ON THE MINIMIZATION OF k-VALUED LOGIC FUNCTIONS IN THE CLASS OF DISJUNCTIVE NORMAL FORMS

In the world, research devoted to adjusting the results of heuristic methods based on forecasting, recognition, classification, and determining the absolute extremum of a multidimensional function is relevant and widely used in such fields as medicine, geology, hydrology, management, and computer technology. In this regard, it is important to construct optimal correctors of heuristic algorithms based on control materials. Therefore, checking the completeness of classes of kvalued logical functions and developing methods and algorithms for minimizing functions in the class of canonical normal forms, estimating the number of monotonic functions of kvalued logic, constructing minimal bases of special classes of correcting functions for correcting incorrect algorithms remains one of the important problems of computational and discrete science. mathematics. Currently, a lot of scientific research is being carried out around the world aimed at expanding the integration of science and industry, in particular the development of the theory of k -valued logical functions for correcting the results of heuristic algorithms. In this case, an important role is played by the construction of formulas in the class of canonical normal forms, the coding of elementary conjunctions and the application of the rules of gluing, absorption and idempotency for them, and checking the completeness of systems of correcting functions. Consequently, the development of effective numerical computational methods and algorithms for constructing correction functions based on k -valued logic to improve the accuracy of the results of heuristic methods is considered a targeted scientific research. The paper considers the representation of k -valued logical functions in the class of disjunctive normal forms. Various classes of monotone functions of k -valued logic are studied. Theorems are proved on the coincidence of abbreviated and shortest disjunctive normal forms of k -valued functions. For a certain class of k -valued monotone functions, we prove an estimate for the number of functions from this class. criteria for the absorption of elementary conjunctions by a first -order neighborhood of disjunctive normal forms of k -valued functions are proved.