Abstract
Attractors of network dynamics represent the long-term behaviours of the modelled system. Understanding the basin of an attractor, comprising all those states from which the evolution will eventually lead into that attractor, is therefore crucial for understanding the response and differentiation capabilities of a dynamical system. Building on our previous results [2] allowing to find attractors via Petri net Unfoldings, we exploit further the unfolding technique for a backward exploration of the state space, starting from a known attractor, and show how all strong or weak basins of attractions can be explicitly computed.
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Notes
- 1.
Which Cousot et al. [6] have recently use as theoretical foundation for capturing which entity of a program is responsible of a given behavior.
- 2.
Note that infinite-state Petri nets do not have finite complete prefixes in our sense.
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Acknowledgments
This research was supported by Agence Nationale de la Recherche (ANR) with the ANR-FNR project AlgoReCell (ANR-16-CE12-0034); Labex DigiCosme (project ANR-11-LABEX-0045-DIGICOSME) operated by ANR as part of the program “Investissement d’Avenir” Idex Paris-Saclay (ANR-11-IDEX-0003-02).
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Haar, S., Paulevé, L., Schwoon, S. (2020). Drawing the Line: Basin Boundaries in Safe Petri Nets. In: Abate, A., Petrov, T., Wolf, V. (eds) Computational Methods in Systems Biology. CMSB 2020. Lecture Notes in Computer Science(), vol 12314. Springer, Cham. https://doi.org/10.1007/978-3-030-60327-4_17
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