Begell House Inc. Journal of Automation and Information Sciences JAI(S) 1064-2315 51 7 2019
Algorithms for Solving the Systems of Linear Constraints with Integer Coefficients in the Set &#123;0, 1&#125; 1-23 Sergey L. Kryvyi Kiev National Taras Shevchenko University, Kiev Vasiliy T. Antonyuk Kiev National Taras Shevchenko University, Kiev The basis concepts of linear homogeneous and inhomogeneous equations and inequalities in the domain &#123;0, 1&#125; are considered, the properties of the TSS-algorithm, which may be applied for solving those systems are described. The procedures for clearing the sets of solutions and determining the linearly dependent equations of the system during the process of the TSS-algorithm are shown. Based on the basis concepts and properties, a modification of the TSS-algorithm for solving systems of linear homogeneous equations and inequalities with integer coefficients in the domain &#123;0, 1&#125;, sufficiently economical relatively to memory, is offered. A description of the proposed algorithm using pseudo-code and an estimate of the time complexity are given. Algorithms for solving a separate class of systems of linear homogeneous equations and inequalities whose coefficients belong to the set &#123;-1, 0, 1&#125; are considered. A series of theorems that prove the correctness of the proposed algorithms are given. It is described their application to the following problems: finding the sets of independent vertices of an undirected graph; finding deadlocks and traps in the Petri net; analysis of multiple disjunctions for contradiction/consistency. For the task of finding sets of independent vertices of an undirected graph, a detailed description of reducing the problem to a system of linear homogeneous inequalities is given, two solution algorithms are proposed, as well as a modification of the second algorithm. Examples with a detailed explanation of the solution via each of the algorithms are given and their time characteristics of work are described. For problems of finding deadlocks and traps in the Petri net, a method for reducing it to systems of linear inequalities with coefficients in the set &#123;-1, 0, 1&#125; and solutions in the set &#123;0, 1&#125; is proposed. An example with the solution explanation and time characteristics of the work of the offered algorithm is described. The algorithm for analyzing the set of disjunctions for inconsistency is presented in a pseudo-code form. In addition to checking for the inconsistency of a given set of disjunctions, it allows one to find the minimal inconsistent subsets of disjunctions if they exist. The operation of the algorithm is illustrated with examples with time characteristics.
Optimal Control of Intensity of Water Point Sources in Unsaturated Porous Medium 24-33 Sergey I. Lyashko Kiev National Taras Shevchenko University, Kiev Dmitriy A. Klyushin Kiev National Taras Shevchenko University, Kiev Andrey A. Timoshenko Kiev National Taras Shevchenko University, Kiev Nataliya I. Lyashko V.M. Glushkov Institute of Cybernetics of National Academy of Sciences of Ukraine, Kiev Elena S. Bondar Kiev National Taras Shevchenko University, Kiev Moisture transfer in an unsaturated porous medium with point sources, described by the Richards−Klute equation is a very complicated and unstable computational process. This can be explained by the fact that the physical process, described by this equation, is characterized by a large number of diverse parameters. For reduction of this complexity we propose the approach, based on the Kirchhoff transformation, which enables reduction of the quasilinear parabolic initial-boundary problem to a linear and dimensionless problem. In this paper a two-dimensional quasilinear problem of optimal control using point sources for a rectangular unsaturated porous medium with known initial conditions, fixed humidity at the bottom bound and the given target humidity, is considered. In this statement the problem is studied and solved for the first time. To solve the linear dimensionless optimal control problem on non-stationary moisture transport in an unsaturated porous medium obtained using the Kirchhoff transformation, the variation algorithm of identifying the optimal source power is used, which allows modeling the process under realistic assumptions. The correctness of linearized dimensionless problem of moisture transfer is proved. In particular, theorems of existence and uniqueness of the generalized solution are proven as well as the existence and the uniqueness of the optimal control of power of the immersed sources. Modelling of moisture transfer from an immersed source in a dry ground area is done. The results of numerical experiments showing high accuracy of the method are adduced. The proposed method allows solving the urgent problem of selection of the optimal parameter for a drip irrigation system and improvement of its efficiency.
Methods of Solving the Problems of Mathematical Safe on Elementary Graphs 34-46 Artem L. Gurin National Technical University of Ukraine "Igor Sikorsky Kiev Polytechnic Institute", Kiev Andrey G. Donets National Aviation University, Kiev Sergey P. Zagorodnyuk Kiev National Taras Shevchenko University, Kiev The problem of mathematical safe consisting of a certain system of interrelated locks with given initial states is under consideration. Such system can be represented in the form of oriented or non-oriented graph, which vertexes are locks. In this paper, we consider graphs of sufficiently simple structures, such as path, contour, chain, cycle, fantail, stairs with a prescribed quantity of steps, and complicated stairs. In the general case, solution of this problem is reduced to solving a system of linear equations in the class of subtracts in absolute value, which is equal to the number of states of every safe lock. In fact, this number equals to the number of key turns in each lock for reaching finally transition of the safe in the state when all locks are open. To solve this problem, two original methods are suggested, namely, the method of separation of variables and the method of summary representations. The essence of first method consists in the following. For some elementary graphs there is a potential of singling out some equations for their immediate solving relative to one arbitrary variable. Further, substituting successively the obtained solutions into the corresponding equations, we obtain the solution of the system. This method was used for solving the problem for the graph of a cycle type. The essence of the second method consists in the introduction of a special parameter called the sum of unknowns. Some graphs make possible to present the system variables by this parameter. Summing these variables we obtain the equation relative to this parameter. Having solved this equation we obtain the value of this parameter as well as the values of all variables. This method was used for solving the problem for the graphs of window and stairs types. Every problem for the prescribed types of safe is shown by examples and is supplemented by verification of the solution.
