Received 23.11.2021, Revised 17.02.2022, Accepted 24.03.2022

Mathematical description of logic-time functions of multiple-valued logic and some operations over them

Nataliia Sachaniuk-Kavets’ka, Olena Prozor

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

logical-temporal function of multiple-valued logic, productive word, index form, time-ordering operator
111-118
Sachaniuk-Kavets’ka, N., & Prozor, O. (2022). Mathematical description of logic-time functions of multiple-valued logic and some operations over them. Information Technologies and Computer Engineering, 19(2), 111-118. https://doi.org/10.31649/1999-9941-2022-53-1-111-118

References

[1] Bazilevsky, Yu.Ya. (1958). Questions of the theory of temporary logical functions. In Yu.Ya. Bazilevsky (Eds.) Questions of the theory of mathematical machines (Vol. 1, pp. 59-104). Moscow: State publishing house of physical and mathematical literature.

[2] Pospelov, D.A. (1960). Synthesis of schemes whose operation is described by time Boolean functions. Automation and Telemechanics, 21(10), 1410-1413.

[3] Rabinovych, Z.L. (1968). Vector-time switching functions (VP-functions) as a language for describing information processing schemes and processes. Cybernetics, 3, 36-42.

[4] Sachanyuk-Kavetska, N.V., & Kozhemyako, V.P. (2004). Elements of eye-processor image processing in a logical-temporal environment. Vinnytsia: UNIVERSUM.

[5] Sachanyuk-Kavetska, N.V., & Bondarenko, I.O. (2018). Identification of subjects in access control systems using the identification logic-time function as an effective method of complex information protection. Optical-electronic Information and Energy Technologies, 1(35), 14-23.

[6] Sachanyuk-Kavetska, N., Kozhemiako, V., Wojcik, W., Kassymkhanova, D., & Kalizhnova A. (2015). The use polynomials as a possible variant analytical processing on logic-time functions. In Optical fibers and their applications 2015: Proceedings of SPIE (article number 9816). Lublin: SPIE.

[7] Miller, D.M., & Thornton, M.A. (2007). Multiple-valued logic: Concepts and representations. San Rafael: Morgan & Claypool Publishers. doi: 10.2200/S00065ED1V01Y200709DCS012