The paper proposes to consider individual heuristics as unreliably operating parts of the information processing system. In a separate case, several different heuristics are adopted to solve the same problem, and the results obtained are adjusted in a certain way. In this case, problems arise that are close in methodology to the problems of synthesizing reliable circuits from unreliable elements or making a collective expert decision. The work solves the problem of constructing an optimal correction function based on control material; classes of functions of k-valued logic under monotonicity restrictions are studied. A theorem on the completeness of the class of monotonic functions of k-valued logic for arbitrary k is proved, and a basis in the given class is proved and constructed. The problem of constructing an optimal corrector in the class of disjunctive normal forms of k-valued functions is solved.

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 k valued logical functions and developing methods and algorithms for minimizing functions in the class of canonical normal forms, estimating the number of monotonic functions of k valued 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 algorithmsfor 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 therepresentation 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

This manuscript proves specific theorems for transforming Boolean expressions of logical formulas when moving from one basis to another, simplifying the solution of complex equations, especially for cryptographic applications. The paper develops methods for solving specific nonlinear systems of Boolean equations used in cryptographic S-boxes using transformations to simpler forms, such as disjunctive normal forms (DNFs) and Zhegalkin polynomials. The main contributions include a mathematical basis for transforming formulas, a complexity-reducing grouping method, and the RLSY program for practical implementation. A rigorous theory, cryptographic relevance, and a detailed description of the algorithm are proposed. The grouping method reduces the system complexity by a factor of $2^{11}$, as shown in a test example, improving computational efficiency. A solution to a special class of systems of nonlinear Boolean equations of the second degree, which are a logical model of algebraic cryptanalysis, is also proposed. Test examples of logical formula transformations are given.