Abstract
The classification of monotone Boolean functions (MBF) into types is given. The notion of the maximum type of MBF is introduced, and the shift-sum types are constructed. The matrices of type distribution by rank are constructed. Convenient algorithms for finding the number of maximum types and the maximum types themselves are presented. The proposed methods can be used to analyze large MBF ranks.
Highlights
In this paper we introduce the concept of the maximum type, which was not previously encountered in the literature
In 1997 Engel entered the concept of the profile of monotone Boolean function [1]
Given an n-variable monotone Boolean functions (MBF) f where f ≡/ 1, the profile of f is a vector of length n ( a1, a2,..., an ), where the ith entry is equal to the number of minimal terms of f which are i-sets
Summary
In this paper we introduce the concept of the maximum type, which was not previously encountered in the literature. A vector T = (a0 , a1,..., ai ,..., an ) is an MBF type if the i-th component of the vector ai is equal to the number of conjunctive clauses in the form of DNF, which consist of i For rank 2, the maximal is 3 types: (0,0,1), (0,2,0) and variables, i.e. have length i.
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