Abstract
The notion of automaticity has been widely studied in groups and some progress has been made in understanding the notion in the wider context of semigroups. The purpose of this paper is to study automatic completely-simple semigroups. We show that, if \(S\) is a completely-simple semigroup \(M[H;I;J;P]\) (with \(I\) and \(J\) finite), then \(S\) is automatic if and only if the group \(H\) is automatic. As a consequence, we deduce that automatic completely-simple semigroups are finitely presented. We also show that automatic completely-simple semigroups are characterized by the fellow traveller property and also that the existence of an automatic structure is independent of the choice of generating set.
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