OPTIMAL SYNTHESIS OF DIGITAL COUNTERS IN THE FIBONACCI CODES WITH THE MINIMAL FORM OF REPRESENTATION (p. 4-10)

At present, requirements for speed performance and noise immunity in the work of the counters increase. Among the existing structures, the Fibonacci counters meet such requirements. Their drawback is transfer while calculating from the minimal form of representation of the Fibonacci numbers to the maximal form and, consequently, to the use of operations of convolution and deconvolution, which de-creases speed, noise immunity and increases required hardware expenses. We propose for the Fibonacci counters to use only minimal form of representation of the Fibonacci numbers, which excludes operations of convolution and deconvolution. Based on it, the method of the Fibonacci calculation in the minimal form is developed and its logical model is built in the form of a set of logical operations, whose fulfillment leads to the Fibonacci calculation. It gives the possibility to design the method of synthesis of the Fibonacci counters with the optimal ratio of performance speed, noise immunity and amount of hardware expenses for specific conditions of its work. The advantage of the Fibonacci counters with the minimal form is their increased noise immunity. It is due to both the nature of the Fibonacci calculation itself, which works in the excess codes, and to the absence of transfers to the maximal form, where it is permitted to have the forbidden combinations. In this case, the probability of detecting errors grows with an increase in the number of bits of counter.


Mourad Aouati
The problem of the accuracy of classification, determined by the share of the correctly classified objects with the use of parametric methods of pattern recognition, is examined. In particular, we analyzed the influence of deviation from the normal law of distribution of variables of the space of features -random variables, in essence -and the inequality of covariance matrices of classes on the accuracy of classification. It was found that the inequality of covariance matrices of the divided classes leads to the shift of the dividing surface; however, the magnitude of this displacement may not become the essential factor, which influences the accuracy of classification. It is shown for the space of variables of dimensionality (N×2) that for the randomly selected classes inside the square with the length of the edge, equal to two, the accuracy of classification for classes A and B proves to be different and depends on the position of the straight line, which divides the classes. It is shown that localization of vectors-patterns in the space of features can be selected in accordance with the plans of full factorial experiment (FFE). Due to this localization, the equality of covariance matrices of the classes is ensured and the share of the correctly classified objects increases. We proposed, to overcoming the main shortcoming of the given research, connected to the absence of functional dependencies, which make it possible to quantitatively evaluate the accuracy of classification at various variants of arrangement of FFE plans, to use the methods of experimental optimization. Its purpose is the selection of such coordinates of the centers of plans and their geometric characteristics for classes A and B, which ensure the maximum share of the correctly classified objects based on the obtained decision rules. The realization of this approach may become the reserve for the increase in the accuracy of classification with application of the methods of parametric optimization.
Keywords: parametric classification, covariance matrix, pattern recognition, accuracy of classification of objects, vector-pattern, cluster.

Natalia Kondratenko, Olha Snіhur
Modeling natural systems and processes often requires making decisions under conditions of data uncertainty. There are a number of applications, in which obtaining data about the system is a time-and resource-consuming process. That is why it is advisable to develop decision making mathematical models and methods capable of functioning on input data that has gaps.
In the scope of this research an aggregated interval type-2 fuzzy data classification model was built. Interval type-2 fuzzy set mathematics operates membership grades in an interval form. This allows to take uncertainties intrinsic for an input vector into account, and enables working with an input vector that has gaps instead of some of the values. The proposed system supports involving one or more experts on early stages of the decision making process, more specifically in the phase of informative feature extraction. A feature set provided by every expert generates a separate model with an interval output. Such an approach achieves incorporating expert's knowledge and experience into the decision making process along with information accumulated in the experimental data set. The results of multiple models are subsequently aggregated into a single interval, which is a generalized interval estimation of the system's status based on data available at the moment, and allows to get an idea of the uncertainty associated with the decision taken.
It is also allowed to integrate third party models based on other decision making methods and technologies, such as a modification of the PCM cluster analysis method with interval membership grades.
The aggregated model was adapted for approximate evaluation of groundwater extraction perspective on different states of hydrogeological exploration. It was determined that in some cases it can save significant cost and human resources.
Keywords: fuzzy logic system, interval fuzzy sets, uncertainty, cluster analysis.

