  The problem on how to determine the observability of Boolean control networks
(BCNs) has been open for five years already. In this paper, we propose a
unified approach to determine all the four types of observability of BCNs in
the literature. We define the concept of weighted pair graphs for BCNs. In the
sense of each observability, we use the so-called weighted pair graph to
transform a BCN to a finite automaton, and then we use the automaton to
determine observability. In particular, the two types of observability that
rely on initial states and inputs in the literature are determined. Finally, we
show that no pairs of the four types of observability are equivalent, which
reveals the essence of nonlinearity of BCNs.
