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Sibirskii Matematicheskii Zhurnal, 2022, Volume 63, Number 5, Pages 953–974
DOI: https://doi.org/10.33048/smzh.2022.63.501
(Mi smj7706)
 

This article is cited in 8 scientific papers (total in 8 papers)

Finitely generated structures computable in polynomial time

P. E. Alaev

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
Full-text PDF (455 kB) Citations (8)
References:
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.
Keywords: computable structure, polynomial computability, algorithm complexity, semigroup, group, ring, field.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation FWNF-2022-0011
Russian Foundation for Basic Research 20-01-00300
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).
Received: 18.12.2021
Revised: 23.04.2022
Accepted: 15.06.2022
English version:
Siberian Mathematical Journal, 2022, Volume 63, Issue 5, Pages 801–818
DOI: https://doi.org/10.1134/S0037446622050019
Bibliographic databases:
Document Type: Article
UDC: 510.52+510.67+512.5
MSC: 35R30
Language: Russian
Citation: P. E. Alaev, “Finitely generated structures computable in polynomial time”, Sibirsk. Mat. Zh., 63:5 (2022), 953–974; Siberian Math. J., 63:5 (2022), 801–818
Citation in format AMSBIB
\Bibitem{Ala22}
\by P.~E.~Alaev
\paper Finitely generated structures computable in polynomial time
\jour Sibirsk. Mat. Zh.
\yr 2022
\vol 63
\issue 5
\pages 953--974
\mathnet{http://mi.mathnet.ru/smj7706}
\crossref{https://doi.org/10.33048/smzh.2022.63.501}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4494004}
\transl
\jour Siberian Math. J.
\yr 2022
\vol 63
\issue 5
\pages 801--818
\crossref{https://doi.org/10.1134/S0037446622050019}
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  • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Full-text PDF :33
    References:29
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