Transformation Method for Solving System of Boolean Algebraic Equations

Dostonjon Barotov, Aleksey Osipov, Sergey Korchagin, Ekaterina Pleshakova, Dilshod Muzafarov, Ruziboy Barotov and Denis Serdechnyy
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Dostonjon 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
Aleksey Osipov: Department of Data Analysis and Machine Learning, Financial University under the Government of the Russian Federation, 4-th Veshnyakovsky Passage, 4, 109456 Moscow, Russia
Sergey Korchagin: Department of Data Analysis and Machine Learning, Financial University under the Government of the Russian Federation, 4-th Veshnyakovsky Passage, 4, 109456 Moscow, Russia
Ekaterina Pleshakova: Department of Data Analysis and Machine Learning, Financial University under the Government of the Russian Federation, 4-th Veshnyakovsky Passage, 4, 109456 Moscow, Russia
Dilshod Muzafarov: Department of Mathematical Analysis, Khujand State University, 1 Mavlonbekova, Khujand 735700, Tajikistan
Ruziboy Barotov: Department of Mathematical Analysis, Khujand State University, 1 Mavlonbekova, Khujand 735700, Tajikistan
Denis Serdechnyy: Department of Innovation Management, State University of Management, Ryazansky pr., 99, 109542 Moscow, Russia

Mathematics, 2021, vol. 9, issue 24, 1-12

Abstract: In recent years, various methods and directions for solving a system of Boolean algebraic equations have been invented, and now they are being very actively investigated. One of these directions is the method of transforming a system of Boolean algebraic equations, given over a ring of Boolean polynomials, into systems of equations over a field of real numbers, and various optimization methods can be applied to these systems. In this paper, we propose a new transformation method for Solving Systems of Boolean Algebraic Equations (SBAE). The essence of the proposed method is that firstly, SBAE written with logical operations are transformed (approximated) in a system of harmonic-polynomial equations in the unit n -dimensional cube K n with the usual operations of addition and multiplication of numbers. Secondly, a transformed (approximated) system in K n is solved by using the optimization method. We substantiated the correctness and the right to exist of the proposed method with reliable evidence. Based on this work, plans for further research to improve the proposed method are outlined.

Keywords: harmonic functions; Boolean polynomials; logical operations; systems of Boolean algebraic equations; algebraic cryptanalysis; approximation; Boolean satisfiability problem; optimization; Universal SAT problem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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