An Approach for Mathematical Modeling and Investigation of Computer Processes at a Macro Level

Abstract

In the digital age, the role of information technology and computer processes is growing. This requires refining the development of software by optimizing the communications between program components and seeking effective interaction in the implementation of processes. Complex module structures are usually developed, which require high compatibility between components and their proper functioning. The purpose of this article is to propose an approach for investigation of a set of connected computer processes executed on a macro level by using deterministic modelling. A formal technological procedure for conducting a deterministic investigation of the interaction between processes was developed. It allows for the transition from the object-original to an adequate mathematical model with its program realization. The core of the constructed procedure is the phases “mathematical formalization”, “mathematical description”, and “program realization”. The goal was to present an application of the procedure to investigate all possible realizations of connected processes, presented as nodes in a directed graph scheme of algorithms by determining the reachability. The program language APL2 was used as a tool for program description of the defined mathematical models, which were realized in the software system TryAPL2 for research automation. A preliminary mathematical formalization of interacting processes was made by presenting an example graph scheme and its transformation into an ordered structure. On the basis of the mathematical description, we developed two program models for automation of the transition to an ordered graph scheme and determination of all possible paths in it for activation of sequences of processes. The proposed models are part of a generalized environment for program investigation of the computer processing organization.