Finite state machines, being a mathematical abstraction, allow you to perceive information from the control object, process it and give signals to control the object. The disadvantages of the representation of complex production systems by a set of finite state machines include the complexity of carrying out logical and set-theoretic operations on them and the complexity of describing the parallelism that occurs in the operation of complex production systems. When specifying a finite state machine in the matrix–predicate form, due to the information redundancy, it is possible to avoid these difficulties. Matrix–predicate method allows you to uniquely set the finite state machine square matrix, which makes it possible to use the methods of the theory of matrices during the set–theoretic operations on them and it is possible to avoid isomorphism. The paper presents the developed methods of representation of a finite state machine using a multi-place predicate, which greatly simplifies its task.

Keywords: finite state machine, graph, matrix, predicate, algorithm, matrix–predicate method, graph incident, tuple, Cartesian product, complex production systems

At present, modern information technologies are actively used in the design of complex equipment at various industrial enterprises – automated systems for end-to-end CAD/CAM/CAE class design, which provide complex execution of design work with a significant reduction in their execution time while improving the quality of work. When this is achieved the main objective which is the update of the nomenclature of products, reducing costs, improving reliability, efficiency, etc. In view of this, the task of constructing and visualizing solid-state models is relevant today. From the analysis of the literature, it was concluded that today there are not enough methodological techniques for building models, and the existing developments do not contain optimal algorithms for creating 3D models of parts of varying complexity. Therefore, to implement the above problem, an algorithm for constructing a 3D model with a cutout was proposed.

Keywords: CAD/CAM/CAE, graphic packages, projection drawing, computer graphics, construction algorithm, geometric body, solid modeling, software, 3D model, surface toning

The article shows the possibility of describing complex objects with parallel functioning components in the form of structures built on the basis of neural networks. The neural network is represented by an operator matrix, that is, a formal description that gives a universal way to solve many non-standard control problems. Matrix apparatus is shown to significantly improve the efficiency of the method compared to previously known. It is concluded that the representation of the neural network by the operator matrix provides a universal way to solve the problems of transport and information flows management; neuron-like systems based on such representation of the neuron are able to catch complex nonlinear relationships, self-improvement, learning in the process of use. Their use provides ample opportunities for finding and implementing effective solutions to the problems of management and control of flows

Keywords: graph, parallelism, transport and information flow, neural network, synaptic weight, predicate, activation function, operator matrix, neuron, complex systems