Concave continuations of Boolean-like functions and some of their properties
The Bulletin of Irkutsk State University. Series Mathematics, Tome 51 (2025), pp. 82-100
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In this paper, we present concave continuations of discrete functions defined on the vertices of an $n$-dimensional unit cube, an $n$-dimensional arbitrary cube, and an $n$-dimensional arbitrary parallelepiped. It is constructively proved that, firstly, for any discrete function $f_D$ defined on the vertices of $\mathbb{G}$, where $\mathbb{G}$ is one of these three sets, the cardinality of the set of its concave continuations on $\mathbb{G}$ is equal to infinity, and, secondly, there is a function $f_{NR}$ that is the minimum among all its concave continuations on $\mathbb{G}$. The uniqueness and continuity of the function $f_{NR}$ on $\mathbb{G}$ are also proved.
Keywords:
discrete functions, concave continuations of discrete functions, pseudo-Boolean functions, Boolean functions.
@article{IIGUM_2025_51_a5,
author = {D. N. Barotov},
title = {Concave continuations of {Boolean-like} functions and some of their properties},
journal = {The Bulletin of Irkutsk State University. Series Mathematics},
pages = {82--100},
publisher = {mathdoc},
volume = {51},
year = {2025},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/IIGUM_2025_51_a5/}
}
TY - JOUR AU - D. N. Barotov TI - Concave continuations of Boolean-like functions and some of their properties JO - The Bulletin of Irkutsk State University. Series Mathematics PY - 2025 SP - 82 EP - 100 VL - 51 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/IIGUM_2025_51_a5/ LA - ru ID - IIGUM_2025_51_a5 ER -
D. N. Barotov. Concave continuations of Boolean-like functions and some of their properties. The Bulletin of Irkutsk State University. Series Mathematics, Tome 51 (2025), pp. 82-100. http://geodesic.mathdoc.fr/item/IIGUM_2025_51_a5/