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@article{1610817,
author = {Kolčák, Juraj and Šafránek, David and Haar, Stefan and Paulevé, Loïc},
article_number = {April},
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},
language = {eng},
issn = {0304-3975},
journal = {Theoretical Computer Science},
title = {Parameter space abstraction and unfolding semantics of discrete regulatory networks},
url = {http://dx.doi.org/10.1016/j.tcs.2018.03.009},
volume = {765},
year = {2019}
}
TY - JOUR
ID - 1610817
AU - Kolčák, Juraj - Šafránek, David - Haar, Stefan - Paulevé, Loïc
PY - 2019
TI - Parameter space abstraction and unfolding semantics of discrete regulatory networks
JF - Theoretical Computer Science
VL - 765
IS - April
SP - 120-144
EP - 120-144
PB - Elsevier
SN - 03043975
KW - Boolean networks
KW - Thomas networks
KW - Parametrised discrete dynamics
KW - Asynchronous systems
KW - Concurrency
KW - Systems biology
UR - http://dx.doi.org/10.1016/j.tcs.2018.03.009
L2 - http://dx.doi.org/10.1016/j.tcs.2018.03.009
N2 - 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.
ER -
KOLČÁK, Juraj, David ŠAFRÁNEK, Stefan HAAR and Loïc PAULEVÉ. Parameter space abstraction and unfolding semantics of discrete regulatory networks. \textit{Theoretical Computer Science}. Elsevier, 2019, vol.~765, April, p.~120-144. ISSN~0304-3975. Available from: https://dx.doi.org/10.1016/j.tcs.2018.03.009.
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