Formalization of a synthesis problem and methods for its solution

A formal formulation is proposed for the synthesis problem of finding objects with certain properties described only by a collection of precedents. A key feature of this formalization is that it is closely related to the pattern recognition theory. A general approach to solving the synthesis problem is described, and particular solution methods are presented in two important cases. For this purpose, a new recognition method is proposed that exhibits a high speed as applied to the data of the structure under study. The performance of the methods is demonstrated on actual data.