A FORMAL DESCRIPTION OF A DECOMPOSITION ALGORITHM FOR COMPLEX
SYSTEMS BASED ON PETRI NETS USING TENSOR METHODS

Martyashin Georgiy Viktorovich, Postgraduate student, Penza State University (40 Krasnaya street, Penza, Russia), nowargore@gmail.com
Tarkhov Kirill Yur'evich, Postgraduate student, Penza State University (40 Krasnaya street, Penza, Russia), soulesspnz@gmail.com
Kalachev Andrey Valentinovich, Student, Penza State University (40 Krasnaya street, Penza, Russia), andrei.kalachev@gmail.com
Bal'zannikova Elena Alekseevna, Master’s degree student, Penza State University (40 Krasnaya street, Penza, Russia), elenabalzannikova@gmail.com
Pashchenko Dmitriy Vladimirovich, Doctor of engineering sciences, professor, head of sub-department of computerengineering, Penza State University (40 Krasnaya street, Penza, Russia), dmitry.pashchenko@ gmail.com

004.94

10.21685/2072-3059-2016-3-6

Background. The research object is a complex system in the form of a Petri net. The research subject a way of decomposition of the complex system to primitive fragments of Petri nets. The aim of the study is formally describe a decomposition algorithm for complex systems using tensor transformations.
Materials and methods. The formal description of the algorithm was carried outusing the Petri nets apparatus and tensor methodology.
Results. The algorithm presented in this article allows to implement the operation of the module of CAD structures of parallel computing systems on the basis of tensor calculation of network models.
Conclusions. The research results can be used for solving problems of develop-ment and improvement of complex systems.

Petri nets, tensor transformation, decomposition of complex systems.

1. Simankov V. S., Tolkachev D. M. Vestnik Adygeyskogo gosudarstvennogo universiteta. Ser. 4. Estestvenno-matematicheskie i tekhnicheskie nauki [Bulletin of Adygea State University. Series 4. Natural, mathematical and engineering sciences]. 2012, no. 4, pp. 84–92.
2. Kizilov E., Pashenko D., Trokoz D., Konnov N. 5th International Workshop on Com-puter Sci-ence and Engineering Information Processing and Control Engineering, WCSE 2015-IPCE. 2015, pp. 185–190
3. Domnin A., Konnov N., Mekhanov V.Communication in Computer and Information Science.2014,pp.81–86.
4. Volchikhin V. I., Pashchenko D. V., Trokoz D. A. Izvestiya vysshikh uchebnykh zavedeniy. Povolzhskiy region. Tekhnicheskie nauki [University proceedings. Volga re-gion. Engineering sciences]. 2010, no. 3 (15), pp. 37–48.
5. Diaz Michel Petri Nets: Fundamental Models, Verification and Applications. Hoboken, NJ, USA: John Wiley & Sons, Wiley-ISTE, 2013, 656 p.
6. Pashchenko D. V., Trokoz D. A. Materials of the International scientific: practical conference. Praga, 2014, pp. 550–556.
7. Pashenko D., Trokoz D., Konnov N. Procedia Computer Science. 2015, pp. 99–103.
8. Kulagin V. P. Automatic Control and Computer Sciences. 1989, pp. 55–61.
9. Boris Obsieger Metoda Rubnih Elementata I. Createspace, 2015, 432 p.
10. Jeevanjee N. An Introduction to Tensors and Group Theory for Physicists. Second Edition. Birkhauser: Springer, 2015, 305 p.
11. Patil S., Dubinin V., Pang C., Vyatkin V. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). GOROD 2015, pp. 93–97
12. Dai W. W., Christensen J. H., Vyatkin V., Dubinin V. Proceedings – 2014: 12th IEEE International Conference on Industrial Informatics, INDIN. 2014, pp. 64–70
13. Leslie Hogben Handbook of Linear Algebra. Second Edition. Chapman and Hall/CRC, 2013, 1904 p.
14. Kron Gabriel Tensor Analysis of Networks. Facsimile Publisher, 2015, 662 p.