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Cellular Automata and Groups

  • Tullio Ceccherini-Silberstein
  • Michel Coornaert

Part of the Springer Monographs in Mathematics book series (SMM)

Table of contents

  1. Front Matter
    Pages I-XIX
  2. Tullio Ceccherini-Silberstein, Michel Coornaert
    Pages 1-36
  3. Tullio Ceccherini-Silberstein, Michel Coornaert
    Pages 37-55
  4. Tullio Ceccherini-Silberstein, Michel Coornaert
    Pages 57-75
  5. Tullio Ceccherini-Silberstein, Michel Coornaert
    Pages 77-110
  6. Tullio Ceccherini-Silberstein, Michel Coornaert
    Pages 111-149
  7. Tullio Ceccherini-Silberstein, Michel Coornaert
    Pages 151-232
  8. Tullio Ceccherini-Silberstein, Michel Coornaert
    Pages 233-281
  9. Tullio Ceccherini-Silberstein, Michel Coornaert
    Pages 283-342
  10. Tullio Ceccherini-Silberstein, Michel Coornaert
    Pages 343-349
  11. Tullio Ceccherini-Silberstein, Michel Coornaert
    Pages 351-358
  12. Tullio Ceccherini-Silberstein, Michel Coornaert
    Pages 359-366
  13. Tullio Ceccherini-Silberstein, Michel Coornaert
    Pages 367-377
  14. Tullio Ceccherini-Silberstein, Michel Coornaert
    Pages 379-381
  15. Tullio Ceccherini-Silberstein, Michel Coornaert
    Pages 383-385
  16. Tullio Ceccherini-Silberstein, Michel Coornaert
    Pages 387-389
  17. Tullio Ceccherini-Silberstein, Michel Coornaert
    Pages 391-401
  18. Tullio Ceccherini-Silberstein, Michel Coornaert
    Pages 403-408
  19. Tullio Ceccherini-Silberstein, Michel Coornaert
    Pages 409-416
  20. Back Matter
    Pages 417-439

About this book

Introduction

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.

Keywords

Group theory Sofic group amenable group automata cellular automation garden of Eden theorem linear cellular automation

Authors and affiliations

  • Tullio Ceccherini-Silberstein
    • 1
  • Michel Coornaert
    • 2
  1. 1.Fac. IngegneriaUniversita SannioBeneventoItaly
  2. 2.Inst. Recherche Mathématique Avancée, CNRSUniversité Strasbourg IStrasbourgFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-14034-1
  • Copyright Information Springer-Verlag Berlin Heidelberg 2010
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-642-14033-4
  • Online ISBN 978-3-642-14034-1
  • Series Print ISSN 1439-7382
  • Buy this book on publisher's site