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

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悶熱

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

certitude

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,

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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

PHIL

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.

有效

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.