New controllability condition for WS3PR nets

As a structural object of a Petri net, siphons are widely used in deadlock control. Researchers pay more attention to the study of siphon controllability. For system of sequential systems with shared resources (S4R), the existing deadlock control policies based on max, max\´ or max"-controlled siphons tend to overly restrict the behavior of a controlled system. For a subclass of S4R, WS3PR, this paper proposes a new concept called W-controlled condition and concludes that a WS3PR is deadlock-free if and only if all its siphons are W-controlled. Examples are given to demonstrate this sufficient and necessary condition.