Enforcing Liveness in a Subclass of PN with any Acceptable Initial Marking

This study focuses on developing a control mechanism to prevent deadlocks in a specific subclass of Petri Nets. The designed control guarantees deadlock-freeness for every acceptable initial marking of the net. The novelty of this method lies in the removal of some output transitions of siphons by establishing a specific synchronic distance between the output and internal transitions of the siphons. This approach is shown in <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$S^{3} P R$</tex> nets. An example is presented to illustrate the proposed approach.