Weak Petri net languages in supervisory control

We present a notion of terminal behavior for place/transition nets, called weak behavior. The classes of weak and marked languages generated by deterministic nets are incomparable. Thus, also taking into account the weak behavior of deterministic nets (in addition to the marked behavior) we extend the control problems that can be modeled by Petri nets. Deterministic weak languages are DP-closed, i.e., they represent closed-loop terminal behaviors that may be enforced by Petri net supervisors. The main properties of interest in supervisory control are decidable when this class of languages is considered. The class of deterministic weak PN languages is not closed under the supremal controllable sublanguage operator