On the reduction of a system of Boolean equations to an equivalent system of polynomial equations
Year: 2024
Type: article
Abstract: In this paper, we study the problem of constructing a special continuation of a Boolean function to the entire space Rπ, thanks to which, without adding any restrictions, asystem of Boolean equations is transformed into an equivalent system of polynomial equations. As a result of the study, for any Boolean function (π₯1, π₯2, ..., π₯π), a corresponding infinitely differentiable rational function (π₯1, π₯2, ..., π₯π) is constructed such thatππ (π₯1, π₯2, ..., π₯π) β {0, 1} ββππ (π₯1, π₯2, ..., π₯π) β {0, 1} ββ.).)ππ1122π π 1122{ (π₯1, π₯2, ..., π₯π) β {0, 1}ππ (π₯ , , ..., π₯π) = (π₯ , , ..., (π₯ , , ..., π₯π) = (π₯ , , ..., π (π₯ , , ..., π₯π) = (π₯ , , ..., (π₯ , , ..., π₯π) = (π₯ , , ..., Thanks to the constructed function (π₯1, π₯2, ..., π₯π), firstly, without adding any restrictions, an arbitrary system of Boolean equations is transformed into an equivalent system of rational equations, and secondly, the solution of the transformed an equivalent system of rational equations is reduced to the problem of numerical minimization of some infinitely differentiable target function, solved by optimization methods, and to an equivalent system of polynomial equations, solved and analyzed by the F4 algorithm.
Authors: D.N. Barotov, R.N. Barotov
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W4402997101