Control of Safe Ordinary Petri Nets Using Unfolding

International audienceIn this paper we deal with the problem of controlling a safe place/transition net so as to avoid a set of forbidden markings "F" . We say that a given set of markings has property REACH if it is closed under the reachability operator. We assume that all transitions of the net are controllable and that the set of forbidden markings "F" has the property REACH. The technique of unfolding is used to design a maximally permissive supervisor to solve this control problem. The supervisor takes the form of a set of control places to be added to the unfolding of the original net. The approach is also extended to the problem of preventing a larger set "F" of impending forbidden marking. This is a superset of the forbidden markings that also includes all those markings from which—unless the supervisor blocks the plant—a marking in "F" is inevitably reached in a finite number of steps. Finally, we consider the particular case in which the control objective is that of designing a maximally permissive supervisor for deadlock avoidance and we show that in this particular case our procedure can be efficiently implemented by means of linear algebraic techniques

Unfoldings of Unbounded Petri Nets

Net unfoldings have attracted much attention as a powerful technique for combating state space explosion in model checking. The method has been applied to verification of 1-safe (finite) Petri nets, and more recently also to other classes of finite-state systems such as synchronous products of finite transition systems. We show how unfoldings can be extended to the context of infinite-state systems. More precisely, we apply unfoldings to get an efficient symbolic algorithm for checking safety properties of unbounded Petri nets. We demonstrate the advantages of our method by a number of experimental results