Solvable Cellular Automata: Methods and Applications
暫譯: 可解的細胞自動機：方法與應用

Fukś, Henryk

Solvable Cellular Automata: Methods and Applications
  • 出版商: Springer
  • 出版日期: 2024-10-11
  • 售價: $6,460
  • 貴賓價: 9.5 折 $6,137
  • 語言: 英文
  • 頁數: 296
  • 裝訂: Quality Paper - also called trade paper
  • ISBN: 3031387023
  • ISBN-13: 9783031387029

    • 海外代購書籍(需單獨結帳)

商品描述

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.

商品描述(中文翻譯)

本書的主要焦點是細胞自動機的可解性，即通過明確的公式表達在給定步數後某個特定細胞的狀態。作者考慮了兩種類型的細胞自動機初始值問題的解決方案：確定性問題和隨機性問題。在第一章中，介紹了細胞自動機理論的基本概念。接下來介紹了確定性初始值問題，並針對選定的簡單規則提供了解決方案。在隨後的章節中，介紹了解決確定性問題的各種技術，並以逐漸增加複雜性的基本細胞自動機規則作為示例。本書的第二部分介紹了在細胞自動機背景下的概率測度概念，以及針對確定性和隨機性規則的隨機初始值問題。本書配有豐富的示例和應用，如密度分類問題、交通模型中的相變化或創新擴散模型。在附錄中，列出了超過60個基本細胞自動機規則的解決公式（包括確定性和隨機性）。此外，還提供了所有88個最小基本細胞自動機的Ruelle-Frobenius-Perron方程。

作者簡介

Henryk Fukś is a Professor at the Department of Mathematics and Statistic of Brock University in St. Catharines, Canada. He received his Ph.D. at the University of Illinois at Chicago in 1997, and afterwards held the NSERC postdoctoral fellowship at the University of Guelph and the Fields Institute for Research in Mathematical Sciences in Toronto. He published over 70 research papers, mostly in the field of cellular automata. In addition to cellular automata, his research interests include complex systems, cooperative phenomena, phase transitions, mathematical modelling as well as history of mathematics.

作者簡介(中文翻譯)

亨利克·福克斯（Henryk Fukś）是加拿大聖凱瑟琳斯的布洛克大學（Brock University）數學與統計系的教授。他於1997年在伊利諾伊大學芝加哥分校（University of Illinois at Chicago）獲得博士學位，之後在圭爾夫大學（University of Guelph）和多倫多的數學科學研究領域研究所（Fields Institute for Research in Mathematical Sciences）擔任NSERC博士後研究員。他發表了超過70篇研究論文，主要集中在細胞自動機（cellular automata）領域。除了細胞自動機外，他的研究興趣還包括複雜系統（complex systems）、合作現象（cooperative phenomena）、相變（phase transitions）、數學建模（mathematical modelling）以及數學史（history of mathematics）。

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