Geodesic
On properties of multiaffine predicates on a finite set
Diskretnaya Matematika, Tome 33 (2021) no. 4, pp. 141-152

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We consider predicates on a finite set that are invariant with respect to an affine operation $f_G$, where $G$ is some Abelian group. Such predicates are said to be multiaffine for the group $G$. Special attention is paid to predicates that are affine for a group $G_q$ of addition modulo $q = p^s$, where $p$ is a prime number and $s \geqslant 1$. We establish the predicate multiaffinity criterion for a group $G_q$. Then we introduce disjunctive normal forms (DNF) for predicates on a finite set and obtain properties of DNFs of predicates that are multiaffine for a group $G_q$. Finally we show how these properties can be used to design a polynomial algorithm that decides satisfiability of a system of predicates which are multiaffine for a group $G_q$, if predicates are specified by DNF.
Keywords: predicate on a finite set, function on a finite set, affine operation, multiaffinity, disjunctive normal form, algorithm, complexity, polynomial algorithm. 
@article{DM_2021_33_4_a11,
     author = {S. N. Selezneva},
     title = {On properties of multiaffine predicates on a finite set},
     journal = {Diskretnaya Matematika},
     pages = {141--152},
     publisher = {mathdoc},
     volume = {33},
     number = {4},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2021_33_4_a11/}
}
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S. N. Selezneva. On properties of multiaffine predicates on a finite set. Diskretnaya Matematika, Tome 33 (2021) no. 4, pp. 141-152. http://geodesic.mathdoc.fr/item/DM_2021_33_4_a11/