Geodesic
Polylinear continuations of some discrete functions and an algorithm for finding them
Numerical methods and programming, Tome 24 (2023) no. 1, pp. 10-23.

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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.
Keywords: polylinear functions, harmonic functions, systems of Boolean equations, pseudo-Boolean functions, algorithms. 
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     author = {Dostonjon N. Barotov and Ruziboy N. Barotov},
     title = {Polylinear continuations of some discrete functions and an algorithm for finding them},
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     url = {http://geodesic.mathdoc.fr/item/VMP_2023_24_1_a0/}
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Dostonjon N. Barotov; Ruziboy N. Barotov. Polylinear continuations of some discrete functions and an algorithm for finding them. Numerical methods and programming, Tome 24 (2023) no. 1, pp. 10-23. http://geodesic.mathdoc.fr/item/VMP_2023_24_1_a0/