Analysis and Recurrent Calculation of 8th Rank MBF of Maximal Types

摘要

This paper is a continuation of the study of monotone Boolean functions (MBFs) of maximal types using MBF partitioning into schemes. When factor out any of the variables out of the brackets, two MBFs are formed: left (in brackets) and right. It proved the possibility of such that take the one of the variables out of the brackets such that any conjunctive clause in the left MBF consists of fewer variables than any conjunctive clause in the right MBF. In addition, the left MBF absorbs the right MBF. For the first time, an important class of MBF of rank 8 - MBF of maximal types was studied and analyzed. The number of MBFs of maximal types of rank 8 and the number of isomorphic classes of such MBFs obtained from pairs of MBFs 7 rank are calculated. An example of the recursive construction MBF 8 rank is shown. Tables and schemes for MBF 8th rank are given. The dependences found between the maximal types MBF nth rank and rank n–1 make it possible to reduce the enumeration of MBFs by constructing rank 8 equivalence classes from rank 7 equivalence classes. The proposed methods are convenient for the analysis of large MBF ranks.