On a Decidable Class of Partially Controlled Petri Nets With Liveness Enforcing Supervisory Policies

We identify a class of partially controlled Petri net (PN) structures, which is denoted by G, that strictly includes the class of partially controlled free-choice (FC) PN structures. We show that there is a supervisory policy that enforces liveness in an arbitrary instance N(m⁰), where N ∈ G, if and only if there is a similar policy for an FCPN that results when the construction procedure enunciated in this paper is executed with N and its controllable transition set as input. Since the existence of a supervisory policy in an arbitrary partially controlled FCPN is decidable, it follows that the existence of similar policies for any N(m⁰), where N ∈ G, is also decidable. Furthermore, when it exists, the minimally restrictive supervisory policy that enforces in a member of G is characterized by a right-closed set of markings.