On some group properties of the functional presentation of information

Abstract

Abstract The paper provides an overview of research results on processing the information represented as Boolean functions. Actions of the hyperoctahedral group (or the Jevons group) are set on these functions. Information objects transformed by such actions have special frequency (entropy) characteristics. Such actions can be used to generate information messages with equal frequency and / or entropy characteristics. Preservation of the frequency characteristics of informational messages also allows us to solve one of the problems of classifying Boolean functions with respect to the Jevons group action. This problem has existed since the Harvard catalog was created and it has not been solved until the results of the studies covered in the paper were applied. Additionally, the possibilities of optimizing the calculation of actions tens and hundreds of times due to the properties of the elements of the Jevons group and modern processors are highlighted. This optimization allows the construction of information processing algorithms using the Jevons transformations for real data (commensurate with 1 MiB).