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Sibirskii Matematicheskii Zhurnal, 2025, Volume 66, Number 3, Pages 450–464
DOI: https://doi.org/10.33048/smzh.2025.66.310 (Mi smj7956) 		 
The np-completeness of the consistency problem for systems of Diophantine equations over finite configurations

N. T. Kogabaevab

a Sobolev Institute of Mathematics, Novosibirsk, Russia
b Novosibirsk State University, Novosibirsk, Russia
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DOI: https://doi.org/10.33048/smzh.2025.66.310
Abstract: Studying finite systems of Diophantine equations over finite configurations, we prove that the consistency problem for such systems is NP-complete.
Keywords: configuration, incidence, system of equations, nondeterministic Turing machine, NP-complete problem.
Funding agency Grant number
Russian Science Foundation 23-11-00170
The work was supported by the Russian Science Foundation (Project 23–11–00170, https://rscf.ru/project/23-11-00170/).
Received: 14.11.2024
Revised: 14.11.2024
Accepted: 25.04.2025
English version:
Siberian Mathematical Journal, 2025, Volume 66, Issue 3, Pages 702–714
DOI: https://doi.org/10.1134/S0037446625030103
Document Type: Article
UDC: 510.522+514.146
Language: Russian
Citation: N. T. Kogabaev, “The np-completeness of the consistency problem for systems of Diophantine equations over finite configurations”, Sibirsk. Mat. Zh., 66:3 (2025), 450–464; Siberian Math. J., 66:3 (2025), 702–714
Citation in format AMSBIB
\Bibitem{Kog25}
\by N.~T.~Kogabaev
\paper The np-completeness of the consistency problem for systems of Diophantine equations over finite configurations
\jour Sibirsk. Mat. Zh.
\yr 2025
\vol 66
\issue 3
\pages 450--464
\mathnet{http://mi.mathnet.ru/smj7956}
\transl
\jour Siberian Math. J.
\yr 2025
\vol 66
\issue 3
\pages 702--714
\crossref{https://doi.org/10.1134/S0037446625030103}
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