Cellular Automata and Groups [[electronic resource] /] / by Tullio Ceccherini-Silberstein, Michel Coornaert

• Autore: Ceccherini-Silberstein Tullio
• Pubblicazione: Cham : , : Springer International Publishing : , : Imprint : Springer, , 2023
• Edizione: 2nd ed. 2023.
• Descrizione fisica: 1 online resource (562 pages)
• Disciplina: 515.39
• Soggetto topico: Algebra; Dynamical systems; Computer science; Dynamical Systems; Computer Science Logic and Foundations of Programming; Autòmats cel·lulars
• Soggetto genere / forma: Llibres electrònics
• Altri autori: CoornaertMichel
• Nota di contenuto: 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.
• Sommario/riassunto: 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.
• Titolo autorizzato: Cellular Automata and Groups
• ISBN: 3-031-43328-9
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910800115703321
• Lo trovi qui: Univ. Federico II
• Serie: Springer Monographs in Mathematics, . 2196-9922