  Boolean control networks (BCNs) are discrete-time dynamical systems with
Boolean state-variables and inputs that are interconnected via Boolean
functions. BCNs are recently attracting considerable interest as computational
models for genetic and cellular networks with exogenous inputs.
  The topological entropy of a BCN with m inputs is a nonnegative real number
in the interval [0,m*log 2]. Roughly speaking, a larger topological entropy
means that asymptotically the control is "more powerful". We derive a necessary
and sufficient condition for a BCN to have the maximal possible topological
entropy. Our condition is stated in the framework of Cheng's algebraic
state-space representation of BCNs. This means that verifying this condition
incurs an exponential time-complexity. We also show that the problem of
determining whether a BCN with n state variables and m=n inputs has a maximum
topological entropy is NP-hard, suggesting that this problem cannot be solved
in general using a polynomial-time algorithm.