Automatic Vulnerability Detection Algorithm for the SQL-Injection 47-54 Askar T. Rakhmanov Muhammad al-Khwarizmi Tashkent University of Information Technologies, Uzbekistan Rustam Kh. Khamdamov Scientific Innovation Center of Information and Communication Technologies of Muhammad al-Khwarizmi Tashkent University of Information Technologies, Uzbekistan Komil F. Kerimov Muhammad al-Khwarizmi Tashkent University of Information Technologies, Uzbekistan Shukhrat K. Kamalov Muhammad al-Khwarizmi Tashkent University of Information Technologies, Uzbekistan Attacks to web applications are a relatively new type of attack. If the web application does not filter incoming parameters properly, then attackers can get the opportunity to falsify the database using the form on the web page or by changing other incoming data. Mathematical modeling and identification of information objects play an important role in solving problems of pattern recognition. One of these tasks is to detect attacks or normal requests for web applications. Studies on the detection of attacks or normal requests for web applications began relatively recently. Nevertheless, there is a lot of research in this direction. Attack of the SQL-injection is a common way of hacking web applications that have a database. Our paper proposes a mathematical method for identifying SQL-injection attacks using a function bounded below that depends on the input string. To build such function, we used special characters and key words that are often found in the construction of attacks by intruders. In our proposed method, we can detect SQL-injection attacks using a single character. Nevertheless, we experimentally have shown that the proposed detection method using a set of numerous symbols allows us to determine the vulnerability of the SQL-injection type more accurately. In the proposed method, we created a character set that combines both attack and normal detections, and the previously known threshold, using the approximate data of the attackers and normal strings. According to experiments with artificial data, the set contains a space, semicolon and right bracket that are most suitable for detecting an attack or normal request.
On Nonstationary Problem of Motion Control in Conflict Situation 55-66 Vladimir A. Pepelyaev V.M. Glushkov Institute of Cybernetics of National Academy of Sciences of Ukraine, Kiev Alexey A. Chikriy V.M. Glushkov Institute of Cybernetics of National Academy of Sciences of Ukraine, Kyiv Kirill A. Chikriy V.M. Glushkov Institute of Cybernetics of National Academy of Sciences of Ukraine, Kiev The mathematical theory of control under conflict and uncertainty provides a wide range of fundamental methods to study controlled dynamic processes of various nature. This paper considers the game problems of pursuit for nonstationary controlled processes of general type with a cylindrical terminal set. The investigation is closely related to L.S. Pontryagin first direct method and the method of resolving functions. The purpose of the paper is to derive sufficient conditions for the game termination for some guaranteed time in favor of the first player to provide the control implementing this result. In the development of the method of resolving functions the upper and lower resolving functions of two types are introduced in the form of support functions of special multivalued mappings. This made it possible to obtain conditions for the game termination in the class of quasi- and stroboscopic strategies. The comprehensive analysis of properties of special maltivalued mappings and their selectors allowed us to choose measurable controls by virtue of measurable choice theorem. A comparison of the guaranteed times of the above mentioned methods is given. In so doing the properties of L × B -measurability of the key multivalued mappings and the corresponding resolving functions − the support functions of these mappings are used. The property of superpositional measurability of above mentioned objects plays essential role in the method design. As a rule, in specific model examples the resolving functions are the large positive roots of certain quadratic equations that makes it possible to obtain solution in an analytical form.
Probabilistic-Mathematical Models for Formation of Information Flows in Aircraft Fire Alarm System 67-80 Ali Al-Ammori National Transport University, Kiev Andrey N. Dmytrychenko National Transport University, Kiev Hasan A. Al-Ammori National Transport University, Kiev The article deals with solving the problem urgent for aviation practice which consists in providing the aircraft crew with reliable information from primary sources of information (sensors of controlled parameters) in normal and special flight situations. To solve this problem we have developed the probabilistic-physical model of processes of information flows formation in aircraft fire alarm system and showed geometric probabilistic characteristics: the probabilities of correct fire detection, non-detection and false alarm. The article has proved mathematically the conditions ensuring simultaneously equal degree of reducing the probabilities of non-detection and false alarm so that they would be simultaneously equal and minimum. It is proposed to consider the fire extinguishing system using the structural diagram of the state graph of the information-redundant system. The analysis of formation and creation of the control flows in the fire alarm system has been carried out and it has been proved that the system probabilities form a complete group of events that can be afterwards considered by the mathematical and probabilistic analysis methods to predict the state of the fire alarm system. The mathematical formulas for comparing the probabilities of non-detection and false alarm are obtained and their graphical dependences with respect to probability of correct detection and the number of sensors in the system are shown. We have obtained the mathematical dependence of growth coefficient of probability of correct fire detection compared with the false alarm probability considering the number of sensors. It is proved that with the increased number of sensors the growth coefficient increases in exponential function. Therefore in special conditions it makes sense to desensitize the sensors raising the actuation threshold and in so doing maintaining conditions ensuring the minimum values of probabilities of non-detection and false alarm of fire alarm system.