Zhang B. Development of methods and algorithms for solving the mathematical safe problem

Thesis deals with the development of methods for solving certain positional games which may be defined on various mathematical objects such as matrix, graph etc, and are called by the mathematical safe problem. It is shown that, regardless of mathematical object, such problem can be reduced to solving a system of linear comparisons in a class of residues in a finite modulus. Depending of the lock types, the mathematical safes can be divided into three groups: those having two-state locks, safes with locks of equal quantity of states, and safes with different-type locks. For each group of safes defined on graph or matrix, either explicit expressions for solutions of corresponding system of comparisons are found or algorithms for finding these solutions are derived.