7. Monoids and Machines

  1. William J. Gilbert1 and
  2. W. Keith Nicholson2

Published Online: 20 JAN 2004

DOI: 10.1002/0471469882.ch7

Modern Algebra with Applications, Second Edition

Modern Algebra with Applications, Second Edition

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

Author Information

  1. 1

    University of Waterloo, Department of Pure Mathematics, Waterloo, Ontario, Canada

  2. 2

    University of Calgary, Department of Mathematics and Statistics, Calgary, Alberta, Canada

Publication History

  1. Published Online: 20 JAN 2004
  2. Published Print: 24 OCT 2003

Book Series:

  1. Pure and Applied Mathematics

Book Series Editors:

  1. Myron B. Allen III,
  2. David A. Cox and
  3. Peter Lax

ISBN Information

Print ISBN: 9780471414513

Online ISBN: 9780471469889



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


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.