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Sibirskii Matematicheskii Zhurnal, 2023, Volume 64, Number 2, Pages 321–338
DOI: https://doi.org/10.33048/smzh.2023.64.207 (Mi smj7764) 		 
Systems of diophantine equations over finite configurations

N. T. Kogabaev

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
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DOI: https://doi.org/10.33048/smzh.2023.64.207
Abstract: Under study are the finite systems of Diophantine equations over finite configurations. We propose some consistency verification procedure for such a system and use the output of the procedure to constructing the complete solution set. We estimate the running time of the procedure in general and distinguish the class of systems for which the consistency problem is decidable in polynomial time.
Keywords: configuration, incidence, system of equations, computational complexity.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation FWNF-2022-0011
The work was carried out in the framework of the State Task to the Sobolev Institute of Mathematics (Project FWNF–2022–0011).
Received: 27.11.2022
Revised: 27.11.2022
Accepted: 10.01.2023
English version:
Siberian Mathematical Journal, 2023, Volume 64, Issue 2, Pages 325–337
DOI: https://doi.org/10.1134/S0037446623020076
Bibliographic databases:
Document Type: Article
UDC: 510.52+514.146
MSC: 35R30
Language: Russian
Citation: N. T. Kogabaev, “Systems of diophantine equations over finite configurations”, Sibirsk. Mat. Zh., 64:2 (2023), 321–338; Siberian Math. J., 64:2 (2023), 325–337
Citation in format AMSBIB
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\by N.~T.~Kogabaev
\paper Systems of diophantine equations over finite configurations
\jour Sibirsk. Mat. Zh.
\yr 2023
\vol 64
\issue 2
\pages 321--338
\mathnet{http://mi.mathnet.ru/smj7764}
\crossref{https://doi.org/10.33048/smzh.2023.64.207}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4567667}
\transl
\jour Siberian Math. J.
\yr 2023
\vol 64
\issue 2
\pages 325--337
\crossref{https://doi.org/10.1134/S0037446623020076}
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