Polylinear continuations of some discrete functions and an algorithm for finding them

Authors

DOI:

https://doi.org/10.26089/NumMet.v24r102

Keywords:

polylinear functions, harmonic functions, systems of Boolean equations, pseudo-Boolean functions, algorithms

Abstract

In this paper, we study the existence and uniqueness of polylinear continuations of some discrete functions. It is proved that for any Boolean function, there exists a corresponding polylinear continuation and it is unique. An algorithm for finding a polylinear continuation of a Boolean function is proposed and its correctness is proved. Based on the result of the proposed algorithm, explicit forms of polylinear continuations are found first for a Boolean function and then for an arbitrary function defined only at the vertices of an n-dimensional unit cube, an arbitrary cube, and a parallelepiped, and in each particular case the uniqueness of the corresponding polylinear continuations is proved.

Author Biographies

Dostonjon N. Barotov

Financial University under the Government of the Russian Federation
Department of Data Analysis and Machine Learning
• Senior Lecturer

Ruziboy N. Barotov

Khujand state university named after academician Bobojon Gafurov
Department of Mathematical Analysis named after Professor A. Mukhsinov
• Doctoral Student

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Published

21-01-2023

How to Cite

Баротов Д. Н., Баротов Р. Н. Polylinear Continuations of Some Discrete Functions and an Algorithm for Finding Them // Numerical Methods and Programming (Vychislitel’nye Metody i Programmirovanie). 2023. 24. 10-23. doi 10.26089/NumMet.v24r102

Issue

Section

Methods and algorithms of computational mathematics and their applications