We study two subclasses of the class of automatic structures: automatic structures of polynomial growth and Presburger structures. We present algebraic characterisations of the groups and the equivalence structures in these two classes.

翻译：我们研究了自动结构类的两个子类：多项式增长自动结构与普雷斯伯格结构。我们为这两个类别中的群结构与等价结构提供了代数特征刻画。