A study is made of Clifford semigroups (strong semilattices of groups) admitting automatic structures. It is shown to be decidable whether an automatic semigroup is a Clifford semigroup. A geometric characterization of automatic structures for Clifford semigroups is developed. Some properties of automatic groups, such as finite presentability, admitting a prefix-closed automatic structure, and invariance of automaticity under change of generators, are found to generalize to Clifford semigroups. Conditions are investigated under which a Clifford semigroup consisting of a strong semilattices of free groups or a strong semilattices of abelian groups is automatic.
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