# 7. Monoids and Machines

Published Online: 20 JAN 2004

DOI: 10.1002/0471469882.ch7

Copyright © 2004 John Wiley & Sons, Inc.

Book Title

## Modern Algebra with Applications, Second Edition

Additional Information

#### How to Cite

Gilbert, W. J. and Nicholson, W. K. (2003) Monoids and Machines, in Modern Algebra with Applications, Second Edition, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/0471469882.ch7

#### Publication History

- Published Online: 20 JAN 2004
- Published Print: 24 OCT 2003

#### Book Series:

#### Book Series Editors:

- Myron B. Allen III,
- David A. Cox and
- Peter Lax

#### ISBN Information

Print ISBN: 9780471414513

Online ISBN: 9780471469889

- Summary
- Chapter

### Keywords:

- monoid;
- semigroup;
- concatenation;
- finite-state machine;
- automation;
- state diagram;
- quotient monoid

### Summary

Chapter 7 introduces an algebraic structure that is more general than a group, namely a monoid, or semigroup with identity. An important example that is used in computer science is that of a free monoid generated by a finite alphabet. These are used in mathematical models of finite-state machines, or automata. The effect of a machine can be described by means of a quotient monoid of the free monoid generated by the input symbols.