Regular Algebra and Finite Machines

by John Horton Conway

Overview

World-famous mathematician John H. Conway based this classic text on a 1966 course he taught at Cambridge University. Geared toward graduate students of mathematics, it will also prove a valuable guide to researchers and professional mathematicians.
His topics cover 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 event classes and operator classes, some regulator algebras, context-free languages, communicative regular algebra, axiomatic questions, the strength of classical axioms, and logical problems. Complete solutions to problems appear at the end.

Product Details

ISBN-13:	9780486485836
Publisher:	Dover Publications
Publication date:	07/17/2012
Series:	Dover Books on Mathematics
Edition description:	Unabridged
Pages:	160
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