Regular Algebra and Finite Machines

by John Horton Conway

Overview

A world-famous mathematician explores Moore's theory of experiments, Kleene's theory of regular events and expressions, Kleene algebras, the differential calculus of events, factors and the factor matrix, and the theory of operators. Additional subjects include context-free languages, communicative regular algebra, axiomatic questions, and logical problems. Solutions to problems. 1971 edition.

Product Details

ISBN-13:	9780486485836
Publisher:	Dover Publications
Publication date:	07/17/2012
Series:	Dover Books on Mathematics Series
Edition description:	Unabridged
Pages:	158
Sales rank:	1,286,690
Product dimensions:	5.30(w) x 8.40(h) x 0.50(d)

About the Author

John Horton Conway is a Professor of Mathematics at Princeton and active in the theory of finite groups, number theory, coding theory, knot theory, and combinatorial game theory. The author of ten books, he has also contributed to many branches of recreational mathematics, including the invention of "The Game of Life."

Table of Contents

Preface vii

Preliminaries to the Moore Theory 1

1 Moore's theory of experiments 7

2 Bombs and detonators 15

3 Kleene's theory of regular events and expressions 24

4 Kleene algebras: the one-variable theorem 34

5 The differential calculus of events 41

6 Factors and the factor matrix 47

7 The theory of operators: biregulators 56

8 Event classes and operator classes 65

9 Some regulator algebras 71

10 Context-free languages 79

11 Commutative regular algebra 91

12 Some axiomatic questions 100

13 The strength of the classical axioms 109

14 Some computational techniques 120

15 Some logical problems 130

Solutions to problems 140

Index 143