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Anthony Spiteri Staines



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Anthony Spiteri Staines


WSEAS Transactions on Computers


Print ISSN: 1109-2750
E-ISSN: 2224-2872

Volume 18, 2019

Notice: As of 2014 and for the forthcoming years, the publication frequency/periodicity of WSEAS Journals is adapted to the 'continuously updated' model. What this means is that instead of being separated into issues, new papers will be added on a continuous basis, allowing a more regular flow and shorter publication times. The papers will appear in reverse order, therefore the most recent one will be on top.



Alternative Matrix Representation of Ordinary Petri Nets

AUTHORS: Anthony Spiteri Staines

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ABSTRACT: This work provides some basic concepts how to represent basic or elementary Petri nets by building on previous work presented in [11],[12]. Here the three main types of matrices used for Petri net representation are the input, output and incidence matrices. These are defined and explained. Some toy examples are used as proof of concept. The main raison d’être for this paper is to show that matrices are suitable to provide alternative description of Petri nets from the traditional graphical approach that is normally used. It is clearly indicated that several properties can be inferred or derived from simple examination of these matrices. A few definitions and examples are used.

KEYWORDS: Representation, Matrices, Ordinary Petri nets, System Modelling

REFERENCES:

[ 1] T. Murata, Petri nets: Properties, Analysis and Applications, Proc. of IEEE, vol. 77, i ssue 4, 1989, pp. 541-580.

[2] M. Zhou, K. Venkatesh, Modeling, Simulation, And Control Of Flexible Manufacturing Systems: A Petri Net Approach (Series in Intelligent Control and Intelligent Automation), World Scientific, 1999.

[3] C. A. Petri, Introduction to General Net Theory, Net Theory and Applications, LNCS Springer Verlag, vol. 84, 1990, pp. 1-19.

[4] T. Spiteri Staines, Representing Petri Nets as Directed Graphs, Proceedings of the 10th WSEAS international conference on Software engineering, parallel and distributed systems, SEPADS'11, WSEAS, Cambridge UK, 2011, pp. 30-35.

[5] A. Spiteri Staines, Some Fundamental Properties of Petri Nets, International Journal of Electronics Communication and Computer Engineering, IJECCE, vol.4, Issue 3, 2013, pp. 1103-1109.

[6] A. Spiteri Staines, Modelling Simple Network Graphs Using the Matrix Vector Transition Net, CSSCC 2016, INASE, Vienna, 2016.

[7] K.M. van Hee, Information Systems Engineering A Formal Approach, Cambridge University Press, 2009.

[8] E.R. Boer, T. Murata, Generating Basis Siphons and Traps of Petri Nets Using the Sign Incidence Matrix, IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, Vol. 41, No. 4, A pril 1994, pp. 266- 271.

[9] F. Ayres (jr), Theory and Problems of Matrices, Schaum’s Outline Series, Schaum, 1974.

[10] K.M. Abadir and J.R. Magnus, Matrix Algebra, Cambridge University Press, 2005.

[11] A. Spiteri Staines, Matrix Representations for Ordinary Restricted Place Transition Nets, Transactions on Computers, WSEAS, Vol 16, 2017,pp. 23-29.

[12] A. Spiteri Staines, Some Fundamental Properties of Petri Nets, International Journal of Electronics Communication and Computer Engineering, Volume 4, Issue 3, 2013, pp. 1103-1109.

[13] A. Spiteri Staines, Modeling Simple Network Graphs using the Matrix Vector Transition Net, CSSCC 2016, INASE, Vienna, 2016.

[14] A. Spiteri Staines, Bi-Directional Transition Nets, AIP,2017.

[15] A. Poggi, Developing Scalable Applications with Actors, Transactions on Computers, WSEAS, Vol. 14, 2014, pp. 660-669.

[16] V. Kasyanov, T. Zolotuhin, A System for Big Attributed Hierarchical Graph Visualization, Transactions on Computers, WSEAS, Vol. 17, 2018, pp. 151-155.

[17] A. Spiteri Staines, Representing Petri Nets as Directed Graphs, 10th International Conference on Software engineering, parallel and distributed systems, WSEAS, Cambridge, pp. 30-35.

WSEAS Transactions on Computers, ISSN / E-ISSN: 1109-2750 / 2224-2872, Volume 18, 2019, Art. #2, pp. 11-18


Copyright © 2018 Author(s) retain the copyright of this article. This article is published under the terms of the Creative Commons Attribution License 4.0

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