Abstract
The mathematical basics of graph modeling and paradigm programming of applied systems (AS) are presented. The vertices of graph are been the functional elements of the systems and the arcs define the connections between them. The graph is represented by an adjacency and reach ability matrix. A number of graph of program structures and their representation by mathematical operations (unions, connections, differences, etc.) are shown. Given the characteristics of graph structures, complexes, units, and systems created from the modules of the graph. The method of modeling the system on the graph of modules, which describe in the programming languages (LP) and calling them with operations (link, assembling, building, etc.). The standard of configuration (2012) Assembly of heterogeneous software elements in AS of different fields of knowledge is made. Brief descriptions of modern and future programming paradigms for formal theoretical creation of systems from service-components for Internet in the near future are given.
Highlights
Programming theory is a mathematical science, the object of study of which is the mathematical abstraction of the functions of programs with a certain logical and information structure, focused on computer execution
In the early stages of the emergence of the method of assembling large programs and complexes of spent modules in the LP used the theoretical apparatus of graphs to create modular program structures
Graph theory allows to establish the shortest path of program elements and prove the correctness of binding graph modules using adjacency matrices, reachability and mathematical operations in complex program structures
Summary
Programming theory is a mathematical science, the object of study of which is the mathematical abstraction of the functions of programs with a certain logical and information structure, focused on computer execution. With the advent of the LP began to develop new methods of analysis of algorithms of AS problems, the graph theory for the representation the structure AS by separate programs elements, displaying them in the vertices of the graph to create a complex structure of AS (programs, aggregate, complex, system, etc.). Programs elements of missile defense were first called modules, programs, objects, components, services, etc. For the formal specification of these elements were formed the corresponding programming paradigms, allowing from the point of view of the theory and graphs to describe the problems of different AS (medicine, biology, mathematic, chemistry, genetic, etc.)
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