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International Journal of Mathematical, Engineering and Management Sciences

ISSN: 2455-7749


Existence of Forbidden Digraphs for Crisp Boolean Petri Nets

Existence of Forbidden Digraphs for Crisp Boolean Petri Nets

Gajendra Pratap Singh
School of Computational and Integrative Sciences, Jawaharlal Nehru University, New Delhi-110067, India.

Sujit Kumar Singh
School of Computational and Integrative Sciences, Jawaharlal Nehru University, New Delhi-110067, India.

Madhuri Jha
School of Computational and Integrative Sciences, Jawaharlal Nehru University, New Delhi-110067, India.

DOI https://doi.org/10.33889/IJMEMS.2020.5.1.008

Received on March 15, 2019
  ;
Accepted on September 08, 2019

Abstract

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.

Keywords- Petri net, Binary vectors, Boolean Petri net, Crisp Boolean Petri net, Forbidden graphs.

Citation

Singh, G. P., Singh, S. K., & Jha, M. (2020). Existence of Forbidden Digraphs for Crisp Boolean Petri Nets. International Journal of Mathematical, Engineering and Management Sciences, 5(1), 83-95. https://doi.org/10.33889/IJMEMS.2020.5.1.008.

Conflict of Interest

All the authors have no conflict of interest.

Acknowledgements

The first author is thankful to the Department of Science and Technology (SERB) (PID: ECR/2017/003480) and UPOE-II (ID-257) and DST purse grant for providing research facility. The authors are expressing their deep gratitude to anonymous reviewers, editors for their valuable suggestions and comments.

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