MATHEMATICAL DESCRIPTION OF THE INEQUALITY OPERATION IN A LOGIC-TIME ENVIRONMENT

Abstract

Currently, there is an urgent problem of information security, which is related to the preservation of the confidentiality of information processed and stored in computer systems. The integrity and confidentiality of information is of great importance for the competitiveness and reputation of an organization or enterprise. Analytical processing of digital signals in a graphical or purely digital representation is somewhat limited and does not take into account the dynamics of signals and messages. To facilitate the preprocessing of dynamic digital variables and signals, the logic-time function of multivalued logic can be used. The article notes that computational mathematical modeling is becoming the main tool for studying complex dynamic processes and systems. The classical apparatus of logic is insufficient to describe the dynamics of system behavior over time. Therefore, it is important to develop models of so-called Boolean differential calculus, as this approach is based on the general concept of changing the logical variable, which will lead to a universal, in terms of dynamics, system of concepts and operations. It is shown that for the logic-time function of binary logic, this operation coincides with the sum modulo two. You can use the logic-time function of multivalued logic to facilitate the pre-processing of dynamic digital variables and signals. The paper considers one of the important operations - the operation of inequality and some of its properties. Inequality will allow, in the future, to introduce more complex operations on multivalued logical-temporal functions, such as derivative and initial, and to perform encoding, encryption of information in the logical-temporal environment. The possibility of using inequality when constructing indicator operations and variable differential is demonstrated. The implementation scheme of the inequality operation is modeled.