Regular Algebra and Finite Machines

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.

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."

PrefacePreliminaries to the Moore Theory1. Moore's Theory of Experiments2. Bombs and Detonators3. Kleene's Theory of RegularEvents and Expressions4. Kleene Algebra: the One-Variable Theorem5. The Differential Calculus of Events6. Factors and the Factor Matrix7. The Theory of Operators: Biregulators8. Event Classes and Operator Classes9. Some Regulator Algebra10. Context-Free Languages11. Commutative Regular Algebra12. Some Axiomatic Questions13. The Strength of the Classical Axioms14. Some Computational Techniques15. Some Logical ProblemsSolutions to ProblemsIndex