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.

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.

This paper explores the problem of developing correcting functions that replace multiple unreliable (heuristic) recognition algorithms with a single, consistent decision function. The research concept stems from the fact that, in pattern recognition and collective expert decision-making problems, individual algorithms (heuristics) provide inconsistent or incomplete answers, requiring a mathematically sound method for their harmonization (correction) using test data. The methodological content of this paper consists of introducing classes of k-valued logic correcting functions that satisfy the constraints of preserving given sets (Constraint I) and monotonicity (Constraint II), and constructing algorithms for synthesizing a corrector that is optimal with respect to the linear performance functional for each combination of these constraints. The paper also provides a rationale for the optimality of the constructed algorithms (an optimality theorem) and an estimate of their time complexity.