Transformation Method for Solving System of Boolean Algebraic Equations
Dostonjon Barotov,
Aleksey Osipov,
Sergey Korchagin,
Ekaterina Pleshakova,
Dilshod Muzafarov,
Ruziboy Barotov,
Denis Serdechnyy
Affiliations
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
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 Kn with the usual operations of addition and multiplication of numbers. Secondly, a transformed (approximated) system in Kn 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.
