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Testing the Satisfiability of Algebraic Formulas over the Field of Two Elements

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Abstract

We construct a probabilistic polynomial algorithm for testing the satisfiability of algebraic formulas of depth 3 over the two-element field, 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.

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Funding

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.

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Authors and Affiliations

  1. Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences, Moscow, Russia

    M. N. Vyalyi

  2. National Research University—Higher School of Economics, Moscow, Russia

    M. N. Vyalyi

  3. Moscow Institute of Physics and Technology (State University), Moscow, Russia

    M. N. Vyalyi

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  1. M. N. Vyalyi
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Translated from Problemy Peredachi Informatsii, 2023, Vol. 59, No. 1, pp. 64–70. https://doi.org/10.31857/S0555292323010059

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Vyalyi, M.N. Testing the Satisfiability of Algebraic Formulas over the Field of Two Elements. Probl Inf Transm 59, 57–62 (2023). https://doi.org/10.1134/S0032946023010052

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  • DOI: https://doi.org/10.1134/S0032946023010052

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