# AUTOMATIC AND POLYNOMIAL-TIME ALGEBRAIC STRUCTURES

@article{Bazhenov2019AUTOMATICAP,
title={AUTOMATIC AND POLYNOMIAL-TIME ALGEBRAIC STRUCTURES},
author={Nikolay Bazhenov and Matthew Harrison-Trainor and Iskander Sh. Kalimullin and Alexander G. Melnikov and Keng Meng Ng},
journal={The Journal of Symbolic Logic},
year={2019},
volume={84},
pages={1630 - 1669}
}
• Published 1 December 2019
• Computer Science
• The Journal of Symbolic Logic
Abstract A structure is automatic if its domain, functions, and relations are all regular languages. Using the fact that every automatic structure is decidable, in the literature many decision problems have been solved by giving an automatic presentation of a particular structure. Khoussainov and Nerode asked whether there is some way to tell whether a structure has, or does not have, an automatic presentation. We answer this question by showing that the set of Turing machines that represent…
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