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.

The solution to the problem of identifying objects in the IoT ecosystem of the Aral region is analyzed. The problem of constructing a correct algorithm with linear closure operators of a model for calculating estimates for identifying objects in the IoT ecosystem of the Aral region is considered. An algorithm operator is developed, which is considered correct for the problem Z, is the sum of q operators of the assessment calculation model, and is described by a set of numerical parameters $3·n·m·q$, where n is the number of specified features, m is the number of reference objects, and q is the set of recognized objects. Within the framework of the algebraic approach, several variants of linear combinations of recognition operators are constructed, the use of which gives the correct answer on the control material, and this is proven in the form of theorems. The constructed correct recognition algorithms, which are the easiest to use, where there is no optimization procedure, make it possible to quickly solve the issue of identifying incoming information flows in the IoT ecosystem of the Aral region.

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.

Fair water allocation is difficult when claimants share lossy canals and reserve supplies. CTI-RLex (claimant–terminal-invariant robust lexicographic allocation) is a linear-programming workflow that raises the weakest guaranteed monthly service lexicographically across enumerated shortage and outage scenarios, subject to reach capacities, conveyance losses, source limits and a bounded recourse budget. Fairness follows claimants, not delivery records. The guarantee vector is unique in exact arithmetic and holds on every convex combination of the scenarios within the combined budget. On a three-claimant Utah benchmark, the minimum guarantee rises from 0.1077 under utilization maximization to 0.4195 at a 2.57% nominal-delivery cost, and bounded recourse adds 9.22% over a rigid plan. Under gauge-scaled supplies, the plan kept every guarantee in all 33 seasons of 1993–2025. On a fifteen-claimant county instance in nine components, the sorted vectors first differ at position two, 0.0689 against 0.0564 under a common floor. One claimant rather than four stays at the floor, at 0.9% lower nominal delivery. Within decree-priority tiers, it gives the same guarantees unless reservoir storage ranks after every decreed right. Recorded 2025 diversions match the seasonal timing of the modeled demand, but two canals diverted two to three times that demand. Both instances remain uncalibrated benchmarks.