Abstract
We give some simple description for the finitely generated structures with P-computable isomorphic presentation; i.e., presentation computable in polynomial time. The description is close to the formulation of a Remmel and Friedman theorem. We prove that each finitely generated substructure of a P-computable structure also has a P-computable presentation. The description is applied to the classes of finitely generated semigroups, groups, unital commutative rings and fields, as well as ordered unital commutative rings and fields. We prove that every finitely generated commutative ring or a field has a P-computable presentation.
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Acknowledgment
The author is grateful to S.S. Goncharov, N.S. Romanovskii, A.G. Myasnikov, V.L. Selivanov, and E. Mayr for discussions of the paper, and useful advice that improved exposition. The author is also grateful to the anonymous reviewer for pointing out an error in the first version of the article.
Funding
The study was carried out within the framework of the State Task to the Sobolev Institute of Mathematics (Project FWNF–2022–0011) and partially supported by the RFBR (Project 20–01–00300).
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Translated from Sibirskii Matematicheskii Zhurnal, 2022, Vol. 63, No. 5, pp. 953–974. https://doi.org/10.33048/smzh.2022.63.501
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Alaev, P.E. Finitely Generated Structures Computable in Polynomial Time. Sib Math J 63, 801–818 (2022). https://doi.org/10.1134/S0037446622050019
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DOI: https://doi.org/10.1134/S0037446622050019