BSU bulletin. Mathematics, Informatics
, , ON A CERTAIN APPROACH TO MODELING DYNAMIC SYSTEMS // BSU bulletin. Mathematics, Informatics. - 2018. №2. . - С. 95-109.
ON A CERTAIN APPROACH TO MODELING DYNAMIC SYSTEMS
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.
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