  A logical function can be used to characterizing a property of a state of
Boolean network (BN), which is considered as an aggregation of states. To
illustrate the dynamics of a set of logical functions, which characterize our
concerned properties of a BN, the invariant subspace containing the set of
logical functions is proposed, and its properties are investigated. Then the
invariant subspace of Boolean control network (BCN) is also proposed. The
dynamics of invariant subspace of BCN is also invariant. Finally, using outputs
as the set of logical functions, the minimum realization of BCN is proposed,
which provides a possible solution to overcome the computational complexity of
large scale BNs/BCNs.
