Burmistrov S. The synthesis of discrete devices through the use of Boolean functions in the form of orthogonal representation

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.