Today, in the digital age, the problem of pattern recognition is very relevant. In particular, the task of text recognition is important in banking, for the automatic reading of documents and their control; in video control systems, for example, to identify the license plate of a car that violated traffic rules; in security systems, for example, to check banknotes at an ATM and in many other areas. A large number of methods are known for solving the problem of pattern recognition, but the main advantage of neural networks over other methods is their learning ability. It is this feature that makes neural networks attractive to study. The article proposes a basic neural network model. The main algorithms are considered and a programming model is implemented in the Python programming language. In the course of research, the following shortcomings of the basic model were revealed: low learning rate (the number of correctly recognized digits in the first epochs of learning); retraining - the network has not learned to generalize the knowledge gained; low probability of recognition - 95.13%.To solve the above disadvantages, various techniques were used that increase the accuracy and speed of work, as well as reduce the effect of network retraining.

The paper deals with the issues of decomposition of control algorithms for the processes in parallel computing systems and the use of automaton models. When designing parallel processing systems, an important task is the formal presentation of process control algorithms since they allow achieving a packaged solution to the problems of specification, development, implementation, verification, and analysis of complex control systems, including the control of interacting processes and resources in parallel computing systems. It is especially necessary to use formal methods to verify complex information processing systems by model testing. One of the methods for the formal description of control algorithms is based on the use for these purposes of the nondeterministic automaton (NDA) logic, which is a method that allows one to present control algorithms for information processing in the form of systems of canonical equations describing all particular events implemented in the algorithm. The advantage of such a language is that all transitions in the control system are described not in terms of system states, but in terms of particular events, the simultaneous existence of which determines all states and transitions in the system; this allows avoiding a "combinatorial explosion" in the state space to the possibilities of means verification. Purpose of the paper: research of control algorithms for parallel computing systems using the NDA apparatus. The development and research object is parallel decomposition of control algorithms for parallel computing systems using automatic models.

Recently, unmanned aerial vehicles have been an important part of scientific research in various fields. Quadrocopter is an unmanned aerial vehicle with four rotors, two of which rotate clockwise, the other two counterclockwise. Changing the speed of screw rotation allows you to control the movement of the apparatus. The article proposed and tested a mathematical model of a quadcopter. They presented the development of a simple control algorithm that allows to stabilize the height and angular position. The research results show the efficiency of the algorithm and the possibility of its practical implementation. The developed mathematical model can be used instead of a real quadcopter, which will significantly reduce the time during research, as well as avoid the quadrocopter damage, reducing the number of launches.

Managing the systems which behaviour is non-deterministic is one of the most important problems in modern management theory. Today, systems with structural and behavioural complexity are prevalent in all areas of human activity, and therefore, their research is of the utmost importance. Such systems, as opposed to deterministic systems, are called non-deterministic. They are characterised by difficult predictable behaviour determined both by external random influences, and within the systems themselves. A clear example of a non-deterministic system is crowds of people, factories, and computer networks and systems. The problem of non-deterministic behaviour directly within the context of professional activities can be seen using an example of building syntactic analysers. The aim of the paper is to design a class of systems oriented towards supporting elements of a discrete event model. The target of research is to simulate discrete event models. The subject of research is a creation of a discrete event model based on the behaviour of an undetermined finite state automaton. During the preparation of the paper, there was developed and practically implemented an algorithm for the application, which materializes the principle of working with threads. The results obtained in the paper are aimed at solving the problem of parallel data processing based on the parallelism of NFA's (non-deterministic finite automaton) behaviour when reading the input string characters. As a result, this should have a positive impact on the regulation of the simulation processes of a non-deterministic system, increasing its efficiency and stability. In conclusion, the algorithm of the application work is disclosed and conclusions about the effectiveness and efficiency of its development are drawn.

The paper deals with researching and developing the methods that make it possible to account behaviour examples when synthesizing automaton models by temporal formulas. Definitions of the terms and concepts used in work are given; the problem of synthesizing automaton systems according to the specification in the form of temporal formulas and behaviour examples is formulated; a promising algorithm for reducing the problem of synthesizing automaton systems to the Boolean formula satisfiability problem is described; an analysis of the domain and other approaches is carried out. New methods of taking into account behaviour examples in the synthesis of automaton systems according to a specification given in the form of temporal formulas are proposed. Algorithms for constructing graphs of scripts and methods for dividing graphs into clusters are described; they are designed to increase the efficiency of representing behaviour examples used for coding the behaviour examples in the form of Boolean formulas. An experimental study of the proposed methods of accounting for behaviour examples and basic approaches to the presentation of behaviour examples is carried out. The experimental results showed the superiority of the newly developed methods regarding the presentation of scripts in the form of temporal formulas. In summary, the main conclusions of the work carried out are presented.