  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.
