Kovalchuk D. Models and methods for fast data processing based on the use of a residual class system

Kovalchuk D.M. Models and methods for fast data processing based on the use of a residual class system. – Qualification scholarly paper: a manuscript. The dissertation submitted for obtaining the Doctor of Philosophy degree in Information Technology: Speciality 122 – Computer science. V. N Karazin Kharkiv National University, Ministry of Education and Science of Ukraine, Kharkiv, 2024. The dissertation is devoted to increasing the speed of information processing by software and hardware systems and complexes with elements of artificial intelligence due to the use of models and methods of fast data processing based on the application of the residual class system (RCS). The first chapter analyzes the problems of constructing hardware and software systems and complexes with elements of artificial intelligence. The analysis of the capabilities of software and hardware systems and complexes with elements of artificial intelligence indicates that they do not meet the increased requirements for information processing speed, which makes it urgent to study new models and methods. The objectives of the dissertation research are formulated: improvement of the method of adding and subtracting remainders of numbers modulo RCS; improvement of the method of tabular implementation of multiplication of two remainders of numbers due to the ability to perform the operation in the complex domain; improvement of the mathematical model of the process of raising remainders of integers to an arbitrary degree of natural in RCS; practical confirmation of the performance and likelihood of the developed models and methods. Which will be addressed in the following sections of the dissertation. In the second chapter, the method of adding and subtracting the remainders of numbers modulo RCS was further developed, taking into account the design of modulo adders with a correction value ∆QR>0. An HDL model of a modulo mi=17 adder in Verilog has been developed. An adder of a modulo mi=17 has been developed in the Quartus II environment. The considered examples and simulation results of the implementation of the modular addition method for various values of xi and yi modulo mi RCS confirm the practical implementation of the proposed method. An HDL model for performing a subtraction operation on a modulo adder mi=17 in the Verylog language and a block diagram in the Quartus II environment have been developed. The considered examples and simulation results of the implementation of the subtraction operation (xi - yi)mod mi for various residues xi and yi confirm the practical implementation of the proposed method. In the third chapter, the method of tabular implementation of multiplication of two remainders of numbers in a RCS is improved due to the possibility of performing the operation in the complex domain, based on the use of Gauss's first fundamental theorem on isomorphism between the set of real and complex numbers, which increases the speed of implementation of the multiplication operation in the RCS. The mathematical model of the process of raising integers to an arbitrary power of a natural number in the RCS has been improved due to the possibility of performing the operation of raising integers to a power in both positive and negative numerical ranges, which increases the performance of the implementation of the operation of raising integers to a power in the RCS. The results of computer modeling in the Microsoft Visual Studio 2015 environment confirm the practical implementation of the proposed method. The fourth chapter is devoted to the development of an operating device for software and hardware systems and complexes with elements of artificial intelligence that operate of the RCS and analysis of the speed of data processing in the positional number system and the RCS. An operating device for software and hardware systems and complexes with elements of artificial intelligence operating in a RCS has been developed. A calculation and comparative analysis of the data processing speed of software and hardware systems and complexes with elements of artificial intelligence in the RCS for the mathematical model of an artificial neuron was carried out. Calculations and comparative evaluation of performance carried out in the dissertation work showed that with an increase in the grid capacity of software and hardware systems and complexes with elements of artificial intelligence, the efficiency of using a non-positional number system in RCS increases significantly. The totality of new scientific results obtained in the dissertation, a positive assessment of their reliability, scientific and practical significance allow us to consider the formulated scientific task of increasing the speed of information processing by software and hardware systems and complexes with elements of artificial intelligence through the use of models and methods of fast data processing based on the use of a RCS - solved, and the goal set - achieved.