Reduction of the supervisor design problem with firing vector constraints

This paper presents a new result concerning the design of supervisors for specifications involving firing vectors. The result shows that without loss of permissiveness, a solution to the design problem can be found by solving another supervisor design problem, involving only marking specifications, in a transformed Petri net. On one hand, this result shows that the methods for marking specifications can be applied to specifications involving also firing vectors. On the other hand, the specifications involving firing vectors have been shown to be necessary in order to describe the P-type languages of free-labeled Petri nets. Since the method of this paper could be used without loss of permissiveness, it is complementary to our previous work on structural and suboptimal methods for the design of supervisors with firing vector specifications