# The isomorphism problem on classes of automatic structures with transitive relations

@article{Kuske2013TheIP,
title={The isomorphism problem on classes of automatic structures with transitive relations},
author={Dietrich Kuske and J. Liu and Markus Lohrey},
journal={Transactions of the American Mathematical Society},
year={2013},
volume={365},
pages={5103-5151}
}
• Published 20 May 2013
• Mathematics
• Transactions of the American Mathematical Society
Automatic structures are finitely presented structures where the universe and all relations can be recognized by finite automata. It is known that the isomorphism problem for automatic structures is complete for Σ 1 , the first existential level of the analytical hierarchy. Positive results on ordinals and on Boolean algebras raised hope that the isomorphism problem is simpler for transitive relations. We prove that this is not the case. More precisely, this paper shows: (i) The isomorphism…
22 Citations

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