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Polylinear Transformation Method for Solving Systems of Logical Equations

Author

Listed:
  • Dostonjon Numonjonovich Barotov

    (Department of Data Analysis and Machine Learning, Financial University under the Government of the Russian Federation, 4-th Veshnyakovsky Passage, 4, 109456 Moscow, Russia)

  • Ruziboy Numonjonovich Barotov

    (Department of Mathematical Analysis, Khujand State University, 1 Mavlonbekova, Khujand 735700, Tajikistan)

Abstract

In connection with applications, the solution of a system of logical equations plays an important role in computational mathematics and in many other areas. As a result, many new directions and algorithms for solving systems of logical equations are being developed. One of these directions is transformation into the real continuous domain. The real continuous domain is a richer domain to work with because it features many algorithms, which are well designed. In this study, firstly, we transformed any system of logical equations in the unit n -dimensional cube K n into a system of polylinear–polynomial equations in a mathematically constructive way. Secondly, we proved that if we slightly modify the system of logical equations, namely, add no more than one special equation to the system, then the resulting system of logical equations and the corresponding system of polylinear–polynomial equations in K n + 1 is equivalent. The paper proposes an algorithm and proves its correctness. Based on these results, further research plans are developed to adapt the proposed method.

Suggested Citation

  • Dostonjon Numonjonovich Barotov & Ruziboy Numonjonovich Barotov, 2022. "Polylinear Transformation Method for Solving Systems of Logical Equations," Mathematics, MDPI, vol. 10(6), pages 1-10, March.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:6:p:918-:d:770222
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    Cited by:

    1. Dostonjon Numonjonovich Barotov & Ruziboy Numonjonovich Barotov & Vladimir Soloviev & Vadim Feklin & Dilshod Muzafarov & Trusunboy Ergashboev & Khudoyberdi Egamov, 2022. "The Development of Suitable Inequalities and Their Application to Systems of Logical Equations," Mathematics, MDPI, vol. 10(11), pages 1-9, May.

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