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.