# Structural analysis of the compounds of integral objects

## Authors

• Volodymyr Sokolov Institute of special communication and information protection of National technical university of Ukraine “Igor Sikorsky Kyiv polytechnic institute”, Kyiv,

## Keywords:

Structural analysis, structural equivalence, functional equivalence, integral object, integral objects compounds.

## Abstract

The article presents the results of research on methods of analysis of the structure of software, built on architecture based on integral objects. To determine the structural analysis operations, the representation of the compounds of integral objects in the form of formulas of compounds and tables were chosen, and operations of integration and disintegration of compounds were formalized. The integration of compound with formation of a new class consists in encapsulating the compound into the class shell with the integration degree of the class one greater than that of the compound, and the disintegration consists in the reverse process of extracting the compound from the class shell with a decrease of integration degree by one. The table representation of the compounds of objects, which includes both the representation of objects and the connections between them, allows us to apply formal methods for analyzing their structure. The notion of structural equivalence of two compounds as having the same composition and structure of the objects compounds is determined, as well as the notion of functional equivalence of two compounds as those implementing the same composition of functions. As the main structural analysis operations, two basic operations are presented  ̶  the determination of the structural and functional equivalence of the two compounds. The determination of the equivalence of the compounds is reduced to comparing the table representation of the compounds, taking into account the permutation of the rows and columns of the tables. It is shown that the determination of structural equivalence is possible only for compounds of the same integration degree, and for the determination of functional equivalence, it is necessary to bring the compounds to the atomic level. The definition of functional equivalence is reduced to the determination of the structural equivalence of atomic formulas of compounds. The operations of recognition of structurally and functionally equivalent classes for a given compound are chosen as derivative operations, which are based on basic equivalence determination operations, as well as four operations of equivalent transformations of compounds: structurally and functionally equivalent replacement of a compound by an object of the equivalent class and partially structurally and functionally equivalent replacement of a fragment of a compound by an object of the equivalent class. Structural analysis operations are the basis for the equivalent transformation of compounds in the process of designing, verifying and optimizing the system of classes of the problem domain solution during software development.

## Author Biography

### Volodymyr Sokolov, Institute of special communication and information protection of National technical university of Ukraine “Igor Sikorsky Kyiv polytechnic institute”, Kyiv,

candidate of technical sciences, associate professor, associate professor at the cybersecurity and application of information systems academic department

## References

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2018-12-30

## How to Cite

Sokolov, V. (2018). Structural analysis of the compounds of integral objects. Information Technology and Security, 6(2), 68–78. https://doi.org/10.20535/2411-1031.2018.6.2.153491

## Section

MATHEMATICAL AND COMPUTER MODELING