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.