Combinatorial analysis of the solvability properties of the problems of recognition and completeness of algorithmic models. Part 1: Factorization approach

Abstract

In poorly formalized problems of recognition and classification, there are plenty of methods to generate feature descriptions of objects, which are subsequently studied by the methods of computer science. Using the factorization approach (reduction of a recognition/classification problem to a binary form), here we obtain combinatorial criteria for the solvability and regularity properties of the problems and criteria of correctness of algorithms and completeness of algorithmic models (the analysis of which is an important component of the algebraic approach to the synthesis of correct algorithms). The study presents a hierarchy of the criteria and cross-validation methods for assessing their feasibility. Based on the hierarchy of criteria, we formulate a general approach to the analysis of poorly formalized problems.