Objectives. The problem of developing a methodology for generating address sequences with a given switching activity and repeatability of addresses widely used in testing modern computing systems is being solved. The relevance of this problem lies in the fact that the main characteristic of the difference and their effectiveness for address sequences is the switching activity of both individual address bits and their sequences.
Methods. Presented results are based on a universal method for generating quasi-random Sobol sequences, which are effectively used to generate targeted test sequences. As an initial mathematical model, a modification of the indicated generation method proposed by Antonov and Saleev is used. The main idea of proposed approach is based on the use of rectangular (m + k) × m generating matrices V of arbitrary rank r to generate address sequences.
Results. The main properties of sequences generated in accordance with the new mathematical model are determined. A number of statements are given that substantiate the requirements for generator matrices to ensure the maximum period of generated sequences and the multiplicity of repetition of used addresses. The problem of synthesizing the sequences with given values of switching activity F(A) and F(a_i) is solved. It is shown that in order to find a generating matrix for generating such sequences, it is necessary to solve the problem of decomposing an integer into terms. This decomposition represents the value of switching activity in the (m + k)-ary mixed number system, in which the weights of the digits are represented as powers of two from 2⁰ to 2^m+k-1, and the values of the digits w(vi) lie in the range from 0 to m+k-1. On the basis of proposed restrictions, the notion of an integer decomposition diagram similar to the Young diagram is introduced, and the operation of its modification is defined.
Conclusion. The proposed mathematical model expands the possibilities of generating test address sequences with the required values of switching activity of both test sets and their individual bits. The use of generating matrices of non-maximal rank makes it possible to formalize the method of generating address sequences with even repetition of addresses.

Objectives. The objective of the work is to develop the means for recognition (extraction) of high-level structures in circuits on transistor level. This allows to obtain a representation on logical level, equivalent to original flat description on transistor level. Obtaining such a representation significantly reduces the time to perform VLSI topology check, but also provides the basis for reengineering of integrated circuits and reverse engineering for detecting unauthorized attachments.
Methods. Graph based methods and software tools are proposed for recognizing topologically equivalent transistor circuits, which makes it possible to divide the set of subcircuits into topologically equivalent classes. The problem is reduced to checking the isomorphism of labeled graphs defining circuits on transistor level by canonizing them and comparing canonical labeling. The original flat and resulting two-level transistor circuits are presented in SPICE format.
Results. The proposed methods are implemented in C++ as a part of a transistor circuit decompilation program for the case without predetermined cell library. The proposed method of canonization of labeled graphs is used: to recognize topologically equivalent subcircuits among functionally equivalent subcircuits that implement logical elements; to split the set of subcircuits not recognized as logical elements into classes of topologically equivalent ones; to verify the results of extraction of the hierarchical circuit at the transistor-logic level relative to the flat circuit at the transistor level.
Conclusion. The decompilation program has been tested on practical transistor-level circuits. Experiments indicate that this tool is fast enough to process the circuits with more than one hundred thousand transistors in a few minutes on a personal computer.

Objectives. The problem of mathematical modeling of the knowledge in the information support system for decision-making is being solved. The approach is based on the formalization of semantic relations in the language. The formalization of such relations provides an adequate representation of knowledge and serves as a theoretical basis for the algorithmization of user interaction with the system.
When solving the problem of knowledge modeling, three main goals are pursued: the construction of a mathematical model of semantic relations, the study of the properties of marginal syntagmas and the construction of algorithms for the formation of a dictionary of syntagmatic structures.
Methods. Methods of set theory, graph theory and mathematical linguistics are used.
Results. A mathematical model of knowledge representation in the information decision support system has been developed. The concepts of semantic relations in the language are formalized and the properties of marginal syntagmas are investigated. The proven properties of such structures provide the algorithmization of information processes in the system under consideration.
Conclusion. As an implementation of the model proposed in the article, algorithms for creating dictionaries of syntagmas and syntagmatic structures have been developed. When forming a set of syntagmas, the assertions about proved in the article marginal syntagmas are used. A set of syntagmatic structures is built taking into account their typology. Syntagmatic structures in the dictionary acquire the status of communicative fragment, i.e. stable phrases to synthesize the information system language.

