.1007/978-3-031-43328-3
950 $a Mathematics and Statistics (SpringerNature-11649)