The results of an experimental comparison of programs for technologically independent minimization of complexity of multilevel representations of systems of fully defined functions based on the Shannon expansion are described. The main attention is paid to the effectiveness of using, when synthesizing logical circuits, a program that implements an algorithm for solving the problem of extracting from a system of functions such subsystems for which it is advisable to carry out joint minimization of multi-level representations of subsystems in the form of Binary Decision Diagrams, called BDD-representations, and in the form of Boolean net. The complexity of the representation is estimated by the total number of literals of Boolean variables in a set of interrelated logical equations that define a system of Boolean functions. After extracting the subsystems and their joint minimization, the synthesis of logic circuits is carried out in the design library of custom digital CMOS VLSIs, the results are compared in terms of chip area and speed (time delay) on a stream of 39 industrial examples of circuits. It was found that for 20 examples, the subsystem selection algorithm allows one to obtain better solutions than joint or separate minimization of multi-level representations based on Shannon expansion (13 examples). The three best solutions are obtained by applying the well-known Espresso program for minimizing functions in the DNF class, and the three solutions are obtained by the synthesizer using the original (non-optimized) matrix representations of DNF systems of Boolean functions.

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.

Аннотация.В статье приводятся результаты экспериментальных исследований эффективности программ минимизации многоуровневых алгебраических представлений систем булевых функций, выполняемых при синтезе комбинационных схем.Результирующие минимизированные логические описания представлены в виде формул разложений Шеннона или формул, задающих булевы сети

A decisive influence on complexity and speed of a combinational logic circuit of library CMOS elements is exerted by the preliminary stage of technologically independent optimization of the implemented system of Boolean functions. At present, the main methods of such optimization in the logical synthesis of custom CMOS VLSI blocks are methods for minimizing binary decision diagrams — Binary Decision Diagrams (BDD) or their modifications. Graphical representations of BDD are built on the basis of the Shannon expansions of Boolean functions. A BDD graph corresponds to a set of interrelated Shannon expansion formulas that form a multilevel representation of the minimized system of Boolean functions. The efficiency of applying various optimization procedures of minimization for several types of BDD representations of systems of Boolean functions is investigated in the paper. 7hese procedures are used as a technologically independent optimization in the synthesis of multi-output logic circuits of library CMOS elements. In addition to single logical optimization procedures, sequences of such procedures are studied that form various methods of logical optimization of multilevel representations of systems of Boolean functions. The results of experiments on 49 examples of systems of Boolean functions are presented. 25 optimization routes have been studied, efficient routes have been determined for various types of specifications of function systems. The obtained experimental results are compared with the known ones. It has been established that to estimate the complexity of optimized algebraic representations of systems of functions, it is advisable to use such a criterion as the total number of literals (variables or their inversions) of Boolean variables.

Binary decision diagram (BDD) is used for technology-independent optimization, performed as the first stage in the synthesis of logic circuits in the design of application-specific integrated circuits (ASICs). BDD is an acyclic graph defining a Boolean function or a system of Boolean functions. Each vertex of this graph is associated with the complete or reduced Shannon expansion formula. Binary decision diagrams with mutually inverse subfunctions (cofactors) are considered. We have developed algorithms for finding algebraic representations of cofactors of the same BDD level in the form of a disjunction or conjunction of other inverse or non-inverse cofactors of the same BDD level. The algorithms allow reducing the number of literals by replacing the Shannon expansion formulas of a system of Boolean functions. It is proposed to use the developed algorithms for an additional logic optimization of the constructed BDD representations of systems of Boolean functions. The experimental results of application of the corresponding programs in synthesizing the logic circuits in the design library of custom VLSI CMOS circuits are presented.

