Applications of Automata Theory and Algebra: Via the Mathematical Theory of Complexity to Biology, Physics, Psychology, Philosophy, and Games

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More About This Textbook

Overview

This book, originally written in-1969 by Berkeley mathematician John Rhodes is known as the Wild Book, and quickly became an underground classic in manuscript form studied by many leading researchers in mathematics, complex systems, artificial intelligence, and systems biology. Yet it has never been available in-print until now. Nevertheless, it is the founding work of algebraic engineering, an emerging field that uses the unifying scheme of finite state machine models and their complexity to tie together finite group theory, semi group theory, automata and sequential machine theory, finite-phase space physics, metabolic and evolutionary biology, epistemology mathematical theory of psychoanalysis, philosophy, and game theory.

This first published edition has been edited by Chrystopher Nehaniv for the 21st century, and sets the stage for the application of algebraic-automata theory to areas outside mathematics. Its novel and rigorous development of the mathematical theory of complexity via algebraic automata theory reveals deep and unexpected connections between algebra (semigroups) and areas of science, and engineering.

The material and references have been brought up to date by the editor as much as possible, yet the book retains its distinct character and. the bold yet rigorous style of the author. The approach and contents will be of interest to a variety of researchers and students in algebra as well as to the diverse, growing areas of applications of algebra in science and engineering.

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Product Details

  • ISBN-13: 9789812836977
  • Publisher: World Scientific Publishing Company, Incorporated
  • Publication date: 10/28/2009
  • Edition description: New Edition
  • Pages: 292
  • Product dimensions: 6.00 (w) x 8.90 (h) x 0.70 (d)

Table of Contents

Foreword to Rhodes' Applications of Automata Theory and Algebra Morris W. Hirsch vii

Editrial Preface Chrystopher L. Nehaniv xiii

Prologue: Birth, Death, Time, Space, Existence, Understanding, Science, and Religion John Rhodes 1

1 Introduction 7

2 What is Finite Group Theory? 9

Bibliography 14

3 A Generalization of Finite Group Theory to Finite Semigroups 15

Bibliography 33

4 A Reformulation of Physics 35

Bibliography 54

5 Automata Models and the Complexity of Finite State Machines 55

Part I The Prime Decomposition Theorem 55

Part II Complexity of Finite State Machines 67

Bibliography 76

Appendix to Chapter 5 77

Applications of Automata Theory and Algebra

Bibliography 108

6 Applications 111

Introduction 111

Part I Analysis and Classification of Biochemical Reactions 114

Bibliography 175

Part II Complexity of Evolved Organisms 176

Appendix to Part II 195

Bibliography 201

Part III The Lagrangian of Life 203

A The Laws of Growing and Evolving Organisms 203

Bibliography 219

B Complexity, Emotion, Neurosis and Schizophrenia 220

Bibliography 239

Part IV Complexity of Games 241

Bibliography 256

Index 257

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