Parameter Space Abstraction and Unfolding Semantics of Discrete Regulatory Networks

Juraj Kolčák 1, 2 David Šafránek 1 Stefan Haar 2 Loïc Paulevé 3
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
3 BioInfo - LRI - Bioinformatique (LRI)
LRI - Laboratoire de Recherche en Informatique
Abstract : The modelling of discrete regulatory networks combines a graph specifying the pairwise influences between the variables of the system, and a parametrisation from which can be derived a discrete transition system. Given the influence graph only, the exploration of admissible parametrisations and the behaviours they enable is computationally demanding due to the combinatorial explosions of both parametrisation and reachable state space. This article introduces an abstraction of the parametrisation space and its refinement to account for the existence of given transitions, and for constraints on the sign and observability of influences. The abstraction uses a convex sub-lattice containing the concrete parametrisation space specified by its infimum and supremum parametrisations. It is shown that the computed abstractions are optimal, i.e., no smaller convex sublattice exists. Although the abstraction may introduce over-approximation, it has been proven to be conservative with respect to reachability of states. Then, an unfolding semantics for Parametric Regulatory Networks is defined, taking advantage of concurrency between transitions to provide a compact representation of reachable transitions. A prototype implementation is provided: it has been applied to several examples of Boolean and multi-valued networks, showing its tractability for networks with numerous components.
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Juraj Kolčák, David Šafránek, Stefan Haar, Loïc Paulevé. Parameter Space Abstraction and Unfolding Semantics of Discrete Regulatory Networks. Theoretical Computer Science, Elsevier, 2018, ⟨10.1016/j.tcs.2018.03.009⟩. ⟨hal-01734805⟩



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