In [1], Fig. 1 with the constraint was given inadvertently as an example for which it was claimed that there exists no optimal Petri net (PN)-based (monitor) controller.
Synthesized monitor place (controller) to enforce the constraint control the example PN of [1].
Example PN, which does not admit an optimal PN-based monitor controller for the constraint .
It is true that the method proposed in [2], as cited by [1], fails to provide an optimal PN-based (monitor) controller for the given example. By using another method [3], [4], it is possible to obtain an optimal PN-based (monitor) controller for this problem. The monitor place C1, which enforces the constraint optimally on this net, which can be synthesized by [3] and [4], is shown in Fig. 1. One example [5] for which there exists no optimal PN-based (monitor) controller is the PN as shown in Fig. 2 with the constraint . Another example is the same PN as in [1], Fig. 1, with the constraint as used in [6].