Automatic completely-simple semigroups
The main result of the article states that a Rees matrix semigroup \(M[H;I,J;P]\) with finite \(I\) and \(J\) is automatic if and only if the group \(H\) is automatic. As a corollary, it is verified that an automatic Rees matrix semigroup is finitely presented. The authors also show that automatic completely simple semigroups are characterized by the fellow traveller property. One more result is that the existence of an automatic structure for a Rees matrix semigroup is independent of the choice of the generating set.
scientific article; zbMATH DE number 1822374