On Asymptotically Eecient Solutions for a Class of Supervisory Control Problems

We consider restricted sequences of forbidden-string 23], and forbidden-state 22] problems and show the limiting problem instance deened by a sequence has a solution if and only if each problem instance in the sequence has a solution. Furthermore, the supervisor that enforces the desired behavior in the limiting problem instance also enforces the desired behavior in each problem instance in the sequence. In essence, the storage requirement for supervisory control of each instance is bounded above by that of the limiting problem instance. In addition, if the limiting problem instance is available, a similar observation can be made regarding the complexity of supervisory control. This observation coupled with recent results on the solvability of the supervisory control problem involving certain classes of non-regular behaviors 29, 28, 5] and nite-representations of innnite-state systems 13, 14] is suggested as an eeective procedure to combat the computational and storage issues in supervisory control. We conclude with an incomplete list of future research directions.