On conditions for the liveness of weakly persistent nets

Authors:
GuanJun Liu;ChangJun Jiang
Affiliations:
Department of Computer Science and Technology, Tongji University, Shanghai 201804, P.R. China;Department of Computer Science and Technology, Tongji University, Shanghai 201804, P.R. China
Venue:
Information Processing Letters
Year:
2009

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Abstract

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.