Existence of Forbidden Digraphs for Crisp Boolean Petri Nets
Boolean Petri net (BPN) and Crisp Boolean Petri net (CBPN) is a well-studied graph model since 2010 which has several applications in mathematical modeling of complex or tricky networks. Modeling any network with Petri net which can generate binary numbers as marking vectors in its reachability tree...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Ram Arti Publishers
2020-02-01
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| Series: | International Journal of Mathematical, Engineering and Management Sciences |
| Subjects: | |
| Online Access: | https://www.ijmems.in/volumes/volume5/number1/8-IJMEMS-5-ICQRIT2019-51-8395-2020.pdf |
| _version_ | 1819049696875773952 |
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| author | Gajendra Pratap Singh Sujit Kumar Singh Madhuri Jha |
| author_facet | Gajendra Pratap Singh Sujit Kumar Singh Madhuri Jha |
| author_sort | Gajendra Pratap Singh |
| collection | DOAJ |
| description | Boolean Petri net (BPN) and Crisp Boolean Petri net (CBPN) is a well-studied graph model since 2010 which has several applications in mathematical modeling of complex or tricky networks. Modeling any network with Petri net which can generate binary numbers as marking vectors in its reachability tree is still has much uses. In CBPN with a minimum number of transition and minimum number of steps of reachability tree, minimal execution time to run the machine has not been noted till date, thus it’s necessary to sort out this problem. Possibly it may occur due to some forbidden structure which hinders any 1-safe Petri net to be a CBPN. In this paper, we present some forbidden digraphs whose presence interrupts the generation of binary n-vectors exactly once. Any 1-safe Petri net is not a CBPN if it contains any of the subnet induced to the four forbidden structures discussed in this paper. |
| first_indexed | 2024-12-21T11:36:16Z |
| format | Article |
| id | doaj.art-7dda136e937f49a792610037f6c64f61 |
| institution | Directory Open Access Journal |
| issn | 2455-7749 2455-7749 |
| language | English |
| last_indexed | 2024-12-21T11:36:16Z |
| publishDate | 2020-02-01 |
| publisher | Ram Arti Publishers |
| record_format | Article |
| series | International Journal of Mathematical, Engineering and Management Sciences |
| spelling | doaj.art-7dda136e937f49a792610037f6c64f612022-12-21T19:05:26ZengRam Arti PublishersInternational Journal of Mathematical, Engineering and Management Sciences2455-77492455-77492020-02-0151839510.33889/IJMEMS.2020.5.1.008Existence of Forbidden Digraphs for Crisp Boolean Petri NetsGajendra Pratap Singh0Sujit Kumar Singh1Madhuri Jha2School of Computational and Integrative Sciences, Jawaharlal Nehru University, New Delhi-110067, IndiaSchool of Computational and Integrative Sciences, Jawaharlal Nehru University, New Delhi-110067, IndiaSchool of Computational and Integrative Sciences, Jawaharlal Nehru University, New Delhi-110067, IndiaBoolean Petri net (BPN) and Crisp Boolean Petri net (CBPN) is a well-studied graph model since 2010 which has several applications in mathematical modeling of complex or tricky networks. Modeling any network with Petri net which can generate binary numbers as marking vectors in its reachability tree is still has much uses. In CBPN with a minimum number of transition and minimum number of steps of reachability tree, minimal execution time to run the machine has not been noted till date, thus it’s necessary to sort out this problem. Possibly it may occur due to some forbidden structure which hinders any 1-safe Petri net to be a CBPN. In this paper, we present some forbidden digraphs whose presence interrupts the generation of binary n-vectors exactly once. Any 1-safe Petri net is not a CBPN if it contains any of the subnet induced to the four forbidden structures discussed in this paper.https://www.ijmems.in/volumes/volume5/number1/8-IJMEMS-5-ICQRIT2019-51-8395-2020.pdfpetri netbinary vectorsboolean petri netcrisp boolean petri netforbidden graphs |
| spellingShingle | Gajendra Pratap Singh Sujit Kumar Singh Madhuri Jha Existence of Forbidden Digraphs for Crisp Boolean Petri Nets International Journal of Mathematical, Engineering and Management Sciences petri net binary vectors boolean petri net crisp boolean petri net forbidden graphs |
| title | Existence of Forbidden Digraphs for Crisp Boolean Petri Nets |
| title_full | Existence of Forbidden Digraphs for Crisp Boolean Petri Nets |
| title_fullStr | Existence of Forbidden Digraphs for Crisp Boolean Petri Nets |
| title_full_unstemmed | Existence of Forbidden Digraphs for Crisp Boolean Petri Nets |
| title_short | Existence of Forbidden Digraphs for Crisp Boolean Petri Nets |
| title_sort | existence of forbidden digraphs for crisp boolean petri nets |
| topic | petri net binary vectors boolean petri net crisp boolean petri net forbidden graphs |
| url | https://www.ijmems.in/volumes/volume5/number1/8-IJMEMS-5-ICQRIT2019-51-8395-2020.pdf |
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