Characterization of Reachable Attractors Using Petri Net Unfoldings

Thomas Chatain 1, 2 Stefan Haar 1, 2 Loïg Jezequel 1, 2 Loïc Paulevé 3, 4 Stefan Schwoon 1, 2
2 MEXICO - Modeling and Exploitation of Interaction and Concurrency
LSV - Laboratoire Spécification et Vérification [Cachan], ENS Cachan - École normale supérieure - Cachan, Inria Saclay - Ile de France, CNRS - Centre National de la Recherche Scientifique : UMR8643
4 AMIB - Algorithms and Models for Integrative Biology
LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau], LRI - Laboratoire de Recherche en Informatique, UP11 - Université Paris-Sud - Paris 11, Inria Saclay - Ile de France
Abstract : Attractors of network dynamics represent the long-term behaviours of the modelled system. Their characterization is therefore crucial for understanding the response and differentiation capabilities of a dynamical system. In the scope of qualitative models of interaction networks, the computation of attractors reachable from a given state of the network faces combinatorial issues due to the state space explosion. In this paper, we present a new algorithm that exploits the concurrency between transitions of parallel acting components in order to reduce the search space. The algorithm relies on Petri net unfoldings that can be used to compute a compact representation of the dynamics. We illustrate the applicability of the algorithm with Petri net models of cell signalling and regulation networks, Boolean and multi-valued. The proposed approach aims at being complementary to existing methods for deriving the attractors of Boolean models, while being %so far more generic since it applies to any safe Petri net.
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Thomas Chatain, Stefan Haar, Loïg Jezequel, Loïc Paulevé, Stefan Schwoon. Characterization of Reachable Attractors Using Petri Net Unfoldings. CMSB 2014, Nov 2014, Manchester, United Kingdom. pp.14, ⟨10.1007/978-3-319-12982-2_10⟩. ⟨hal-01060450⟩

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