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Many of the applied algorithms that have been developed for solving a system of logical equations or the Boolean satisfiability problem have solved the problem in the Boolean domain. However, other approaches have recently been developed and improved. One of these developments is the transformation of a system of logical equations to a real continuous domain. The essence of this development is that a system of logical equations is transformed into a system in a real domain and the solution is sought in a real continuous domain. A real continuous domain is a richer domain, as it involves many well-developed algorithms. In this paper, we have constructively transformed the solution of any system of logical equations with a unique solution into an optimization problem for a polylinear target function in a unit n -dimensional cube K n . The resulting polylinear target function in K n does not have a local minimum. We proved that only once by calculating the gradient of the polylinear target function at any interior point of the K n cube, we can determine the solution to the system of logical equations. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]