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Titlebook: Exercises in Cellular Automata and Groups; Tullio Ceccherini-Silberstein,Michel Coornaert Textbook 2023 The Editor(s) (if applicable) and

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發(fā)表于 2025-3-21 19:14:41 | 只看該作者 |倒序?yàn)g覽 |閱讀模式
書(shū)目名稱Exercises in Cellular Automata and Groups
編輯Tullio Ceccherini-Silberstein,Michel Coornaert
視頻videohttp://file.papertrans.cn/319/318507/318507.mp4
概述This is the first exercise book on cellular automata over groups.The presentation is detailed and self-contained.Contains several exotic examples and counterexamples
叢書(shū)名稱Springer Monographs in Mathematics
圖書(shū)封面Titlebook: Exercises in Cellular Automata and Groups;  Tullio Ceccherini-Silberstein,Michel Coornaert Textbook 2023 The Editor(s) (if applicable) and
描述.This book complements the authors’ monograph?.Cellular Automata and Groups.?[CAG] (Springer Monographs in Mathematics).?It consists of more than 600 fully solved exercises?in symbolic dynamics and geometric group theory with connections to geometry and topology, ring and module theory, automata theory and theoretical computer science. Each solution is detailed and entirely self-contained, in the sense that it only requires a standard undergraduate-level background in abstract algebra and general topology, together with results established in [CAG] and in previous exercises. It includes a wealth of gradually worked out examples and counterexamples presented here for the first time in textbook form. Additional comments provide some historical and bibliographical information, including an account of related recent developments and suggestions for further reading. The eight-chapter division from [CAG] is maintained. Each chapter begins with a summary of the maindefinitions and results contained in the corresponding chapter of [CAG]. The book is suitable either for classroom or individual use..Foreword by Rostislav I. Grigorchuk.
出版日期Textbook 2023
關(guān)鍵詞Group; Cellular Automaton; Kaplansky conjecture; Group Ring; Sofic group; Gromov-Weiss Theorem; Surjunctiv
版次1
doihttps://doi.org/10.1007/978-3-031-10391-9
isbn_softcover978-3-031-10393-3
isbn_ebook978-3-031-10391-9Series ISSN 1439-7382 Series E-ISSN 2196-9922
issn_series 1439-7382
copyrightThe Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl
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沙發(fā)
發(fā)表于 2025-3-21 21:02:06 | 只看該作者
Finitely Generated Groups,Schreier index-rank formula are given. The Euler characteristic of some finitely generated virtually free groups is computed. Groups acting on rooted trees, self-similar groups, Mealy machines, and automata groups are introduced and studied in detail..Sofic subshifts over the integers and their labe
板凳
發(fā)表于 2025-3-22 02:21:43 | 只看該作者
Linear Cellular Automata,d the linear version of the Garden of Eden theorem. The leitmotif is the interplay between properties of a group and those of its associated group ring. This leads in particular to connections with some of the celebrated Kaplansky conjectures. Noetherian rings, UPR-rings, von Neumann regular rings,
地板
發(fā)表于 2025-3-22 07:34:46 | 只看該作者
Textbook 2023fully solved exercises?in symbolic dynamics and geometric group theory with connections to geometry and topology, ring and module theory, automata theory and theoretical computer science. Each solution is detailed and entirely self-contained, in the sense that it only requires a standard undergradua
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發(fā)表于 2025-3-22 12:28:24 | 只看該作者
1439-7382 mples and counterexamples.This book complements the authors’ monograph?.Cellular Automata and Groups.?[CAG] (Springer Monographs in Mathematics).?It consists of more than 600 fully solved exercises?in symbolic dynamics and geometric group theory with connections to geometry and topology, ring and mo
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Finitely Generated Groups,ts of irreducible sofic subshifts have strictly smaller entropies. The notion of a diamond in a labeled graph yields a characterization of pre-injectivity and, as an application, a Garden of Eden theorem for irreducible subshifts of finite type is established.
10#
發(fā)表于 2025-3-23 09:02:33 | 只看該作者
Is Consciousness Information or Algorithm?, and pre-injectivity of maps is investigated. Topological entropy of dynamical systems with amenable acting group and entropy of subshifts over amenable groups are studied and explicitly computed for some examples including the golden mean, the even, and the Morse subshifts. The Moore and Myhill properties for subshifts are discussed.
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