DOI: 10.17587/prin.7.29-36

About Actions of the Jevons Group on Sets of Binary Vectors and Boolean Functions for Engineering Solutions of Information Processing

A. M. Kukartsev, amkukarcev@yandex.ru, A. A. Kuznetsov, kuznetsov@sibsau.ru, Siberian State Aerospace University named after academician M. F. Reshetnev, Krasnoyarsk, 660014, Russian Federation

Corresponding author: Kukartsev Anatolii M., Senior Lecturer, Siberian State Aerospace University named after academician M. F. Reshetnev, Krasnoyarsk, 660014, Russian Federation, e-mail: amkukarcev@yandex.ru

Actions of the Jevons group on the set of binary vectors of the Boolean functions allow to build engineering solutions for the submission and processing of information. The materials are a continuation of the article "Constructive representation of the Jevons group for engineering solutions of information processing". In this case information will be presented as a binary vector of length 2n, associated with the Boolean function. The binary vector is a column of values of the Boolean function. This part provides rules for computing and commutating on the set of Boolean vectors and Boolean functions. The notion of equivalent actions (equimorphisms) on the set of Boolean functions is presented. Equimorphisms are allowed to improve significantly the performance of software and hardware implementations. As a result (along with the previous article) we offer a complete mathematical apparatus for converting information by means of elements of the Jevons group. It concludes with recommendations on the use of equimorphisms in real problems' descriptions and solutions. We have developed the library of software functions "domain operations processor" (or dop) based on the rules. The library is licensed under the GNU Lesser General Public License.

Keywords: information representation, the Jevons group, action on the set, binary vectors, Boolean functions, computational tools

pp. 29–36

For citation:
Kukartsev A. M., Kuznetsov A. A. About Actions of the Jevons Group on Sets of Binary Vectors and Boolean Functions for Engineering Solutions of Information Processing, Programmnaya Ingeneria, 2016, vol. 7, no 1, pp. 29—36.

This work was supported by the Grant of Russian Federation President, project no. MD-3952.2015.9