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Modeling and analysis of colored petri net based on the semi-tensor product of matrices

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Abstract

This paper applies the model petri net method based on the semi-tensor product of matrices to colored petri net. Firstly, we establish the marking evolution equation for colored petri net by using the semitensor product of matrices. Then we define the concept of controllability and the control-marking adjacency matrix for colored petri net. Based on the marking evolution equation and control-marking adjacency matrix, we give the necessary and sufficient condition of reachability and controllability for colored petri net. The algorithm to verify the reachability of colored petri net is given, and we analyze the computational complexity of the algorithm. Finally, an example is given to illustrate the effectiveness of the proposed theory. The significance of the paper lies in the application of the model petri net method based on the semitensor product of matrices to colored petri net. This is a convenient way of verifying whether one marking is reachable from another one as well as finding all firing sequences between any two reachable markings. Additionally, the method lays the foundations for the analysis of other properties of colored petri net.

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant Nos. 61573199, 61573200), Tianjin Natural Science Foundation of China (Grant Nos. 14JCYBJC18700, 13JCYBJC17400).

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Correspondence to Zengqiang Chen.

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Zhao, J., Chen, Z. & Liu, Z. Modeling and analysis of colored petri net based on the semi-tensor product of matrices. Sci. China Inf. Sci. 61, 010205 (2018). https://doi.org/10.1007/s11432-017-9283-7

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Keywords

  • colored petri net
  • reachability
  • controllability
  • marking evolution equation
  • semi-tensor product of matrices