東華大學圖書館 |

Language: English

Help

回圖書館首頁

手機版館藏查詢

Back

Switch To: Labeled | MARC Mode | ISBD

Solvable cellular automata = methods...

Fuks, Henryk.

Linked to FindBook

Google Book

Amazon

博客來

Solvable cellular automata = methods and applications /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Solvable cellular automata/ by Henryk Fuks.
Reminder of title:	methods and applications /
Author:	Fuks, Henryk.
Published:	Cham :Springer Nature Switzerland : : 2023.,
Description:	xix, 296 p. :ill. (some col.), digital ;24 cm.
[NT 15003449]:	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.
Contained By:	Springer Nature eBook
Subject:	Cellular automata. -
Online resource:	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:

536282
Cellular automata.

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

Dewey Class. No.: 006.3822

Solvable cellular automata = methods and applications /
LDR:02719nmm a2200337 a 4500 001 2335707
003 DE-He213
005 20231009134932.0
006 m d
007 cr nn 008maaau
008 240402s2023 sz s 0 eng d
020 $a 9783031387005 $q (electronic bk.)
020 $a 9783031386992 $q (paper)
024 7 $a 10.1007/978-3-031-38700-5 $2 doi
035 $a 978-3-031-38700-5
040 $a GP $c GP
041 0 $a eng
050 4 $a QA267.5.C45 $b F84 2023
072 7 $a GPFC $2 bicssc
072 7 $a SCI055000 $2 bisacsh
072 7 $a GPFC $2 thema
082 0 4 $a 006.3822 $2 23
090 $a QA267.5.C45 $b F961 2023
100 1 $a Fuks, Henryk. $3 3668305
245 1 0 $a Solvable cellular automata $h [electronic resource] : $b methods and applications / $c by Henryk Fuks.
260 $a Cham : $b Springer Nature Switzerland : $b Imprint: Springer, $c 2023.
300 $a xix, 296 p. : $b ill. (some col.), digital ; $c 24 cm.
490 1 $a Understanding complex systems, $x 1860-0840
505 0 $a 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.
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.
650 0 $a Cellular automata. $3 536282
650 1 4 $a Complex Systems. $3 1566441
650 2 4 $a Theory of Computation. $3 892514
650 2 4 $a Applied Dynamical Systems. $3 3538870
650 2 4 $a Mathematical Physics. $3 1542352
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer Nature eBook
830 0 $a Understanding complex systems. $3 1568162
856 4 0 $u https://doi.org/10.1007/978-3-031-38700-5
950 $a Physics and Astronomy (SpringerNature-11651)