МЕТОД СУМАРНИХ ПРЕДСТАВЛЕНЬ ДЛЯ РОЗВ’ЯЗКУ ЗАДАЧ ПРО МАТЕМАТИЧНИЙ СЕЙФ НА ГРАФАХ

• Datum: 2025
• 1. Verfasser: Gurin, A.L.
• Format: Artikel
• Sprache: English
• Veröffentlicht: V.M. Glushkov Institute of Cybernetics of NAS of Ukraine 2025
• Schlagworte: математичний сейф; система рівнянь; вектор початкового стану сейфа; неорієнтований граф; метод сумарних представлень
• Online Zugang: https://jais.net.ua/index.php/files/article/view/688
• Назва журналу: Problems of Control and Informatics

We explore one of the methods, first formulated in our previous papers, namely, the method of summarized representations which was used in these papers on merely intuitive level. In this paper, theoretical substantiation of the method is given. The gist of the method consists in search of special parameter S , called the sum of unknowns, representing the solution of original system of equations. Some graphs in design are susceptible to express unknowns of the system through the above mentioned parameter.In such cases, the problem reduces to evaluation of the parameter value. The indepth analysis of the problem at hand shows that this can be achieved by solving special auxiliary system of equations. The latter presents itself as the weighted sum of original equations, namely, the sum of original system of equations multiplied by coefficients di , i =1,2, ..., n . It should be noted that the above mentioned sum equals dS with d being an unknown constant. Upon solving the auxiliary system of equations we obtain the values of di , i =1, 2, ..., n, d , and S , as well as the values of all original system variables. The method is demonstrated on two examples confirming its efficiency. In both examples special attention is given to the particular case of solution nonexistence. This is the case when d is K fold, where K is the number of states in each safe lock. For the solution to exist the initial safe state is adjusted in such a way that the sum Σni=1 di bi becomes K-fold (bi , i =1,2, ..., n, are the safe states). Then the problem is solved using the general scheme of the method.