Research Article
Existence and Uniqueness of a Minimum Crisp Boolean Petri Net
|
International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
|
| Volume 73 - Issue 20 |
| Published: July 2013 |
| Authors: Gajendra Pratap Singh, Sangita Kansal, Mukti Acharya |
10.5120/13013-0316
|
Gajendra Pratap Singh, Sangita Kansal, Mukti Acharya . Existence and Uniqueness of a Minimum Crisp Boolean Petri Net. International Journal of Computer Applications. 73, 20 (July 2013), 35-41. DOI=10.5120/13013-0316
@article{ 10.5120/13013-0316,
author = { Gajendra Pratap Singh,Sangita Kansal,Mukti Acharya },
title = { Existence and Uniqueness of a Minimum Crisp Boolean Petri Net },
journal = { International Journal of Computer Applications },
year = { 2013 },
volume = { 73 },
number = { 20 },
pages = { 35-41 },
doi = { 10.5120/13013-0316 },
publisher = { Foundation of Computer Science (FCS), NY, USA }
}
%0 Journal Article
%D 2013
%A Gajendra Pratap Singh
%A Sangita Kansal
%A Mukti Acharya
%T Existence and Uniqueness of a Minimum Crisp Boolean Petri Net%T
%J International Journal of Computer Applications
%V 73
%N 20
%P 35-41
%R 10.5120/13013-0316
%I Foundation of Computer Science (FCS), NY, USA
Abstract
In the continuing research towards characterizing 1-safe Petri nets with n-places and generating all the 2n binary n-vectors as marking vectors exactly once, the problem of determine minimum Petri nets; 'minimum' in the sense that the number of transitions is kept minimum possible for the generation of all the 2n binary n-vectors has been found. In this paper, the existence and uniqueness of a minimum Petri net which generates all the 2n binary n-vectors exactly once has been shown. For brevity, a 1-safe Petri net that generate all the binary n-vectors as marking vectors is called a Boolean Petri net and a 1-safe Petri net that generates all the binary n-vectors exactly once is called crisp Boolean Petri net.
References
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- 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.
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- 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.
- Singh, G. P. , Some advances in the theory of Petri nets, Ph. D. Thesis, submitted to the University of Delhi, Delhi, December 5, 2012.
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