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Construction of a Crisp Boolean Petri Net from a 1-safe Petri Net

by Gajendra Pratap Singh, Sangita Kansal, Mukti Acharya
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International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 73 - Number 17
Year of Publication: 2013
Authors: Gajendra Pratap Singh, Sangita Kansal, Mukti Acharya
10.5120/12830-0245

Gajendra Pratap Singh, Sangita Kansal, Mukti Acharya . Construction of a Crisp Boolean Petri Net from a 1-safe Petri Net. International Journal of Computer Applications. 73, 17 ( July 2013), 1-4. DOI=10.5120/12830-0245

@article{ 10.5120/12830-0245,
author = { Gajendra Pratap Singh, Sangita Kansal, Mukti Acharya },
title = { Construction of a Crisp Boolean Petri Net from a 1-safe Petri Net },
journal = { International Journal of Computer Applications },
issue_date = { July 2013 },
volume = { 73 },
number = { 17 },
month = { July },
year = { 2013 },
issn = { 0975-8887 },
pages = { 1-4 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume73/number17/12830-0245/ },
doi = { 10.5120/12830-0245 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T21:40:19.732802+05:30
%A Gajendra Pratap Singh
%A Sangita Kansal
%A Mukti Acharya
%T Construction of a Crisp Boolean Petri Net from a 1-safe Petri Net
%J International Journal of Computer Applications
%@ 0975-8887
%V 73
%N 17
%P 1-4
%D 2013
%I Foundation of Computer Science (FCS), NY, USA
Abstract

The concept of a Petri net, a tool for the study of certain discrete dynamical systems, was invented in 1939 by Carl Adam Petri. In the attempt to characterize Boolean Petri nets, we discovered a subclass of Boolean Petri net called the crisp Boolean Petri net, viz. , the one that generates every binary vector as its marking vectors exactly once. In this paper, the construction of a crisp Boolean Petri net from a 1-safe Petri net has been shown.

References
  1. Kansal, S. , Singh, G. P. and Acharya, M. , On Petri nets generating all the binary n-vectors, Scientiae Mathematicae Japonicae, 71(2), 2010, 209-216, e-2013, 113-120.
  2. Kansal, S. , Acharya, M. and Singh, G. P. , Boolean Petri nets. In: Petri nets — Manufacturing and Computer Science (Ed. : Pawel Pawlewski), 381-406; Chapter 17. In- Tech Global Publisher, 2012, ISBN 978-953-51-0700-2.
  3. Peterson, J. L. , Petri net theory and the modeling of systems, Englewood Cliffs, NJ: Prentice-Hall, Inc. , 1981.
  4. Harary, F. , Graph theory, Addison-Wesley, Massachusettes, Reading, 1969.
  5. Jensen, K. , Coloured Petri nets, Lecture notes in computer science, 254, Springer-Verlag, Berlin, 1986, 248- 299.
  6. Reisig, W. , Petri nets, Springer-Verleg, New York, 1985.
  7. Murata, T. , Petri nets: Properties, analysis and applications, Proc. IEEE, 77(4), 1989, 541-580.
  8. Singh, G. P. , Some advances in the theory of Petri nets, Ph. D. Thesis, submitted to the University of Delhi, Delhi, December 5, 2012.
  9. Kansal, S. , Singh, G. P. and Acharya, M. , 1-Safe Petri nets generating every binary n-vector exactly once, Scientiae Mathematicae Japonicae, 74(1), 2011, 29-36, e-2011, 127- 134.
  10. Kansal, S. , Acharya, M. and Singh, G. P. , Uniqueness of minimal 1-safe Petri net generating every binary n-vectors as its marking vectors exactly once, Scientiae Mathematicae Japonicae, e-2012, 75-78.
  11. Acharya, B. D. , Set-indexers of a graph and set-graceful graphs, Bull. Allahabad Math. Soc. 16, 2001, 1-23.
Index Terms

Computer Science
Information Sciences

Keywords

1-safe Petri nets graph theory reachability tree binary n-vector hypercube.

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