The paper describes the research results of application efficiency of minimization programs of functional descriptions of combinatorial logic blocks, which are included in digital devices projects that are implemented in FPGA. Programs are designed for shared and separated function minimization in a disjunctive normal form (DNF) class and minimization of multilevel representations of fully defined Boolean functions based on Shannon expansion with finding equal and inverse cofactors. The graphical form of such representations is widely known as binary decision diagrams (BDD). For technological mapping the program of "enlargement" of obtained Shannon expansion formulas was applied in a way that each of them depends on a limited number of k input variables and can be implemented on one LUT-k – a programmable unit of FPGA with k input variables. It is shown that a preliminary logic minimization, which is performed on the domestic programs, allows improving design results of foreign CAD systems such as Leonardo Spectrum (Mentor Graphics), ISE (Integrated System Environment) Design Suite and Vivado (Xilinx). The experiments were performed for FPGA families’ Virtex-II PRO, Virtex-5 and Artix-7 (Xilinx) on standard threads of industrial examples, which define both DNF systems of Boolean functions and systems represented as interconnected logical equations.

Purpose. Study of the influence of psychotherapeutic assistance on the rehabilitation of persons who have undergone limb amputation. Materials and methods. A study of the psychological characteristics of 48 patients who underwent amputation of the lower extremity was carried out on the basis of the departments of vascular surgery and traumatology of the Samara Seredavin Regional Clinical Hospital. The control group included 25 people (16 men, 9 women), aged 45 to 70 years. Amputations of the extremities were performed by him in connection with the developed gangrene due to obliterating vascular diseases. The main group consisted of 23 people (14 men, 9 women) aged 35 to 60 years with a stable and prosperous social status, who received an acute sudden injury that ended in amputation of one or both lower extremities. The examination was carried out on the 3-5th day of the postoperative period, depending on the patient's condition. For the study, the following psychodiagnostic methods and techniques were used: 1) clinical conversation; 2) coping test by R. Lazarus, S. Folkman; 3) methodology for diagnosing the type of attitude to the disease; 4) Hamilton Depression Scale; 5) S. Rosenzweig's test of drawing frustration. Results. The difference between the group of patients and the control group was statistically confirmed in terms of “seeking social support” (higher in the control group), “confrontation” and “flight – avoidance” (higher in the group of patients) (p < 0.05). In the control group, depression is absent in 85% of the subjects, in 15% of patients there is a mild depressive state (p < 0.05). According to S. Rosenzweig's method, the predominance of extrapunitive reactions was revealed in both groups (E = 59.6 in the main group of patients and 44.1 in the control group) due to reactions of the ego-protective type (ED = 56.2 in the main group of patients and 46.3 – in the control group). Conclusion. Patients who underwent surgery for limb amputation and who took a conscious and active part in individual and group psychotherapy by the time of discharge from the hospital showed a decrease in anxiety and depressive manifestations, a decrease in the manifestations of outward aggression, the construction of optimistic prospects) than in patients who categorically refuse to receive psychological help and support. The provision of psychotherapeutic assistance to persons after amputation of limbs should begin in the first days after the operation.

The design of the TUK-109T large-size container developed at the All-Russia Research Institute of Experimental Physics (VNIIEF) for transporting ampuls with bundles of spent fuel pins is described. The results of full-scale tests and three-dimensional simulation modeling for strength validation for mechanical actions occurring under normal operating conditions and during emergencies are presented. The computational validation of strength was performed in a three-dimensional formulation based on a finite-element model and a validated methodology of modeling dynamic deformation of structures, implemented in the highly parallelized LOGOS software. The validation of the methodology was performed by comparing numerical results with full-scale design tests. The computational prediction is shown to be highly accurate.

The parallel automaton is considered which is the functional model of a discrete control device which allows taking into account the parallel character of logical control devices. The verification of parallel automata lies in testing all transitions in the graph of the complete states of automata and is conducted based on simulation. The software tools for constructing the compact tests for verifying the parallel automaton and for obtaining the VHDL model of parallel automata aimed at implementing their scheme are proposed. The obtained algorithmic VHDL models of the automata are synthesizable, which allows obtaining the scheme implementations of parallel automata in various design libraries.

