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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 16, 2017

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.



Matrix Representations for Ordinary Restricted Place Transition Nets

AUTHORS: Anthony Spiteri Staines

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ABSTRACT: Matrix representation provides for a concise representation of restricted or simple Petri nets and place transition nets. This main property is often ignored. Matrices are useful for identifying basic fundamental properties that are mainly related to the static structure of a net as presented in this work. Matrices can be used for identifying some very important basic properties. This paper contains the following sections: i) introduction, ii) motivation and problem why matrices can be used to represent basic petri nets iii) incidence matrix representation types for Petri nets iv) basic Petri net properties in terms of matrices are defined, discussed and explained v) simple examples of the properties observed from the matrices are given. Finally vi) some useful observations and vii) conclusions are given.

KEYWORDS: Matrices, Matrix Representation of Petri Nets, Modeling, Network Modeling, Petri Net Theory

REFERENCES:

[1] T. Murata, Petri nets: Properties, Analysis and Applications, Proc. of IEEE, vol. 77, issue 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, April 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.

WSEAS Transactions on Computers, ISSN / E-ISSN: 1109-2750 / 2224-2872, Volume 16, 2017, Art. #3, pp. 23-29


Copyright © 2017 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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