On syntactic monoids of biunitary submonoids determined by homomorphisms from free semigroups onto completely simple semigroups
We deal with the maximal bifix code construction which is a natural generalization of a group code construction. For a surjective morphism phi from a free monoid A* onto a completely simple semigroup with an adjoined identity M (G; I, J; Sigma)(1) and a submonoid S of M (G; I, J; Sigma)(1), under certain conditions, the base of a submonoid phi(-1) (S) is a maximal bifix code X. We investigate the relationships between the surjective morphism phi and the syntactic monoid of the monoid generated by X. (c) 2005 Elsevier B.V. All rights reserved.
syntactic monoid completely simple semigroup bifix code group code