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Monogenic endomorphisms of a free monoid

Published online by Cambridge University Press:  18 May 2009

Mario Petrich
Mario Petrich
Affiliation:
Department of Mathematics and Statistics, Simon Fraser University, Burnaby, British Columbia, Canada V5A 1S6
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Free monoids play a central role in the theory of formal languages. Their endomorphisms appear naturally in the context of deterministic OL-schemes which trace their origin to biology. Closely related to such a scheme is a DOL-system which consists of a triple (X, φ, w) where X is a finite set, φ is an endomorphism of the free monoid X* and w ∈ X. The associated language is defined as the set {w, φw, φ2w,…} called a DOL-language. For a full discussion of this subject, we recommend the book [2] by Herman and Rozenberg.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 31 , Issue 1 , January 1989 , pp. 87 - 101
Copyright
Copyright © Glasgow Mathematical Journal Trust 1989

References

1.Fountain, J. and Petrich, M., Completely 0-simple semigroups of quotients, J. Algebra 101 (1986), 365–402.CrossRefGoogle Scholar
2.Herman, G. T. and Rozenberg, G., Developmental systems and languages (North Holland, 1975).Google Scholar
3.Petrich, M., Translational hull in semigroups and rings, Semigroup Forum 1 (1970), 283–360.CrossRefGoogle Scholar
4.M. Petrich, Introduction to semigroups (Merrill, 1973).Google Scholar