# Computer Sciences

## Fuzzy Linear Automata Testing

The article deals with the problem of synthesis of tests for fuzzy linear automata (FLA). Now several varieties of FLA are used as models of real fuzzy systems. The article introduces and investigates one particular type of FLA. The fuzziness of the behavior of the automaton is suggested to appear due to the use of elements of a special type in the characteristic matrices. Each such element is a certain set of elements of the field over which the FLA is given.

## Administration of Virtual Data Processing Center over OpenFlow

This paper researches the building principles and administration of virtual data processing centers based on hyper-converged systems over OpenFlow. We provide the implementation features of such virtual centers on the basis of software-defined networking that is managed by a dedicated controller (a server). We suggest the graph administration model of hyper-converged system resources compliant with required performance on the one hand and economic requirements on the other.

## The Use of a Genetic Algorithm in Modeling the Electrophysical Properties of a Layered Nanocomposite

The research proposes an approach to solving the problem of selecting layered nanocomposite components with given electrical properties. The known methods for modeling the nanocomposites electrical characteristics are based on a preliminary analysis of such characteristics as the dielectric constant and electrical conductivity of the materials that make up a nanocomposite. The study proposes an algorithm for the selection of components of a layered nanocomposite using a genetic algorithm.

## Estimation of Quality of Non-Stationary Systems on the Return Frequency Characteristic Plane

Direct quality parameters, such as time of regulation, overshoot, damping decrement are widely used for estimation of linear systems quality. Alongside with direct parameters indirect estimations of quality are used. One of such quality parameters for nonlinear systems is the degree of stability or response speed. A number of research studies show that properties of nonlinear systems investigation is reduced to the analysis of absolute stability of processes.

## Prevention of Accidental Combinations of Events in the Control of Human-Machine Systems

In the work the problem of accidental combinations of events is investigated. An accidental combination of events is a set of defects in equipment, software and human errors, relatively non-dangerous separately but leading to an accident when they occur in a certain order at a certain time interval. Modern warning tools can parry mainly individual adverse effects and to effectively prevent critical modes it is necessary to provide mathematical analysis of systems for accidental combinations of events at different time intervals.

## Zero-Knowledge Proof Authentication Protocols

The paper presented the comparative analysis of the authentication Shnorr’s protocol and the authentication protocol based on the task of finding a Hamilton cycle in the graph. It is shown that with the use of CUDA technology the productivity of protocols on graphs is a shighas Shnorr’s protocol productivity. Theim portance of such research is that protocols on graphs (the authentication protocol on the basis of the proof of graph isomorphism, the authentication protocol based on the task of finding a Hamilton cycle in the graph, etc.) have the property of zero-know ledge proof.

## Multiple Hedging on Energy Market

The article is devoted to the calculation of the dynamic hedge ratio based on three different types of volatility models, among which S-BEKK-GARCH model takes into account cross-sectional dependence. The hedging strategy is built for eight stock-futures pairs on energy market in Russia.

## Hybrid Automation Extended Model

An extended model of hybrid automata for dynamic systems is considered, where, along with a discrete control subsystem and control objects with lumped parameters, there are control objects with distributed parameters (linear and stationary from the point of view of automatic control theory). The possibility of software implementation of an extended model of hybrid automata on embedded computing systems is shown.

## Learning Neural Network Controllers for Stabilizing Hybrid Dynamic Systems

Control modules based on artiﬁcial neural networks (NN) are often used for controlling objects with lumped parameters. Controled objects in such systems have ﬁnite set of natural oscillation frequencies.

## On a Goodman–Hedetniemi Sufﬁcient Condition for the Graph Hamiltonicity

In 1859 the Irish mathematician Sir William Rowan Hamilt onpropose daga mein which it was required to ﬁnd a dodeca hedron bypass around its edges with a return to the starting point. In his honor, the corresponding path in the graph was later called the Hamiltonian cycle: it is the spanning cycle in the graph, that is, the cycle passing through all the vertices of the graph. A graph containing a Hamiltonian cycle is said to be Hamiltonian.