On conditions for the liveness of weakly persistent nets

This paper first proves that each minimal siphon in a weakly persistent net is a trap if its pre-set is nonempty. Therefore, each minimal siphon contains a marked trap if a weakly persistent net is live for an initial marking. Next, it is proved that the condition, each minimal siphon contains a marked trap, is both necessary and sufficient for the liveness of weakly persistent nets if these nets additionally satisfy the asymmetric choice property or the intrinsic fairness.