Abstract
Membrane systems are a very powerful computational modeling language inspired by the internal organization of living cells. In this paper we explore the use of colored stochastic Petri nets to model an attractive variant of membrane systems—stochastic membrane systems with active membranes. In our approach, each object is modeled as a place and each membrane as a color. As a result, we can easily represent large-scale membrane systems as compact colored Petri nets. Moreover, using dynamic color sets, we can conveniently model membrane systems with active membranes. We take the virus infection process as an example to illustrate our approach. Our paper demonstrates that colored Petri nets with dynamic color sets are a compelling tool for representing and analyzing dynamic membrane systems, and thus do contribute to the description and analysis of their dynamic behavior.
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Notes
It is not essential, as the color can be not used any more instead of removal. However, non-removal of unused colors might in the end unnecessarily blow up the color sets.
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Acknowledgments
This work has been supported by Germany Federal Ministry of Education and Research (0315449H), Natural Scientific Research Innovation Foundation in Harbin Institute of Technology (HIT.NSRIF.2009005), and National Natural Science Foundation of China (61273226). We would like to thank David Gilbert and Wolfgang Marwan for many fruitful discussions, and Mary Ann Blätke, Mostafa Herajy, Christian Rohr, and Martin Schwarick for their assistance in model construction, software development and model checking. We also would like to thank the anonymous referees for their constructive comments.
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Liu, F., Heiner, M. Modeling membrane systems using colored stochastic Petri nets. Nat Comput 12, 617–629 (2013). https://doi.org/10.1007/s11047-013-9367-8
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DOI: https://doi.org/10.1007/s11047-013-9367-8