  An analytical approach for a dynamic cyber-security problem that captures
progressive attacks to a computer network is presented. We formulate the
dynamic security problem from the defender's point of view as a supervisory
control problem with imperfect information, modeling the computer network's
operation by a discrete event system. We consider a min-max performance
criterion and use dynamic programming to determine, within a restricted set of
policies, an optimal policy for the defender. We study and interpret the
behavior of this optimal policy as we vary certain parameters of the
supervisory control problem.
