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Problemy Peredachi Informatsii, 2023, Volume 59, Issue 1, Pages 64–70
DOI: https://doi.org/10.31857/S0555292323010059 (Mi ppi2391) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Large Systems

Testing the satisfiability of algebraic formulas over the field of two elements

M. N. Vyalyiabc

a Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences, Moscow, Russia
b National Research University—Higher School of Economics, Moscow, Russia
c Moscow Institute of Physics and Technology (State University), Moscow, Russia
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DOI: https://doi.org/10.31857/S0555292323010059
Abstract: We construct a probabilistic polynomial algorithm for testing the satisfiability of algebraic formulas of depth 3 over the two-elementfield, with addition as the top operation in the formulas. An algorithm with the same characteristics exists for the problem of testing whether a polynomial given by formulas of this type is identically zero (PIT problem). However, these problems and algorithms for their solution are essentially different. The probabilistic algorithm for the PIT problem is based on the Schwartz–Zippel lemma, whereas the satisfiability testing algorithm proposed in this paper is based on the Valiant–Vazirani lemma.
Keywords: satisfiability of Boolean formulas, probabilistic algorithm, algebraic formulas.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 0063-2019-0003
HSE Basic Research Program
The research was carried out under the Fundamental Research Program of the Higher School of Economics; it was also supported in part within the framework of the State Assignment no. 0063-2019-0003.
Received: 18.12.2022
Revised: 12.02.2023
Accepted: 13.02.2023
English version:
Problems of Information Transmission, 2023, Volume 59, Issue 1, Pages 57–62
DOI: https://doi.org/10.1134/S0032946023010052
Bibliographic databases:
Document Type: Article
UDC: 621.391 : 519.16
Language: Russian
Citation: M. N. Vyalyi, “Testing the satisfiability of algebraic formulas over the field of two elements”, Probl. Peredachi Inf., 59:1 (2023), 64–70; Problems Inform. Transmission, 59:1 (2023), 57–62
Citation in format AMSBIB
\Bibitem{Vya23}
\by M.~N.~Vyalyi
\paper Testing the satisfiability of algebraic formulas over the field of two elements
\jour Probl. Peredachi Inf.
\yr 2023
\vol 59
\issue 1
\pages 64--70
\mathnet{http://mi.mathnet.ru/ppi2391}
\crossref{https://doi.org/10.31857/S0555292323010059}
\edn{https://elibrary.ru/RMKBBO}
\transl
\jour Problems Inform. Transmission
\yr 2023
\vol 59
\issue 1
\pages 57--62
\crossref{https://doi.org/10.1134/S0032946023010052}
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    • This publication is cited in the following 1 articles:
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