  In this paper, we shall formulate and address a problem of covert actuator
attacker synthesis for cyber-physical systems that are modelled by
discrete-event systems. We assume the actuator attacker partially observes the
execution of the closed-loop system and is able to modify each control command
issued by the supervisor on a specified attackable subset of controllable
events. We provide straightforward but in general exponential-time reductions,
due to the use of subset construction procedure, from the covert actuator
attacker synthesis problems to the Ramadge-Wonham supervisor synthesis
problems. It then follows that it is possible to use the many techniques and
tools already developed for solving the supervisor synthesis problem to solve
the covert actuator attacker synthesis problem for free. In particular, we show
that, if the attacker cannot attack unobservable events to the supervisor, then
the reductions can be carried out in polynomial time. We also provide a brief
discussion on some other conditions under which the exponential blowup in state
size can be avoided. Finally, we show how the reduction based synthesis
procedure can be extended for the synthesis of successful covert actuator
attackers that also eavesdrop the control commands issued by the supervisor.
