On properties of multiaffine predicates on a finite set
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Svetlana N. Selezneva
Abstract
We consider predicates on a finite set that are invariant with respect to an affine operation fG, 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 Gq of addition modulo q=ps, where p is a prime number and s=1. We establish the predicate multiaffinity criterion for a group Gq. 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 Gq. 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 Gq, if predicates are specified by DNF.
Note
Originally published in Diskretnaya Matematika (2021) 33, №4, 141–152 (in Russian).
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© 2023 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- On distance-regular graphs Γ of diameter 3 for which Γ3 is a triangle-free graph
- Limit theorems for the maximal tree size of a Galton – Watson forest in the critical case
- Short complete diagnostic tests for circuits with two additional inputs in some basis
- Nonlinearity of functions over finite fields
- The limit joint distributions of statistics of three tests of the NIST package
- On properties of multiaffine predicates on a finite set
- On the universality of product for classes of linear functions of two variables
Artikel in diesem Heft
- Frontmatter
- On distance-regular graphs Γ of diameter 3 for which Γ3 is a triangle-free graph
- Limit theorems for the maximal tree size of a Galton – Watson forest in the critical case
- Short complete diagnostic tests for circuits with two additional inputs in some basis
- Nonlinearity of functions over finite fields
- The limit joint distributions of statistics of three tests of the NIST package
- On properties of multiaffine predicates on a finite set
- On the universality of product for classes of linear functions of two variables