Mykhailo Solomko, Liudmyla Zubyk, Peter Olshansky, Vitalii Nazaruk
The paper considers the operation of summation of binary codes in the scheme of a multi digit parallel adder without carry. The process of the operation of summation uses a pairing algorithm that provides for a logarithmic complexity to the algorithm of the calculation in the adder's scheme. Since the codes for the operation of summation, known in the literature, such as Galois field codes, the XAND codes, are defined by the systems of recurrent codes that contain one of the initial codes of complete combinatorial system with repetition, then the given codes are a particular case of the class of combinatorial systems of binary codes with a ring structure and initial code of complete combinatorial system with repetition. Therefore, the only basis of the mentioned systems of binary codes indicates the usefulness of their classification generalization, within the framework of the operation of summation, on the basis of a single criterion -an object of binary codes. Thus, the generalization of the classification of binary codes simplifies the structure of the subject area, increases the variety of systems of binary codes, in particular, for their application in arithmetic operations with binary numbers. It was established that the properties of the recurrent method of the synthesis of binary codes allow focusing the principle of building codes in the range of complete combinatorial system with repetition, which ensures reduction of the thesaurus of the parallel adder of binary codes without carry.
The results of this study may be a component of the technology of designing electronic computing systems because: -they expand the apparatus of obtaining recurrent binary codes for their application in the information technology; -they provide a possibility to control the selection of the code at the stage of designing a computing device; -they help predict the impact of the implementation of the selected code for the solution of problems of the information systems; -they minimize hardware costs associated with the selection of the system of binary code for the calculation.
Keywords: adder, combinatorial system with repetition, binary codes, summation of binary codes, cascade scheme, class of combinatorial systems, instance of the class, thesaurus, logarithmic complexity.

Artem Pohorelov, Vadym Savanevych, Serhii Udovenko
We investigated the influence of the reduction model power on the accuracy of the object's position assessment using the relative method. The research considered reduction polynomials of the third and fifth power, their influence on the accuracy of the celestial object's position assessment and distribution of reference stars in the frame. The result of the analysis showed the presence of a sinusoidal component in the dependence of the residual of parameters of celestial objects when the cubic reduction model is used. It also showed almost complete elimination of this component in case of using the fifth-power reduction model, which increased the number of reference stars in the frame's edges as well as accuracy indicators of position assessments of celestial objects. The assessment criteria of significance of the reduction model coefficients using the Fisher's f-criteria proved the validity of application of the polynomial model with the power, that is higher than cubic.
The results of the research can be used to improve the accuracy of estimation of celestial objects positions in the frame in the CCD-automated processing systems, which assess the position of objects in the entire field of view of the telescope.
Keywords: astrometric reduction, digital frame, celestial object, reduction model, assessment of accuracy indicators.

Alexander Trunov
Here we propose a new realization of the paradigm of prescribed control on the example of a vector model in the form of nonlinear non-stationary system of differential equations of the first order, for which a control system is synthesized. The estimation of efficiency is introduced as a continuous, three times differentiated, dimensionless function. Dimensionless objective function and the function of Lagrange with the inequalities constraints is formed. The problem of minimization of square deviation is posed for them as the problem of maximization of one of the criteria of adequacy -accuracy. It is written in a formalized way in the form of a system of nonlinear algebraic equations. For construction of its solution, a recurrent approximation of objective function is used, which made it possible to complement the system with new equations and to find, in a general form, expressions of auxiliary vectors independent on the number of components of the vectors of strategies and the Lagrange multipliers. Two additional equations are brought out, which realize maximization of adequacy by two additional criteria: depth and completeness. All this taken together made it possible to complement the system with new nonlinear equations, which, in turn, increased substantially the number of permissible inequalities constraints. This approach considers the properties of a non-stationary nonlinear model, which describes the object independent of the selection of the purpose of control. As a result of the solution of the problem, it was possible to connect the idea about the adequate, prescribed behavior of model and the properties of a nonlinear object, to obtain a differential equation that describes optimal controlling action, which, in this case, maximizes adequacy.
It was demonstrated that in a particular case, under condition of independence of the rate of change in controlling influence on its magnitude, the obtained results coincide with expressions of the method of speed gradient. The estimations of the norm of error in the vector of strategies are presented depending on the properties of object, error in the function of efficiency and synthesized law of controlling action for the prescribed law of the object's functioning.
The set and solved problem demonstrated possibilities to set, with the aid of cybernetic methods, a new type of problems on adequate control. The latter is especially relevant in connection with application of integrated computer technologies. The obtained solutions without artificial assumptions make it possible to synthesize controlling action for the conditions that change over time both in the properties of object and in constraints.
Keywords: prescribed control, maximization of adequacy, additional equations in the problem of optimal control.