the article describes a variant of setting sequential algorithms in the form of bipartite graphs by further defining them, which makes it possible to work with algorithms using graph theory methods in the future. Two forms of the task are considered: modular and functional-predicative. The possibility of setting the algorithm in table-predicate form is shown. It is concluded that in addition to the generally accepted methods of setting the algorithm, it can be set in matrix-predicate or table-predicate form, which allows using methods of matrix theory and methods of predicate theory when working with algorithms. setting the algorithm in matrix-predicate form avoids isomorphism when performing algebraic and set-theoretic operations on it.; setting algorithms in matrix-predicate form allows you to perform almost any operations on them

Keywords: graph-algorithm scheme, sequential algorithm, predicative block, functional block, pre-definition, bipartite graph, table-predicative form, graph theory, isomorphism

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

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