Polylinear Transformation Method for Solving Systems of Logical Equations

Dostonjon Numonjonovich Barotov and Ruziboy Numonjonovich Barotov
Additional contact information
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

Mathematics, 2022, vol. 10, issue 6, 1-10

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.

Keywords: polylinear functions; algorithms; harmonic functions; Zhegalkin polynomials; logical operations; systems of Boolean algebraic equations; algebraic cryptanalysis; approximation; Boolean satisfiability problem; numerical optimization (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
https://www.mdpi.com/2227-7390/10/6/918/pdf (application/pdf)
https://www.mdpi.com/2227-7390/10/6/918/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:10:y:2022:i:6:p:918-:d:770222

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().