On the conditions of complete asymptotics of the power of function classes of \(k\)-valued logic that preserve the finitary predicate
type: Item
instance of: scholarly article
title: On the conditions of complete asymptotics of the power of function classes of \(k\)-valued logic that preserve the finitary predicate
zbMATH Open document ID: 0932.03022
author: A. A. Voronenko
published in: Moscow University Computational Mathematics and Cybernetics
publication date: 2000-02-07T00:00:00Z
review text: An asymptotic for the logarithm of classes of monotone Boolean functions is well known from the results on Dedekind's problem. The asymptotic for the logarithm of a power for monotone \(k\)-valued functions is known as well. The asymptotic equivalence of the form \[ \log_k|F_{n}|\approx k^n , \tag{1} \] where \(F_{n}\) is a predicate-preserving class of functions for \(n \to \infty\) (\(n\) is the number of fixed variables), is proved in the article. Some necessary and some sufficient conditions for fulfilling the relation (1) are presented.
reviewed by: Sergei Georgievich Zhuravlev
Mathematics Subject Classification ID: 03B50
Mathematics Subject Classification ID: 94C10
zbMATH DE Number: 1400325
zbMATH Keywords: Boolean functions
zbMATH Keywords: \(k\)-valued functions
zbMATH Keywords: \(k\)-valued logics
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1400325