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

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

by Chrystopher L Nehaniv, John Rhodes
     
 

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ISBN-10: 9812836977

ISBN-13: 9789812836977

Pub. Date: 10/28/2009

Publisher: World Scientific Publishing Company, Incorporated

This book was originally written in 1969 by Berkeley mathematician John Rhodes. It is the founding work in what is now called algebraic engineering, an emerging field created by using the unifying scheme of finite state machine models and their complexity to tie together many fields: finite group theory, semigroup theory, automata and sequential machine theory,

Overview

This book was originally written in 1969 by Berkeley mathematician John Rhodes. It is the founding work in what is now called algebraic engineering, an emerging field created by using the unifying scheme of finite state machine models and their complexity to tie together many fields: finite group theory, semigroup theory, automata and sequential machine theory, finite phase space physics, metabolic and evolutionary biology, epistemology, mathematical theory of psychoanalysis, philosophy, and game theory. The author thus introduced a completely original algebraic approach to complexity and the understanding of finite systems. The unpublished manuscript, often referred to as “The Wild Book”, became an underground classic, continually requested in manuscript form, and read by many leading researchers in mathematics, complex systems, artificial intelligence, and systems biology. Yet it has never been available in print until now.This first published edition has been edited and updated by Chrystopher Nehaniv for the 21st century. 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. Co-founded by John Rhodes and Kenneth Krohn in 1962, algebraic automata theory has grown into a vibrant area of research, including the complexity of automata, and semigroups and machines from an algebraic viewpoint, and which also touches on infinite groups, and other areas of algebra. This book sets the stage for the application of algebraic automata theory to areas outside mathematics.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. Included are treatments of topics such as models of time as algebra via semigroup theory; evolution-complexity relations applicable to both ontogeny and evolution; an approach to classification of biological reactions and pathways; the relationships among coordinate systems, symmetry, and conservation principles in physics; discussion of “punctuated equilibrium” (prior to Stephen Jay Gould); games; and applications to psychology, psychoanalysis, epistemology, and the purpose of life.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. Moreover, many parts of the book will be intelligible to non-mathematicians, including students and experts from diverse backgrounds.

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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