A Necessary and Sufficient Condition for the Liveness of Normal Nets

Abstract

This paper gives a necessary and sufficient condition for the liveness of normal nets, i.e. a normal net with a given initial marking is live if and only if it is structurally repetitive and each minimal siphon is marked in any reachable marking. Furthermore, it is proved that a normal net is structurally live if and only if it is structurally repetitive. Finally, we prove that a weakly persistent net, which is a special normal net, is live for a given initial marking if and only if it is structurally repetitive and each minimal siphon is marked in the initial marking. That is to say, the liveness of weakly persistent nets can be decided by the net structure and the initial marking only.