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Prikladnaya Diskretnaya Matematika, 2019, Number 45, Pages 85–89
DOI: https://doi.org/10.17223/20710410/45/9
(Mi pdm674)
 

This article is cited in 2 scientific papers (total in 2 papers)

Mathematical Backgrounds of Informatics and Programming

On complexity of the existential and universal theories of finite fields

A. N. Rybalov

Sobolev Institute of Mathematics, Omsk, Russia
Full-text PDF (610 kB) Citations (2)
References:
Abstract: Finite fields are the most important mathematical objects that are used for solving many practical problems of optimization, computer science, information transfer and cryptography. Many such problems can be formulated as problems connected with the solving systems of equations over fields. This leads to the need for the development of algebraic geometry. Algebraic geometry over such objects is closely related to properties of existential and universal theories. From a practical point of view, the most important are questions about decidability and computational complexity of these theories. In this paper, we study the computational complexity of existential and universal theories of finite fields. We prove that the existential theory of finite fields is NP-hard, and the universal theory of finite fields is co-NP-hard. This means that there are no polynomial algorithms that recognize these theories, provided the inequality of classes P, NP and co-NP.
Keywords: finite fields, universal theory, existential theory, NP-hardness.
Funding agency Grant number
Russian Science Foundation 19-11-00209
Bibliographic databases:
Document Type: Article
UDC: 510.52
Language: Russian
Citation: A. N. Rybalov, “On complexity of the existential and universal theories of finite fields”, Prikl. Diskr. Mat., 2019, no. 45, 85–89
Citation in format AMSBIB
\Bibitem{Ryb19}
\by A.~N.~Rybalov
\paper On complexity of the existential and universal theories of finite fields
\jour Prikl. Diskr. Mat.
\yr 2019
\issue 45
\pages 85--89
\mathnet{http://mi.mathnet.ru/pdm674}
\crossref{https://doi.org/10.17223/20710410/45/9}
\elib{https://elibrary.ru/item.asp?id=41192627}
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  • https://www.mathnet.ru/eng/pdm/y2019/i3/p85
  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Прикладная дискретная математика
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    Full-text PDF :74
    References:27
     
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