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Journal of Automation and Information Sciences

Published 12 issues per year

ISSN Print: 1064-2315

ISSN Online: 2163-9337

SJR: 0.173 SNIP: 0.588 CiteScore™:: 2

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Method of Summary Representations for Solving Problems of Mathematical Safe on Graphs

Volume 51, Issue 12, 2019, pp. 1-6
DOI: 10.1615/JAutomatInfScien.v51.i12.10
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ABSTRACT

We consider one of the stated in previous articles methods, namely, the method of summary representations, which was used on a merely intuitive level, and its theoretical substantiation is given. The essence of the method consists in search of a special parameter S, called as a sum of unknowns, which represent the solution of the initial system of equations. According to their structure, some graphs enable the expression of unknowns of the system by the above-mentioned parameter. Therefore, the problem consists in the determination of the value of this parameter. As the conducted theoretical studies showed, this is achieved by solving the special supplementary system of equations, which is a weighted sum of initial equations with the coefficients di, i = 1, 2,..., n, where the sum itself is equal to dS, here d is an unknown constant. Solving this supplementary system of equations we obtain the values di, i = 1, 2,..., n, d, and S, and at the same time the values of all variables of the main system. The method is tested by two examples confirming its efficiency. Moreover, for both examples, special attention is paid to the particular case when the solution does not exist. They appear when the parameter d value is multiple to K, where K is the number of states in each safe lock. In this case for solution existence the correction of the initial state of safes is performed bi i = 1, 2,..., n, such that −Σni=1di,bi, becomes multiple to K. Further, the problem is solved according to the general scheme of the method.

REFERENCES
  1. Donets G.A., Gurin A.L., Zagorodnyuk S.P., Methods of solving the problems of mathematical safe on elementary graphs, Mezhdunarodnyi nauchno-tekhnicheskiy zhurnal "Problemy upravleniya i informatiki", 2019, No. 4, 36-47. .

  2. Kryvyi S.L., Algorithms for solution of systems of linear Diophantine equations in residue fields, Cybernetics and Systems Analysis, 2007, 43(2), 171-178. .

  3. Kryvyi S.L., Solution algorithms for systems of linear equations over residue rings, Cybernetics and Systems Analysis, 2016, 52(5), 149-160. .

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