Polylinear continuations of some discrete functions and an algorithm for finding them - Barotov, Dostonjon N.; Barotov, Ruziboy N. (Numerical Methods and Programming (Vychislitel'nye Metody i Programmirovanie), 2023)
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.