We study the class of countable structures which can be presented by synchronous finite automata. We reduce the problem of existence of an automatic presentation of a structure to that for a graph. We exhibit a series of properties of automatic equivalence structures, linearly ordered sets and permutation structures. These serve as a first step in producing practical descriptions of some automatic structures or illuminating the complexity of doing so for others.
Citation:
Hajime Ishihara, Bakhadyr Khoussainov, Sasha Rubin, "Some Results on Automatic Structures," lics, pp.235, 17th Annual IEEE Symposium on Logic in Computer Science (LICS'02), 2002