The manuscript discusses issues related to the use of mathematical modeling to substantiate the reliability and safety of the Superjet-100 aircraft during the emergency landing. The problem of the passenger airplane airframe dynamic deformation in the landing with partially removed and released the landing gear under given initial conditions of touching the runway of the airfield. Confirmation of the adequacy and reliability of modeling and the accuracy of numerical results are considered.

The study of the features of metabolism in different age periods in children and adolescents, as well as depending on the climatic conditions, should include studies of the peculiarities of the chemical processes in various organs and systems.In addition, in the period of growth and development of children and adolescents, a necessary condition is the consistency of their internal biological processes.We conducted studies on the level of glucose, glycogen, lactate, and pyruvate in the blood of children and adolescents living in the conditions of the plain of Dagestan in the fall and spring at different age periods.The results of the study show that there is a certain regularity in the change in the level (concentration) of glucose, glycogen, pyruvate and lactate in the blood of children and adolescents in the studied age periods.

Предлагается технология проектирования цифровых устройств, позволяющая выполнять логическое моделирование VHDL-описаний комбинационной логики, формировать соответствующие системы булевых функций, проводить их логическую оптимизацию и синтезировать логические схемы в различных технологических библиотеках логических элементов.Интеграция программных средств в рамках этой технологии основывается на использовании скриптов и BAT-файлов, которые поддерживаются современными САПР

Considered problem of model based verification of control systems is the checking whether the system behavior satisfies the requirements fixed in the design specification The testing includes the experiments consisting in simulation of investigated system to see input-output correspondence to the model. The test sequence is generated on the basis of the model that describes the desired behavior of the system. The method to construct a test sequence for verification of hardware (or software) implementation of a control system with behavior parallelism is suggested that is based on traversal of the graph of the states that are reachable in system functioning. A method for constructing the set of reachable global states for a parallel algorithm of the control system behavior and a method to obtain the test sets are described. The description of the system functioning, which is given by the design specification, is assumed to be correct. The hardware (or software) implementation that must conform to this specification is to be verified.

A methodology for numerically modeling 3D processes of acceleration of deformable bodies by detonation products of solid explosives in the air is described. Simultaneous motion of the explosion products, the air and the elastoplastic medium is numerically analyzed in Euler variables, using a modified Godunov scheme, which is applicable for both fluid dynamics and elastoplastic flows, and an exact solution of Riemann problem of discontinuity breakage in the media and along the gas-elastic body interface. The methodology uses three types of spatial grids. The grids of the first type are sets of triangles (STL files) defining the surfaces of the objects and updating those surfaces in the process of motion. The grids of the second type are base fixed Cartesian grids nested into each medium. The grids of the third type are local orthogonal movable grids coupled with each of the triangles of the grids of the first type. The integration of dynamic equations of continua and mutual interpolation of parameters among the different kinds of grids is done on base and local grids. To simulate the detonation propagation process in a solid explosive, an algorithm based on Huygens principle and the account of energy release upon the arrival of the detonation wave into the integrated cell are used. Examples of numerically modeling propagation of elastic and elastoplastic disc-shaped, tetrahedral and cubic bodies of various materials adjacent to the charge are given. The results of the analyses testify to the applicability of the above methodology for modeling coupled processes of acceleration of deform-able bodies by detonation products up to deceleration in the ambient medium. Certain laws of the acceleration process have been found for the case where detonation is initiated in the center of a spherical charge. In particular, the duration of the acceleration of a body is comparable with the time of the arrival of the detonation wave at the surface of the contact; the major residual strains altering the geometry of the bodies occur at the initial stage of the acceleration and affect both the interaction with the detonation products and the parameters of the motion of the bodies; the final acceleration velocity is observed to depend considerably on the initial geometry of the accelerated body, its orientation relative to the detonation front and the deformation properties for the same mass.Keywords: modeling, detonation, 3D processes, multi-grid approach, interpolation, Godunov scheme, nonlinear coupled problems, aeroelastoplasticity, acceleration of bodies.