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.

@article{paperbot4033,
  title = {Simple Classes of Automatic Structures},
  author = {Achim Blumensath},
  journal = {Logical Methods in Computer Science},
  volume = {Volume 22, Issue 1},
  year = {2026},
  doi = {10.46298/lmcs-22(1:5)2026}
}