Variant Logic Construction Under Permutation and Complementary Operations on Binary Logic

Abstract

This chapter presents a binary logic framework whose function elements are invariant under permutation and complementary operations. The entire framework is described using 4 levels of hierarchy: n variables, 2 n states, 2 2 n functions, and 2 n !2 2 n logic functionals. Under the proposed framework, it is possible to determine higher level function complexity by analysing lower levels of organisation characteristics. These characteristics can be determined quite accurately because the symmetry conditions of variable and state organisations have invariant logic functions and a corresponding logic functional organisation. More symmetrical arrangement at state level creates more symmetrical permutations within the function space. Lower level properties are highly influential on the higher level properties of function components within a logic functional space. The proposed framework provides a logic foundation to describe complex binary systems using lower level properties, making analysis of systems more efficient and less calculation intensive. Different global coding schemes are discussed and typical two-variable cases of logic functionals are illustrated.

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“…According to the properties of the genome sequence, a new visualization method of the genome sequence is developed based on the research idea of data visualization technology and based on a variant logic system [24][25][26][27][28]. By adjusting the parameters, it can adapt to the genomic sequence with a large amount of data.…”

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“…According to the properties of the genome sequence, a new visualization method of the genome sequence is developed based on the research idea of data visualization technology and based on a variant logic system [24][25][26][27][28]. By adjusting the parameters, it can adapt to the genomic sequence with a large amount of data.…”