Completeness criteria for classification problems with set-theoretic constraints

Within the framework of the algebraic approach to the synthesis of correct algorithms, a class of problems is described and analyzed in which, for each element of the initial-information space, a corresponding subset of the final-information set (problems with set-theoretic constraints) is defined. The concept of completeness is introduced for models of algorithms and algorithmic operators and for decision rule classes and correcting operations. Relevant completeness criteria are derived and proved.