  This paper studies the minimum observability of probabilistic Boolean
networks (PBNs), the main objective of which is to add the fewest measurements
to make an unobservable PBN become observable. First of all, the algebraic form
of a PBN is established with the help of semi-tensor product (STP) of matrices.
By combining the algebraic forms of two identical PBNs into a parallel system,
a method to search the states that need to be H-distinguishable is proposed
based on the robust set reachability technique. Secondly, a necessary and
sufficient condition is given to find the minimum measurements such that a
given set can be H-distinguishable. Moreover, by comparing the numbers of
measurements for all the feasible H-distinguishable state sets, the least
measurements that make the system observable are gained. Finally, an example is
given to verify the validity of the obtained results.
