BSU bulletin
Mathematics, Informatics

BSU bulletin. Mathematics, Informatics

Bibliographic description:
Nikolaeva D. D.
Shirapov D. S.
Antonov V. I.
ON A CERTAIN APPROACH TO MODELING DYNAMIC SYSTEMS // BSU bulletin. Mathematics, Informatics. - 2018. №2. . - С. 95-109.
DOI: 10.18101/2304-5728-2018-2-95-109UDK: 519.6
When developing complexes of computer programs modeling various dynamic sys- tems, it is often required to build mathematical models of a particular subject area. In the article we constructed such functions that it is possible to construct a super- position of functions (term) for any given programming language. Calculating the above term generates a computational process that occurs when the program is exe- cuted. If the program is designed to model a dynamic system, then the calculation of the algebraic term is an adequate simulation for the dynamic system functioning. Thus, an algebraic model of a programming language is developed for modeling of dynamic systems, where calculation of algebraic terms generates modeling process of dynamical systems. To construct these functions, it is necessary to accurately de- scribe the domain of definition and the range of values of these functions. To con- struct domains of definition and ranges of values for these functions we used con- text-free grammars, and identification operation. In addition to these tools, the con- cept of a multi-level model, the concept of indirect naming (indirect addressing), recursion, and also some simple tools from the theory of algorithms and program- ming theory are used. Thus, a method of computer modeling of various dynamic systems, where an arbitrary program can be represented as an algebraic term of a universal algebra with a signature from the indicated functions, is found to be suffi- ciently broad in practical coverage.
dynamic systems; modeling; mathematical model of language; universal algebra; context-free grammar; recursion; interpreter; semantics.
List of references:
Vasil'ev S. N., Zherlov A. K., Fedosov E. A., Fedunov B. E. Intellektnoe uprav- lenie dinamicheskimi sistemami [Intelligent Control of Dynamic Systems]. Moscow: Fiziko-matematicheskaya literatura Publ., 2000. 352 p.

Semantika yazykov programmirovaniya [Semantics of Programming Languages]. Moscow: Mir Publ., 1980. 395 p. (Transl. from English)

Tuzov V. A. Matematicheskaya model' yazyka [Mathematical Model of Lan- guage]. Leningrad: Leningrad State University, 1984. 176 p.

Tuzov V. A. Podkhod k postroeniyu universal'noi skhemy yazyka. Sintaksis. Pro- grammirovanie [Approach to Construction of a Universal Language Scheme. Syntax. Programming]. 1980. No. 5. Pp. 17–25.