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ABSTRACT
Burmistrov S.V. Synthesis of discrete devices through the use of Boolean functions in
orthogonal form of representation. - Manuscript.
The thesis for the degree of candidate of technical sciences, specialty 05.13.05 – Computer Systems and
Components. - Cherkasy, Cherkasy State Technological University, 2016.
The thesis put and agreed to actual scientific problem of developing methods, models, algorithms for the
synthesis of discrete devices through the use of Boolean functions in the form of orthogonal representation.
For the first time the model of the internal structure of Boolean functions in the form of orthogonal
representations based on the phenomenon of decomposition of Boolean functions by setting fractal genetic
relationships between parent and subsidiaries Boolean functions in the form of fractal genetic embryo subsidiary
of Boolean functions provided a basis for developing a method of minimizing Boolean functions which are the
basis of discrete devices. This model makes it possible while maintaining the coefficients of complexity
implementation SL, SAD, improve the coefficient of SS in the case of commutative selecting logic elements by
10%, use selecting logic elements of a noncommutative input by 32% in the case of all the selecting logic
elements owned relyatyv-group <1 2 times.
Classification of subsets within the complete set of Boolean functions based on common traits described
values of indicators difficulty implementing discrete devices by grouping of Boolean functions in important
structural subsets, which provided the unification of the synthesis of discrete devices in the form of orthogonal
representation. This classification makes it possible to greatly reduce the number of avalanche dependence of the
objects within the complete set of Boolean functions increase the number of arguments and explore not unique
Boolean functions, and subsets of Boolean functions, of which there are several orders of magnitude smaller, and
therefore the systematic study of the whole process set of Boolean functions - several orders of magnitude faster
and easier in time.
For the first time the method of minimizing Boolean functions containing a large number of arguments in
orthogonal form of representation - matrix method of parallel decomposition based on the decomposition of
Boolean functions by introducing basic criteria to minimize that enables advance to predict the degree of
minimization of Boolean functions provided a reduction of time to minimize 4,7 times faster than previous
methods modifications parallel decomposition by increasing or decreasing the base value of the coefficient K.
Developed schematic diagram of cryptographic protection device – the device spelling of encoding
information using the models of the internal structure of Boolean functions, classifications of subsets within the
complete set of Boolean functions, minimization software system.
The research results implemented in enterprises and organizations of the Ministry of Education and
Science of Ukraine.
Keywords: orthogonal presentation of Boolean functions, genetic fractal model of Boolean functions,
basic factor K, matrix method of parallel decomposition, device spelling encoding information

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