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Complexity of some natural problems in automatic structures

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Abstract

We prove that the automatic isomorphism problem for automatic structures, the automatic automorphism problem for an automatic structure, and the automatic embedding problem for automatic structures are ∑ 01 -complete. We also prove that the embedding problem for automatic structures is ∑ 11 -complete.

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References

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    1. N. S. Vinokurov
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    Original Russian Text Copyright © 2005 Vinokurov N. S.

    The author was partially supported by the State Maintenance Program for the Leading Scientific Schools of the Russian Federation (Grant NSh-2112.2003.1).

    Translated from Sibirski \( \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{\imath} \) Matematicheski \( \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{\imath} \) Zhurnal, Vol. 46, No. 1, pp. 71–78, January–February, 2005.

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    Vinokurov, N.S. Complexity of some natural problems in automatic structures. Sib Math J 46, 56–61 (2005). https://doi.org/10.1007/s11202-005-0005-2

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    • DOI: https://doi.org/10.1007/s11202-005-0005-2

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