Applying Infinite Petri Nets to the Cybersecurity of Intelligent Networks, Grids and Clouds
Correctness of networking protocols represents the principal requirement of cybersecurity. Correctness of protocols is established via the procedures of their verification. A classical communication system includes a pair of interacting systems. Recent developments of computing and communication gri...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-12-01
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| Series: | Applied Sciences |
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| Online Access: | https://www.mdpi.com/2076-3417/11/24/11870 |
| _version_ | 1797506765024133120 |
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| author | Dmitry A. Zaitsev Tatiana R. Shmeleva David E. Probert |
| author_facet | Dmitry A. Zaitsev Tatiana R. Shmeleva David E. Probert |
| author_sort | Dmitry A. Zaitsev |
| collection | DOAJ |
| description | Correctness of networking protocols represents the principal requirement of cybersecurity. Correctness of protocols is established via the procedures of their verification. A classical communication system includes a pair of interacting systems. Recent developments of computing and communication grids for radio broadcasting, cellular networks, communication subsystems of supercomputers, specialized grids for numerical methods and networks on chips require verification of protocols for any number of devices. For analysis of computing and communication grid structures, a new class of infinite Petri nets has been introduced and studied for more than 10 years. Infinite Petri nets were also applied for simulating cellular automata. Rectangular, triangular and hexagonal grids on plane, hyper cube and hyper torus in multidimensional space have been considered. Composing and solving in parametric form infinite Diophantine systems of linear equations allowed us to prove the protocol properties for any grid size and any number of dimensions. Software generators of infinite Petri net models have been developed. Special classes of graphs, such as a graph of packet transmission directions and a graph of blockings, have been introduced and studied. Complex deadlocks have been revealed and classified. In the present paper, infinite Petri nets are divided into two following kinds: a single infinite construct and an infinite set of constructs of specified size (and number of dimensions). Finally, the paper discusses possible future work directions. |
| first_indexed | 2024-03-10T04:37:58Z |
| format | Article |
| id | doaj.art-c8edf3a7f9b9406ab957ddfde3c5ba81 |
| institution | Directory Open Access Journal |
| issn | 2076-3417 |
| language | English |
| last_indexed | 2024-03-10T04:37:58Z |
| publishDate | 2021-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Applied Sciences |
| spelling | doaj.art-c8edf3a7f9b9406ab957ddfde3c5ba812023-11-23T03:39:38ZengMDPI AGApplied Sciences2076-34172021-12-0111241187010.3390/app112411870Applying Infinite Petri Nets to the Cybersecurity of Intelligent Networks, Grids and CloudsDmitry A. Zaitsev0Tatiana R. Shmeleva1David E. Probert2Department of Information Technology, Odessa State Environmental University, 15 Lvivska Str., 65016 Odessa, UkraineDepartment of Computer Science, State University of Intelligent Technologies and Telecommunications, 1 Kuznechnaya Str., 65023 Odessa, UkraineVAZA Cybersecurity, Kola Cottage, Berkshire RG14 5TA, UKCorrectness of networking protocols represents the principal requirement of cybersecurity. Correctness of protocols is established via the procedures of their verification. A classical communication system includes a pair of interacting systems. Recent developments of computing and communication grids for radio broadcasting, cellular networks, communication subsystems of supercomputers, specialized grids for numerical methods and networks on chips require verification of protocols for any number of devices. For analysis of computing and communication grid structures, a new class of infinite Petri nets has been introduced and studied for more than 10 years. Infinite Petri nets were also applied for simulating cellular automata. Rectangular, triangular and hexagonal grids on plane, hyper cube and hyper torus in multidimensional space have been considered. Composing and solving in parametric form infinite Diophantine systems of linear equations allowed us to prove the protocol properties for any grid size and any number of dimensions. Software generators of infinite Petri net models have been developed. Special classes of graphs, such as a graph of packet transmission directions and a graph of blockings, have been introduced and studied. Complex deadlocks have been revealed and classified. In the present paper, infinite Petri nets are divided into two following kinds: a single infinite construct and an infinite set of constructs of specified size (and number of dimensions). Finally, the paper discusses possible future work directions.https://www.mdpi.com/2076-3417/11/24/11870cybersecuritycomputing gridcomputing cloudverification of protocolsinfinite Petri net |
| spellingShingle | Dmitry A. Zaitsev Tatiana R. Shmeleva David E. Probert Applying Infinite Petri Nets to the Cybersecurity of Intelligent Networks, Grids and Clouds Applied Sciences cybersecurity computing grid computing cloud verification of protocols infinite Petri net |
| title | Applying Infinite Petri Nets to the Cybersecurity of Intelligent Networks, Grids and Clouds |
| title_full | Applying Infinite Petri Nets to the Cybersecurity of Intelligent Networks, Grids and Clouds |
| title_fullStr | Applying Infinite Petri Nets to the Cybersecurity of Intelligent Networks, Grids and Clouds |
| title_full_unstemmed | Applying Infinite Petri Nets to the Cybersecurity of Intelligent Networks, Grids and Clouds |
| title_short | Applying Infinite Petri Nets to the Cybersecurity of Intelligent Networks, Grids and Clouds |
| title_sort | applying infinite petri nets to the cybersecurity of intelligent networks grids and clouds |
| topic | cybersecurity computing grid computing cloud verification of protocols infinite Petri net |
| url | https://www.mdpi.com/2076-3417/11/24/11870 |
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