Objectives. The purpose of experimental research is to determine the effectiveness of new algorithms for extracting the so-called connected subsystems from formula descriptions of the original system of Boolean functions. Subsequently each of the extracted subsystems is minimized independently of the others, but the functions that make up each connected subsystem are minimized jointly.

Methods. Minimization of subsystems is performed in the class of multilevel BDD representations (BDD – Binary Decision Diagram) or Boolean networks. After obtaining minimized descriptions of circuits, specified as a set of interconnected Shannon expansion formulas that correspond to BDD, or as two-operand logical equations corresponding to Boolean networks, synthesis of logic circuits is carried out in the design library of custom digital CMOS ASIC (Application-Specific Integrated Circuits made using complementary metal oxide semiconductor technology). In Boolean networks, node functions can be the logical operations “conjunction” or “disjunction” over literals of Boolean variables. A literal is a Boolean variable or its inversion. Minimization of BDD representations is carried out according to the number of Shannon decomposition formulas, minimization of Boolean networks – according to the number of literals in the formulas defining the networks.

Results. The resulting logic circuits are compared in terms of chip area and speed (time delay). Experiments were carried out on 39 industrial circuit examples. The advantage (in 29 cases) of using the proposed subsystem extraction algorithms is shown compared to joint or separate minimization of the original system of Boolean functions, which is usually performed as the first stage of the synthesis of logic circuits.

Conclusion. The new algorithms for subsystem extraction proposed in the paper have proven their effectiveness in the execution of various programs for optimizing multilevel representations of systems of Boolean functions. The developed software package allows improving the results of technologically independent optimization used in the implementation of digital system projects in custom digital CMOS ASIC.

Objectives. Financial networks with a rule of constrained equal awards for the distribution of the agent’s estate between its creditors are considered. The aim of the study is to develop an algorithm for constructing greatest clearing matrices for such networks under zero cash reserves of all agents.

Methods. Graph theory and mathematical programming methods are used.

Results. A polynomial-time algorithm for constructing the greatest clearing matrices for financial networks with a rule of constrained equal awards for the distribution of the agent's estate between its creditors is proposed. It is assumed that the cash reserves of each agent are equal to zero (funds received from other agents are distributed among creditors). The algorithm is based on the use of the identified properties of weighted strongly connected graphs. Necessary and sufficient conditions are obtained under which the greatest clearing matrix is different from zero at zero cash reserves of agents'.

Conclusion. The developed approach can be used in constructing clearing algorithms for financial networks with other rules for distributing the agent’s estate between its creditors.

Objectives. Financial networks with a rule of constrained equal awards for the distribution of the agent’s estate between its creditors are considered. The aim of the study is to develop an algorithm for constructing greatest clearing matrices for such networks under zero cash reserves of all agents.

Methods. Graph theory and mathematical programming methods are used.

Results. A polynomial-time algorithm for constructing the greatest clearing matrices for financial networks with a rule of constrained equal awards for the distribution of the agent's estate between its creditors is proposed. It is assumed that the cash reserves of each agent are equal to zero (funds received from other agents are distributed among creditors). The algorithm is based on the use of the identified properties of weighted strongly connected graphs. Necessary and sufficient conditions are obtained under which the greatest clearing matrix is different from zero at zero cash reserves of agents'.

Conclusion. The developed approach can be used in constructing clearing algorithms for financial networks with other rules for distributing the agent’s estate between its creditors.

Objectives. The objective of the work is computer modeling of diffusion in ideal gas mixtures taking into account the dependence of the diffusion coefficient on the entropy of mixing according to the model proposed by one of the authors of the article, in Wolfram Mathematica.

Methods. Built-in function NDSolveValue in Wolfram Mathematica and the default solver were used for the numerical solution of the one-dimensional task; for the numerical solution of the two-dimensional task the same function was used, for which the Numerical Method of Lines was specified as the solver.

Results. The results of computer modeling of diffusion in a mixture of ideal gases are obtained taking into account the dependence of the diffusion coefficient on the entropy of mixing for two tasks in a one-dimensional formulation and one task in a two-dimensional formulation.

Conclusion. The conducted research and the obtained solutions in computer modeling of diffusion in a mixture of ideal gases taking into account the dependence of the diffusion coefficient on the entropy of mixing indicate that for solving tasks in the field of computer modeling of gas mixing in modern software tools could be used a mathematical model that is an alternative to popular modern models based on the description of the hydrodynamic properties of gases and the enthalpy of mixing, as well as other entropy models.

Objectives. The purpose of the work is to create an experimental software for automated recognition of voice signals, which has the capabilities of long-term round-the-clock and round-the-season monitoring of animal species diversity in selected habitats and ecosystems.

Methods. The work uses methods of deep machine learning of convolutional neural networks trained on mel-spectrograms of bird vocalizations, which are built using fast Fourier transform.

Results. The process, methods and approaches to training a deep machine learning model for a system of passive acoustic monitoring of bird populations in Belarus are described, as well as the difficulties identified during testing of the software prototype and the results that were achieved.

Conclusion. A working prototype of the software for automatic recognition of animal (bird) voice signals is presented. It performs the analysis of acoustic recordings of bird voices with the issue of probabilistic assessment of species belonging to animal vocalizations present in the recordings. The software is aimed at increasing the efficiency of bird monitoring, which ensures the implementation of conservation and research activities based on accurate and up-to-date data on species distribution.

Objectives. Study of the method of verification of the authenticity of a human signature made on a tablet with a stylus and given three parameters: coordinates X, Y and pressure on the tablet P.

Methods. N genuine dynamic human signatures are given. Data describing different signatures made by one person always have a different number of points. The main variants of normalization of the original signature data are investigated. A model of an individual image of human signatures is built without calculating dynamic features. The method of dynamic time transformation (DTW) is used to compare similar data of different signatures. The results of this transformation are DTW-distances between the data of pairs of signatures. These distances serve as coordinates of a point in the feature space describing the similarity of a pair of signatures. A set of such points represents a model describing the similarity of genuine human signatures. The parameters of the signature being verified are compared with each of the N authentic signatures used to build the model for their proximity to the model. If more than half of these pairs are further from the model than a certain threshold T, the signature is considered fake.

Results. As a result of comparative experiments, a variant of normalization of initial data of dynamic human signatures was found, which allows verification of such signatures without calculating additional features usually calculated from the initial data X, Y, P.

Conclusion. Experiments to generate individual signature models for each of 230 people from the publicly available MCYT dynamic signature database (a subset of the DeepSignDB database) and verify the authenticity of 11,500 signatures made on behalf of these people showed a verification accuracy of 99.82 %. Half of them were genuine, half were fake.

The work is devoted to theoretical and practical aspects of computer systems design based on the zero trust concept. Based on the system thinking of analyzing existing zero trust systems and theoretical models used in their design, the work describes key problems of implementing zero trust systems. Also, based on design and security patterns, the principles representation of the zero trust concept and the abstract access control model (pattern) of the Zero Trust Architecture are considered.

The principles representation can be used to mine abstract design and security patterns, and the access control pattern – to create derivative patterns and architectures of computer systems based on zero trust. An advance of the access control pattern is the capacity to more fully formulate functional requirements and represent the architectures of the designed systems due to the description of access control levels (network path, session, transaction).