The solution of recognition problems with information given by the enumeration of domains

A model of recognition algorithms for the initial information given in the form of arbitrary bounded domains in an $n$-dimensional Euclidean space $R^n$ is constructed. The correctness of the algebraic closure of this model without constraints imposed on the final sample of control objects is proved, and the stability of the correct algorithm in the closure of finite power is investigated. A basic scheme for constructing the algorithms for recognition problems with a continual control set of objects converging to a certain degree to the correct algorithm is given.