On the solvability and regularity of comparison problems for text fragments

Within the framework of the algebraic approach to the synthesis of correct algorithms, a class of problems is studied in which the elements of the initial-information space are numerical descriptions of pairs of text fragments. Solution algorithms use these descriptions to classify the original pairs of fragments according to the degree of their similarity or dissimilarity (in a certain sense). Solvability and regularity criteria for such problems are derived. The special case of constructing monotone solutions to the problems is discussed. Criteria for the monotone solvability and monotone regularity of the problems are proved.