The Theory Graph Modeling and Programming Paradigm Systems FROM Modules TO the Application Areas

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 modelling the system on the graph of  modules, which describe  in the  programming languages – LP (Algol-60, Fortran, Cobol, PL/1, Smalltalk, etc.) and the advanced operations of association (assembling, make,  weaver, config  etc.). The standard of configuration (2012) Assembly of heterogeneous software elements in AS of different fields of knowledge is made. A brief description of modern and future programming paradigms for formal theoretical creation of systems from intelligent and cloud service elements of the Internet is given.. There is a new direction of nanotechnology in the near future.