Елементи математичного опису логіко-часових функцій багатозначної логіки та окремих операцій над ними

Abstract

The article states that mathematical and computer modeling are the main tools for studying complex dynamic processes and systems. At the level of computing devices, time is a criterion for streamlining the sequence of operations and is implicit, and for specific nodes, time ensures their proper operation and is represented at the level of clocks or clock pulses. The paper shows the expediency of the idea of replacing an arbitrary digital signal (variable) that changes over time with a time logic function, which allows to facilitate the preliminary analytical processing of digital signals and variables using the properties of such functions. The article presents a new mathematical apparatus for describing logic-time functions of multivalued logic and individual operations on them using modeling of known implementation schemes. An index form of representation of functions is proposed, which is quite easy to understand and allows to consider any logical-temporal functions as a numerical sequence. Lukasevich's negation operation and the shift operation are considered as basic operations, which will allow to introduce more complex operations on logical-temporal functions of multivalued logic, such as inequality, differentiation and integration, and to investigate their properties.