Constructive Representation of the Jevons Group for Engineering Solutions of Information Processing

A. M. Kukartsev, Senior Lecturer, e-mail: amkukarcev@yandex.ru, A. A. Kuznetsov, Professor, e-mail: kuznetsov@sibsau.ru, Siberian State Aerospace University named after academician M. F. Reshetnev, Krasnoyarsk

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. 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. There is a correspondence between arguments of the function and coordinates of the vector. The correspondence allows analyzing and converting binary vectors using methods of theory of the Boolean functions. So there is a need for mathematical methods and algorithms which connect the Boolean vectors and the Boolean functions. The main object in the solution of this problem is the Jevons group. It is discussed the constructive representation of the Jevons group in the article. We give correct rules of computation which are needed for creating of software and hardware. The proposed rules have been successfully tested in the solution of equations of the Jevons group's action on the set of the Boolean functions. 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. 25–33