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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2024, Volume 21, Issue 1, Pages 62–69
DOI: https://doi.org/doi.org/10.33048/semi.2024.21.005 (Mi semr1668) 		 
Mathematical logic, algebra and number theory

On complexity of solving of equations over graphs

A. N. Rybalovab

a Sobolev Institute of Mathematics, Pevtsova 13, Omsk, 644099, Russia
b Sobolev Institute of Mathematics, prospekt Koptyuga 4, Novosibirsk, 630090, Russia
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DOI: https://doi.org/doi.org/10.33048/semi.2024.21.005
Abstract: In this paper the computational complexity of the problem of determining the compatibility of systems of equations without constants over an arbitrary fixed finite graph is studied. In this case, the graph is fixed, and the input is an arbitrary system of equations in the graph language without constants. A criterion is given for NP-completeness and polynomial decidability of this problem. Also its generic decidability in polynomial time is proved.
Keywords: NP-completeness, generic complexity, graphs, equations.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation FWNF-2022-0003
Received November 29, 2023, published February 13, 2024
Document Type: Article
UDC: 510.652
MSC: 11U99
Language: Russian
Citation: A. N. Rybalov, “On complexity of solving of equations over graphs”, Sib. Èlektron. Mat. Izv., 21:1 (2024), 62–69
Citation in format AMSBIB
\Bibitem{Ryb24}
\by A.~N.~Rybalov
\paper On complexity of solving of equations over graphs
\jour Sib. \`Elektron. Mat. Izv.
\yr 2024
\vol 21
\issue 1
\pages 62--69
\mathnet{http://mi.mathnet.ru/semr1668}
\crossref{https://doi.org/doi.org/10.33048/semi.2024.21.005}
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