Publication details

Parameter space abstraction and unfolding semantics of discrete regulatory networks

Authors

KOLČÁK Juraj ŠAFRÁNEK David HAAR Stefan PAULEVÉ Loic

Year of publication 2019
Type Article in Periodical
Magazine / Source Theoretical Computer Science
MU Faculty or unit

Faculty of Informatics

Citation
Web http://dx.doi.org/10.1016/j.tcs.2018.03.009
Doi http://dx.doi.org/10.1016/j.tcs.2018.03.009
Keywords Boolean networks; Thomas networks; Parametrised discrete dynamics; Asynchronous systems; Concurrency; Systems biology
Description 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 sublattice 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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