Objectives. The main purpose of the work is to study the advantages of an activity-based approach, or functional approach in comparison with a subject-based approach, or lecture-based approach for creating a model of a professional field for adaptive educational process. The relevance of the problem being solved is caused by due to the fact, that adaptive educational technologies, thanks to the extensive computerization and informatization of all spheres of human activity, as well as the innovative development of artificial intelligence, have become dominant in teaching systems at all levels, from preschool to higher education institutions. Without a highly effective model of the professional field, it is impossible to successfully implement adaptive learning.
Methods. To achieve the goals and to prove the statements formulated, the method of comparative analysis of the most widely used ways for creating models of the professional field for adaptive learning in modern systems, was used. To do this, we studied: the effectiveness of using the traditional approach, which is based on subjectspecific or lecture-seminar signs of structuring educational material; as well as the effectiveness of using an activity-based approach based on the concept of "Modules of labor competencies" for the formation of educational material.
Results. The analysis of the quality of educational material (a model of a professional field for an adaptive educational process) obtained using the traditional approach, and educational material (the same model for its intended purpose) obtained on the basis of an activity approach in accordance with the concept of "Modules of labor competencies". The results of the analysis are compared and theoretical statements are summarized, taking into account the examples of developed modular materials, as well as the pilot implementation of previously developed modular programs.
Conclusion. The information given in the article can be useful for specialists, researchers and heads of educational institutions of various levels, when planning and creating adaptive learning systems. The conclusions and recommendations fully comply with the requirements of the development of the education system of the Republic of Belarus.

Objectives. The problem of describing the invariant features of a digital image of handwritten signature that describes the distribution of its local features is considered. The formation of fundamentally new approach to the calculation of such features is described.
Methods. Digital image processing methods are used. First an image is converted into a binary representation, then its morphological and median filtering is performed. Then using the method of principal components, the image is rotated to give the signature a horizontal orientation. A rectangle describing the signature is cut out, then it is scaled to the template of a certain size. In the article the template of 300×150 pixels was used. Then the border of the signature is formed. Local binary patterns are calculated from its binary contour, i.e. each pixel is assigned a number from 0 to 255, which describes the location of the edge pixels in 3×3 neighborhood of each pixel. A histogram of calculated patterns for 256 intervals is formed. The first and last intervals are discarded because they correspond to all black and white pixels in the neighborhood and are not informative. The remaining 254 numbers of the array form new local features of the signature.
Results. The studies were performed on the bases of digitized signatures TUIT and CEDAR containing true and fake signatures of 80 persons. The accuracy of correct verification of signatures on these bases was about 78 % and 70 %.
Conclusion. The possibility of using the proposed possibilities for solving the problems of verifying the authenticity of handwritten signatures has been experimentally confirmed.

Objectives. We propose the algorithm for e-commerce image recognition using attention model and neural network YOLACT. A modular architecture is used that applies an attention model to different branches of the network in order to improve the interaction between image cross-features.
Methods. The main methods to recognize e-commerce products are the creation and annotation of a dataset for the neural network training, the choice of architecture and embedding an attention model, the validation and testing, and interpretation of the results.
Results. Convolutional neural network YOLACT has been modified by the attention model to solve image recognition task that allowed to obtain results superior in quality to the results showed by classic YOLACT.
Conclusion. In the course of the experiment, a data set of e-commerce products was prepared, annotated, and two neural networks were built to compare the results. The results of the study showed that the use of the attention model has a positive effect on both the quality of the trained network and on the rate of convergence, which is reflected in improved metrics for object recognition and segmentation.

Objectives. The increase of the efficiency of a separate transport mobile robot in a warehouse due to optimal regulation of the speed of its movement. It is required to control the position, speed, acceleration and direction of movement of the mobile robot at each moment of time along a known route. A method for forced control of the movement of a transport mobile robot was proposed. A control block for various motion maneuvers was developed in Simulink environment, which calculates the distance to the nearest turning point or stop and then by constructed cyclogram the corresponding speed at each moment of time is determined. The proposed control unit can be used in practice for the tasks of optimal movement of transport robots in predetermined area.
Methods. The method of the theory of optimal control according to the criterion of maximum speed, the wave algorithm for finding the shortest path, the method of finite automata for relay control of the acceleration of movement are used.
Results. Based on the proposed method of forced control of the movement of a transport mobile robot in the Simulink environment, a maneuver control system was developed that provides the minimum travel time for each segment of the path. Maneuvers mean the rectilinear movement of the robot, as well as its turn on the spot, in two modes: with and without reaching maximum speed. The technique is based on the assumption that the movement of the transport robot is uniformly accelerated. A side result of the developed control system is that when it is scaled to a group of robots, it becomes possible to predict the time and place of their potential collisions, in order to subsequently take into account a group of robots for effective control.
Conclusion. The developed control system can be used to control a real transport mobile robot equipped with a servo drive in solving the problems of transporting goods around the warehouse.

To the 30th anniversary of the establishment of the Belarusian Association for Analysis and Image Recognition