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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.
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
3 A Generalization of Finite Group Theory to Finite Semigroups 15
4 A Reformulation of Physics 35
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
Appendix to Chapter 5 77
Applications of Automata Theory and Algebra
6 Applications 111
Part I Analysis and Classification of Biochemical Reactions 114
Part II Complexity of Evolved Organisms 176
Appendix to Part II 195
Part III The Lagrangian of Life 203
A The Laws of Growing and Evolving Organisms 203
B Complexity, Emotion, Neurosis and Schizophrenia 220
Part IV Complexity of Games 241