Research Article

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

by  Gajendra Pratap Singh, Sangita Kansal, Mukti Acharya
journal cover
International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 73 - Issue 17
Published: July 2013
Authors: Gajendra Pratap Singh, Sangita Kansal, Mukti Acharya
10.5120/12830-0245
PDF

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 },
                        year    = { 2013 },
                        volume  = { 73 },
                        number  = { 17 },
                        pages   = { 1-4 },
                        doi     = { 10.5120/12830-0245 },
                        publisher = { Foundation of Computer Science (FCS), NY, USA }
                        }
                        %0 Journal Article
                        %D 2013
                        %A Gajendra Pratap Singh
                        %A Sangita Kansal
                        %A Mukti Acharya
                        %T Construction of a Crisp Boolean Petri Net from a 1-safe Petri Net%T 
                        %J International Journal of Computer Applications
                        %V 73
                        %N 17
                        %P 1-4
                        %R 10.5120/12830-0245
                        %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
  • 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.
  • 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.
  • Peterson, J. L. , Petri net theory and the modeling of systems, Englewood Cliffs, NJ: Prentice-Hall, Inc. , 1981.
  • Harary, F. , Graph theory, Addison-Wesley, Massachusettes, Reading, 1969.
  • Jensen, K. , Coloured Petri nets, Lecture notes in computer science, 254, Springer-Verlag, Berlin, 1986, 248- 299.
  • Reisig, W. , Petri nets, Springer-Verleg, New York, 1985.
  • Murata, T. , Petri nets: Properties, analysis and applications, Proc. IEEE, 77(4), 1989, 541-580.
  • Singh, G. P. , Some advances in the theory of Petri nets, Ph. D. Thesis, submitted to the University of Delhi, Delhi, December 5, 2012.
  • 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.
  • 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.
  • 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
No index terms available.
Keywords

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

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