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Solvable cellular automata = methods and applications /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Solvable cellular automata/ by Henryk Fuks.
其他題名:	methods and applications /
作者:	Fuks, Henryk.
出版者:	Cham :Springer Nature Switzerland : : 2023.,
面頁冊數:	xix, 296 p. :ill. (some col.), digital ; : 24 cm.;
Contained By:	Springer Nature eBook
標題:	Mathematical Physics. -
電子資源:	https://doi.org/10.1007/978-3-031-38700-5
ISBN:	9783031387005

Solvable cellular automata = methods and applications /
Fuks, Henryk.

Solvable cellular automatamethods and applications /[electronic resource] :by Henryk Fuks. - Cham :Springer Nature Switzerland :2023. - xix, 296 p. :ill. (some col.), digital ;24 cm. - Understanding complex systems,1860-0840. - Understanding complex systems..

Deterministic cellular automata -- Deterministic initial value problem -- Multiplicative and additive rules -- More complex rules -- Exploiting rule identities -- Rules with additive invariants -- Construction of probability measures -- Probabilistic solutions -- Probabilistic cellular automata -- Applications -- Local structure approximation -- Non-solvable rules -- Appendices.

The main focus of the book is solvability of cellular automata, that is, expressing the state of a given cell after a given number of steps by an explicit formula. The author considers solutions of two types of initial value problems for cellular automata, the deterministic one and the probabilistic one. In the first chapter the basic concepts of cellular automata theory are introduced. Deterministic initial value problem is introduced next and solutions for selected simple rules are also presented. In the following chapters various techniques for solving the deterministic problem are introduced, using elementary CA rules of increasing complexity as examples. The second part of the book introduces the concept of probability measure in the context of cellular automata and the probabilistic initial value problem for both deterministic and probabilistic rules. The book is amply illustrated with examples and applications such as the density classification problem, phase transitions in traffic models or the diffusion of innovations model. In the appendix, solution formulae (both deterministic and probabilistic) for over 60 elementary cellular automata rules are listed. Ruelle-Frobenius-Perron equations for all 88 minimal elementary cellular automata are also provided.

ISBN: 9783031387005

Standard No.: 10.1007/978-3-031-38700-5doiSubjects--Topical Terms:

786661
Mathematical Physics.

LC Class. No.: QA267.5.C45 / F84 2023

Dewey Class. No.: 006.3822

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520 $a The main focus of the book is solvability of cellular automata, that is, expressing the state of a given cell after a given number of steps by an explicit formula. The author considers solutions of two types of initial value problems for cellular automata, the deterministic one and the probabilistic one. In the first chapter the basic concepts of cellular automata theory are introduced. Deterministic initial value problem is introduced next and solutions for selected simple rules are also presented. In the following chapters various techniques for solving the deterministic problem are introduced, using elementary CA rules of increasing complexity as examples. The second part of the book introduces the concept of probability measure in the context of cellular automata and the probabilistic initial value problem for both deterministic and probabilistic rules. The book is amply illustrated with examples and applications such as the density classification problem, phase transitions in traffic models or the diffusion of innovations model. In the appendix, solution formulae (both deterministic and probabilistic) for over 60 elementary cellular automata rules are listed. Ruelle-Frobenius-Perron equations for all 88 minimal elementary cellular automata are also provided.
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