Cellular Automata and Groups - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Cellular Automata and Groups write by Tullio Ceccherini-Silberstein. This book was released on 2010-08-24. Cellular Automata and Groups available in PDF, EPUB and Kindle. 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.
Exercises in Cellular Automata and Groups
Exercises in Cellular Automata and Groups - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Exercises in Cellular Automata and Groups write by Tullio Ceccherini-Silberstein. This book was released on 2023-11-01. Exercises in Cellular Automata and Groups available in PDF, EPUB and Kindle. 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 main definitions and results contained in the corresponding chapter of [CAG]. The book is suitable either for classroom or individual use. Foreword by Rostislav I. Grigorchuk
Cellular Automata on Group Sets
Cellular Automata on Group Sets - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Cellular Automata on Group Sets write by Simon Wacker. This book was released on 2017. Cellular Automata on Group Sets available in PDF, EPUB and Kindle.
Additive Cellular Automata
Additive Cellular Automata - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Additive Cellular Automata write by Parimal Pal Chaudhuri. This book was released on 1997-07-11. Additive Cellular Automata available in PDF, EPUB and Kindle. This book presents an extensive survey and report of related research on important developments in cellular automata (CA) theory. The authors introduce you to this theory in a comprehensive manner that will help you understand the basics of CA and be prepared for further research. They illustrate the matrix algebraic tools that characterize group CA and help develop its applications in the field of VLSI testing. The text examines schemes based on easily testable FSM, bit-error correcting code, byte error correcting code, and characterization of 2D cellular automata. In addition, it looks into CA-based universal pattern generation, data encryption, and synthesis of easily testable combinational logic. The book covers new characterizations of group CA behavior, CA-based tools for fault diagnosis, and a wide variety of applications to solve real-life problems.
The Cellular Automaton Interpretation of Quantum Mechanics
The Cellular Automaton Interpretation of Quantum Mechanics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The Cellular Automaton Interpretation of Quantum Mechanics write by Gerard 't Hooft. This book was released on 2016-09-02. The Cellular Automaton Interpretation of Quantum Mechanics available in PDF, EPUB and Kindle. This book presents the deterministic view of quantum mechanics developed by Nobel Laureate Gerard 't Hooft. Dissatisfied with the uncomfortable gaps in the way conventional quantum mechanics meshes with the classical world, 't Hooft has revived the old hidden variable ideas, but now in a much more systematic way than usual. In this, quantum mechanics is viewed as a tool rather than a theory. The author gives examples of models that are classical in essence, but can be analysed by the use of quantum techniques, and argues that even the Standard Model, together with gravitational interactions, might be viewed as a quantum mechanical approach to analysing a system that could be classical at its core. He shows how this approach, even though it is based on hidden variables, can be plausibly reconciled with Bell's theorem, and how the usual objections voiced against the idea of ‘superdeterminism' can be overcome, at least in principle. This framework elegantly explains - and automatically cures - the problems of the wave function collapse and the measurement problem. Even the existence of an “arrow of time" can perhaps be explained in a more elegant way than usual. As well as reviewing the author’s earlier work in the field, the book also contains many new observations and calculations. It provides stimulating reading for all physicists working on the foundations of quantum theory.
