Affiliation:
1. Lomonosov Moscow State University , Moscow , Russia
Abstract
Abstract
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=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.
Subject
Applied Mathematics,Discrete Mathematics and Combinatorics
Reference15 articles.
1. Schaefer T., “Complexity of satisfiability problems”, Proc. 10th ACM Symp. Theory of Computing, ACM Press, 1978, 216–226.
2. Jeavons P., Coher D., Gyssens M., “Closure properties of constraints”, J. ACM, 44 (1997), 527–548.
3. Gorshkov S. P., “On the complexity of recognizing multiaffinity, bijunctivity, weak positivity and weak negativity”, Obozr. promyshl. i prikl. matem., 4:2 (1997), 216–237 (in Russian).
4. Selezneva S.N., “Multiaffine polynomials over a finite field”, Discrete Math. Appl., 31:6 (2021), 421–430.
5. Selezneva S.N., “On bijunctive predicates over a finite set”, Discrete Math. Appl., 29:1 (2019), 49–58.